ELECTRIC FIELD BASED FABRICATION METHODS
FOR MULTI-SCALE STRUCTURED SURFACES
MASSACHUSETTS INSTITUTE
OF TECIHNOLOGY
BY
AUG 15 2014
YOUNG SOO JOUNG
LiBRA RIES
B.S.,
MECHANICAL ENGINEERING, YONSEI UNIVERSITY,
2004
M.S., MECHANICAL & AEROSPACE ENGINEERING, SEOUL NATIONAL UNIVERSITY, 2006
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING IN PARTIAL FULFILMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING
AT THE
MASSACHUSETTS ISTTITUTE OF TECHNOLOGY
JUNE 2014
C MASSACHUSETTS INSTITUTE OF TECHNOLOGY, 2014. ALL RIGHTS RESERVED.
Signature redacted
SIGNATURE OF A UTHOR.....................................................................
YOUNG SOO JOUNG
DEPARTMENT OF MECHANICAL ENGINEERING
MAY 21, 2014
Signature redacted
CERTIFIED BY
.............................
CULLEN
R. BUIE
ASSISTANT PROFESSOR, MECHANICAL ENGINEERING
THESIS SUPERVISOR
Signature redacted
ACCEPTED BY .......
.......................
DAVID E. HARDT
PROFESSOR, MECHANICAL ENGINEERING
CHAIRMAN, DEPARTMENT COMMITTEE ON GRADUATE STUDENTS
1
2
ELECTRIC FIELD BASED FABRICATION METHODS
FOR MULTI-SCALE STRUCTURED SURFACES
BY
YOUNG Soo JOUNG
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING ON MAY 23, 2014 IN PARTIAL
FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MECHANICAL
ENGINEERING
ABSTRACT
Control of micro/nano scale surface structures and properties is crucial to developing novel
functional materials. From an engineering point of view, the development of scalable and
economical micro/nano-fabrication methods has been in high demand. In this dissertation,
electrophoretic deposition (EPD) and breakdown anodization (BDA) are examined for their
potential to produce multi-scale structured surfaces. EPD uses electrophoresis to deposit thin films
of nanoparticles, dispersed in suspension, onto charged or porous substrates. Depending upon the
dispersion stability, the surface roughness can be modulated in order to affect the resulting
wettability. BDA can be utilized to alter surface features by employing instabilities during high
voltage anodization, which lead to micro scale topography. Different microporous structures are
generated depending on electric potential and electrolyte temperature during BDA. A hybrid
method employing EPD and BDA results in hierarchical surface structures with both nano/micro
scale features. In this work EPD and BDA are utilized for the development of superhydrophobic
and superhydrophilic surfaces; sample applications include anti-wetting fabric, capillarity driven
flow design, and critical heat flux enhancement. In many applications it is critical to understand
how moving liquid water droplets will behave when they encounter these modified surfaces. We
investigate drop impingement on porous thin films produced by BDA and EPD in order to
understand the effects of surface structure and chemical properties on droplet dynamics. Using
dimensional analysis we've discovered a novel dimensionless parameter, named the WashburnReynolds number, which can predict the droplet impingement modes. Intriguingly we've also
discovered that under certain conditions drop impingement results in gas trapped in the spreading
droplet, leading to the generation of aerosol above the droplet when the gas bubbles burst. The
Washburn-Reynolds number also largely dictates the aerosol generation process. Our results inform
the understanding of dynamic interactions between porous surfaces and liquid drops for applications
ranging from droplet microfluidics to aerosol generators. In summary, EPD and BDA provide
promising micro and nano-scale fabrication technologies with reasonable control of surface
morphology and properties in a cost-effective and time-effective and scalable.
Thesis Supervisor: Cullen R. Buie
Title: Assistant Professor of Mechanical Engineering
3
4
Acknowledgements
Five years ago, Professor Buie told me "let's work together." At that time, my wife was expecting
our child and I had a good job in Korea. Without his early confirmation of support, I would not have
decided to come to MIT for a Ph.D. I also remember the moment when he brought a celebration
cake to our group meeting after I passed the doctoral qualification exam. He has always sincerely
supported me throughout my Ph.D. program. I am most grateful to him for all his advice and
support toward my successful achievement of my Ph.D. degree.
I was happy to have Professor Daniel Blankschtein, Professor Gareth McKinley, and Professor
Evelyn Wang as my thesis committee members. I gained deep knowledge of colloid and interface
sciences from Professor Blankschtein. His unique explanation and brilliant understanding gave me
new insights into my scientific findings. Professor McKinley has impressed me with his keen
insight in fluid mechanics. His advice helped me to make firm bridges between my understandings
of liquid transportation on porous media. Professor Wang showed me how a junior faculty member
can successfully develop a new laboratory for new research areas. She was passionate about
teaching students and managing her group, and I learned about effective collaboration while I
worked with her group. I sincerely thank Professor Sang-Gook Kim for his teaching about
micro/nano systems and comments on my research. I am also deeply thankful for the continuous
support and advice from Professor Yoon Young Kim, who is my former adviser during my M.S.
program. I must also thank Dr. Hyuk Chang, who is my former supervisor at Samsung Advanced
Institute of Technology, for his concern and support for my future career.
My research achievements have been earned with great collaborators. Bruno provided me with a
new idea of developing a theoretical model of capillary flows. Dr. Kuang-Han demonstrated great
use for our surfaces in pool boiling. I am grateful to Professor Shao-Horn, Dr. Byon, and Dongkyu
Lee for help with the AFM and XRD measurements. I thank Professor Sangbae Kim and Dr.
Sangok Seok for help with high speed imaging. I am grateful to Dr. Jim Bales and Sandra Lipnoski
of MIT Edgerton Center for sharing their high speed camera. It was my pleasure to have smart and
sincere interns and UROP students; especially Robert McMeeking worked very hard to make the
progress of producing conductive hydrogel films. I was also happy to work with my other labmates:
Dr. William Braff, Zhifei Ge, Andrew Jones, Alisha Schor, Naga Dingari, Qianru Wang, Laura
Gilson, Dr. Paulo Garcia, Dr. Pei Zhang, and Dr. Jeffrey Moran. Their fruitful comments helped me
to improve my research output. I especially enjoyed working with Soon-ju Choi toward developing
practical applications of breakdown anodization. I must also thank all of my Korean friends at MIT
for their help in my successful achievement of Ph.D.
I was only able to attain my Ph.D. degree with the endless trust and support from my family. My
parents, Mr. Chang-ho Joung and Mrs. Jun-sook Hong, and my siblings and their families, Nana,
Hangu, Soo-bin, You-ree, Byung-gook, Ji-hyun, Sung-enu and Young-chan are always standing
behind me. My mother-in-law, father-in-law, and my wife's sister, Mrs. Sun-nyu Lim, Mr. Hak-joo
Kim and Taeun, filled my position and took care of my daughter and wife during my absence from
Korea. Lastly, my wife, daughter and my soon-in-be son, Taejin, Yehwi and Woo-Ju, are all the
reasons for overcoming any challenges in my life. Without the sacrifice and support of all my
family members, I could not have reached this position.
5
6
Table of Contents
Acknowledgements
5
Table of Contents
7
List of Figures
13
List of tables
29
Chapter 1. Introduction: Electrophoretic Deposition and Breakdown Anodization
31
1.1.
Introductory remarks
32
1.2.
Fundamental of electrophoretic deposition
35
1.2.1. Electrophoresis
35
1.2.2. Suspension stability
36
1.2.3. Stability ratio
37
Fundamental of breakdown anodization
39
1.3.1. Anodization process
40
1.3.2. Breakdown potential
41
1.3.3. Effect of electrolyte temperature on oxide films
42
Thesis objective and outline
43
1.3.
1.4.
Chapter 2. Electrophoretic Deposition of Unstable Colloidal Suspensions for Superhydrophobic
Surfaces 49
2.1.
Introduction
50
2.2.
Experimental
50
2.2.1. Suspension preparation
51
2.2.2. Surface characterization
53
Results and Discussion
53
2.3.1. Zeta potential and particle size
53
2.3.
2.3.2.
Optical absorbance and stability ratio
54
2.3.3.
Contact angle
59
61
2.3.4. Surface roughness
2.3.5.
2.4.
63
Mechanical durability
67
Conclusions
Chapter 3. Anti-wetting Fabric Coatings Produced by Electrophoretic Deposition of Polymer
Stabilized Hydrophobic Nanoparticles
7
69
3.1.
Introduction
70
3.2.
Experimental
72
3.2.1
72
3.3.
3.4.
Preparation of materials and suspensions
3.2.2. Electrophoretic deposition for fabric coating
74
Result and discussion
75
3.3.1. Suspension Zeta potential
75
3.3.2. Wettability of coated fabric
77
3.3.3. Scanning Electron Microscopy
79
3.3.4. Color change test
80
3.3.5. Air permeability testing
81
3.3.6.
Coating durability
83
3.3.7.
Patterned anti-wetting fabric
84
Conclusions
86
Chapter 4. A Hybrid Method Employing Breakdown Anodization and Electrophoretic Deposition
for Superhydrophilic Surfaces
89
4.1.
Introduction
90
4.2.
Theory
91
4.2.1. Capillary flow
91
4.2.2. Electrophoretic deposition
93
Experimental
94
4.3.1. Suspension and electrolyte preparation
94
4.3.2. Capillary rise measurement (CRM)
95
4.3.3. Characterization
96
Results and discussion
97
4.4.1. Surface morphology
97
4.42. Capillary pressure and hydraulic diffusivity
99
4.3.
4.4.
4.5.
4.4.3. Relationship between wetting properties and surface structure
103
4.4.4. Surface chemical composition and atomic structure
105
4.4.5. Relationship between the effective pore radius and surface roughness
109
4.4.6. Modification of capillary flows
111
Conclusions
113
8
Chapte r 5. Hybrid Electrophoretic Deposition with Anodization Process for Superhydrophilic
Surfaces to Enhance Critical Heat Flux 115
5.1.
Introduction
116
5.2.
Experimental
117
5.2.1. Hybrid method of electrophoretic deposition of TiO 2 nanoparticles and
117
breakdown anodization of titanium plates
118
5.2.2. Capillary rise measurement
5.2.3.
118
Critical heat flux in pool-boiling
5.3.
Results and discussion
119
5.4.
Summary
124
Chapte r 6. Design of Capillary Flows with Functionally Graded Porous Films Controlled by
Anodization Instability
125
6.1.
Introduction
126
6.2.
Theory
128
6.3.
Experimental
136
6.3.1. Fabrication method
136
6.3.2.
6.4.
137
Sample characterization
137
Results and discussion
6.4.1. Case 1: Capillary flows with constant capillary properties and varying surface
141
width
6.4.2. Case 2: Capillary flows with constant surface width and varying capillary
144
properties
6.5.
152
Conclusions
Chapte r 7. Scaling Laws for Drop Impingement on Thin Porous Media
153
7.1.
Introduction
154
7.2.
Experimental
155
7.2.1. Preparation of micro and nanoporous films
155
7.2.2. Four impingement modes on wettable porous films
157
Theory
158
7.3.1. Energy conservation of a cylindrical model of droplets
158
7.3.2. Kinetic energy
160
7.3.3. Gravitational energy
161
7.3.
9
7.4.
7.3.4. Droplet surface energy
161
7.3.5. Line dissipation
162
7.3.6. Viscous dissipation inside a droplet
163
7.3.7. Matrix potential
164
73.8. Viscous dissipation within the porous media
165
7.3.9.
167
Dimensionless energy equation with the capillary-Weber number
Results and discussion
169
7.4.1. Simplified energy equation at high capillary-Weber number
169
7.4.2. Simplified energy equation at low capillary-Weber number
172
7.4.3. The Washburn-Reynolds number
176
7.4.4. Impingement mode transitions correlate with the Washburn-Reynolds
number
177
7.5.
Conclusions
180
Chapte r 8. Sparkling Droplets: Evidence of Aerosol Generation from Drop Impingement on Porous
Media
181
8.1.
Introduction
182
8.2.
Theory
186
8.2.1. Measurements of hydraulic diffusivity
186
8.2.2.
187
8.3.
-ydraulic diffusivity from the capillary rise measurement
8.2.3. Hydraulic diffusivity from Darcy's law
189
Experimental
190
8.3.1. Preparations and characterizations of porous media
190
8.3.2.
Characteristics of typical soil and rainfall
194
8.3.3.
Characteristics of droplets and bubbles with respect to drop heights
194
8.4.
Results and discussion
197
8.5.
Conclusions
202
Chapte r 9. Thesis Summary and Future Work
203
9.1.
Thesis Summary
204
9.2.
Future Research
207
9.2.1. Porous Thin Film Microfluidic Devices Designed by Breakdown Anodization
207
10
9.2.2. Conductive Hydrogel Produced by Electrophoretic Deposition at the
Interface of Two Immiscible Liquids
211
9.2.3. Dispersion of Carbon Nanotubes in Aqueous Solutions of Ionic Surfactants
212
Bibliography 217
11
12
List of Figures
Figure 2-1. Schematic illustration of the EPD cell. The cell consists of two titanium electrodes with
a 15 mm of gap, a DC power supply (10 V applied), and a suspension consisting of
hydrophobic SiO 2 particles dispersed in a mixture of 90% methanol and 10% DI water
52
by volum e... ....................................................................................................
Figure 2-2. Characterization of PDMS coated SiO 2 particles as a function of pH. (a) Average zeta
potential showing the isoelectric point (IEP) at pH 3. (b) Average agglomerate diameter,
indicating smaller agglomerates at high pH. The error bars shown in (a) and (b)
represent two-standard deviations of three measurements....................
55
Figure 2-3. Change in suspension optical absorbance as a function of time for ten different pH
suspensions with 0.1 g/L PDMS coated Si0 2 particle concentration. The inset shows
absorbance curves for higher pH values (7.4 to 8.3). The low pH curves show fast
............
change of absorbance, which is attributed to rapid coagulation.....
56
Figure 2-4. Stability ratio as a function of suspension pH. Wabs and Wsize are the absorbance based
and size based stability ratios, respectively, calculated by equations (1-8) and (1-11),
respectively. The measured particle size of 304 nm was used as the initial particle size,
........... 57
Dh.,, to obtain Wsize with equation (1-11). .................................................
Figure 2-5. Contact angles on films deposited via EPD. (a) Static contact angle as a function of
deposition time for four suspensions with varying pH. (b) Advancing and receding
contact angles on the surfaces created at suspension pH 7.6. The inset in (b) shows rolloff angles calculated from the advancing and receding contact angles. The error bars
shown in (a) represent two-standard deviations of twelve measurements at each point.
The maximum contact angle was achieved at pH 7.6, corresponding to a stability ratio
of Wab,
=
8 and deposition time of 60 s.....................................
.........
................... 58
Figure 2-6. Patterns of EPD films produced by the pH 7.9 suspension with different deposition
times. All images have the same scale bar in the top and most left picture. Deposition
features grow with deposition time, resulting in a decrease in contact angle when
deposition tim e exceeds 60 sec.......................................................
.... ..................... 61
Figure 2-7. Contact angle as a function of RMS surface roughness. In surface roughness
measurements, the measured area was 40x40 pm 2 and three point values were averaged
13
in each sample. The contact angle is roughly proportional to the surfaces roughness, as
can be expected by the Cassie mode. ........................................................................
62
Figure 2-8. Qualitative schematic of deposition behavior with respect to suspension stability. In
unstable suspensions, particles flocculate and thick deposition layers cannot be formed
due to sedimentation. In contrast, well dispersed (i.e. stable) particles form uniform
films with low surface roughness. At moderate stability ('quasistable') EPD of particle
agglomerates yields high surface roughness. ......................................
I.......................... 63
Figure 2-9. SEM images at two different magnifications of deposited films yielding maximum
contact angles at pH 7.4 (a), 7.6 (b), 7.9 (c), and 8.3 (d). As pH increases the film
become increasingly uniform, consistent with the stability measurements of Figure 2-4.
............
............... . . . ..........................................................................
..
..................... 64
Figure 2-10. Characteristics of EPD films with suspensions including conductive epoxy. (a) Image
of liquid water droplet on EPD modified surface with contact angle of 168*. (b) 40x40
pm2 AFM image of the deposition surface and SEM images [(c)-(e)] at three
magnifications. In (c) Several ten micron scale features composed of flocculated SiO 2
particles were observed under the SEM. In image (d), micron scale porous structures are
visible on the surface, and (e) shows ten nanometer scale SiO 2 particles mechanically
connected by the epoxy additive. ...............................................................................
65
Figure 2-11. Contact angle on EPD surfaces obtained with epoxy (circles) and without epoxy
(squares), after successive 'peel' tests. The static contact angle produced without epoxy
decreases far faster due to the destruction of the deposition layer after each test.
However, the surface obtained with epoxy maintains its superhydrophobicity after
successive peel tests. ..................................................................................................
66
Figure 3-1. Schematic illustrations of the fabrication process suggested for anti-wetting fabric
coating. (a) Step 1: multi-layered polymers are electrostatically deposited on the fabric.
Step 2: nanoparticle are electrostatically deposited on the polymer layers of the fabric.
Step 3: the polymer and nanoparticle assemblies are deposited by electrophoretic
deposition (EPD). Step 4: heat treatment is conducted on the fabric for enhancing
mechanical durability. (b) The EPD cell for Step 3 in (a). The cell consists of two
stainless steel electrodes and a fabric sheet is wrapped around the cathode electrode. . 74
Figure 3-2. Zeta potentials of the polymers and the Si0 2 nanoparticles. (a) Zeta potentials of
poly(sodium 4-styrenesulfonate) (PSS), poly(dimethyl-diammonium chloride) (PDDA),
14
,
SiO 2 nanoparticles with respect to pH. (b) Digital image of the suspensions of SiO 2
polyvinylidene fluoride (PVDF), PDDA, and PSS. (c) The table summarizes the zeta
potentials at pH 8.5. The zeta potential of non-treated polyester fiber was obtained from
a reference.[163] The solvent for the Si0 2 nanoparticle and PVDF suspensions is
composed of methanol 90 vol. % and water 10 vol. %. The others are deionized water.
The concentrations are 8 g/L PSS and PDDA and 1 g/L Si0 2 and 0.5 g/L PVDF with
and without 3.75x 10- g/L PDDA polymers. The error bars indicate + one standard
deviation from three measurements....................................
76
Figure 3-3. Images of water droplets on polyester fabrics modified by the fabrication process
shown in Figure 3-1. Two different fabrics, which color red and yellow, were used to
produce anti-wetting fabrics. Electrophoretic deposition was conducted for 90 sec in
Step 3. (a) The modified fabric does not lose its original color but the droplets show
high contact angles and low roll-off angles. Flexibility of the original fabric is
maintained after modification while wettability changes dramatically from hydrophilic
to superhydrophobic. (b) A water droplet is rapidly absorbed into the original polyester
fabric. The scale bars indicate 1 mm. (c) The brown fabrics do not show significant
difference in their colors before and after the modification. Water droplets show contact
angles higher than 1500 and roll-off angles lower than 50.........................................
78
Figure 3-4. Static contact angle and roll-off angle of fabric produced with different deposition times
for EPD. Contact angles were measured after heat treatment. Water droplets instantly
absorbed into the original fabric resulting in and effective static contact angle of zero
degrees. The static contact angle is 1360 on the fabric coated with polymer and thin
layers of hydrophobic Si0 2 nanoparticles (after Step 2). Static contact angle is
dramatically enhanced after EPD process (after Steps 4). The maximum contact angle
of 1590 and the minimum roll-off angle of 20 are achieved at 90 sec deposition time.
The error bars indicate
one standard deviation from five measurements................ 79
Figure 3-5. SEM images of fabrics produced by electrophoretic deposition (EPD) with different
deposition times. (a) Original polyester fabric has twill weave patterns. The inset shows
a fabric fiber with Si0 2 nanoparticles deposited on the surface (after Step 2 in Figure
3-1). (b) After 30 sec of EPD, Si0 2 nanoparticle layers are observed on the fabric but do
not fully cover the surface. (c) After 60 sec of EPD, the fabric fibers are uniformly and
15
densely coated with SiO 2 nanoparticles. This surface exhibits the maximum contact
angle of 1570 and minimum roll-off angle less than 5 ...................
80
Figure 3-6. Color difference tests using RGB comparison and real images of the modified fabrics.
(a) R G, and B*, which are the relative RGB values to the original fabric, with respect
to deposition time in electrophoretic deposition (EPD). The error bars indicate
one
standard deviation from five measurements. (b) RGB values are obtained by using
image software (Adobe Photoshop CS4) with captured images of fabric produced with
varying EPD time. (c)-(e) Captured images of fabrics produced with three different
fabrication processes and with the same EPD time of 90 sec: (c) Fabric produced with
Steps 1-4 in Figure 3-1, (d) Fabric produced without Steps 1-2. (e) Fabric without
polymeric stabilization of the particles in Step 3. ......................................................
81
Figure 3-7. Water vapor transmission (WVT) rate tests for the original fabric (box symbols) and the
anti-wetting fabric (circle symbols). The anti-wetting fabric was produced with 90 sec
of EPD at 120 V. The WVT rate experiments were conducted with water temperatures
ranging from 35 *C to 65 0C. The error bars indicate
one standard deviation from four
m easurements.................................................................................................................
83
Figure 3-8. Contact angles on the anti-wetting fabric with respect to test time. The durability test
was conducted with a customized skin friction generator. The skin friction was induced
by boundary layers on the fabric with flows circulated by a water pump. The flow speed
was 10 rm/s. The contact angles were measured after the fabric was fully dried on a hot
plate. Each data point is the average contact angle. The error bars indicate
one
standard deviation from five measurements..............................................................
84
Figure 3-9. Patterned anti-wetting fabric using a patterned electrode. (a) An electrode with
honeycomb shaped holes (left) was used to coat hydrophobic nanoparticles on polyester
fabric (right). The fabric coated by the patterned electrode does not show significant
color difference relative to the original fabric. (b)-(e) Water was continuously sprayed
on two different fabrics, which are uniform anti-wetting fabric and patterned antiwetting fabric, and the resulting droplets on the surfaces were imaged with respect to
time. (a) Droplets grow irregularly on the uniform anti-wetting fabric. (c) Droplets grow
with regular patterns and ultimately show similar patterns as the electrode. (d) The
pattern of coalescent droplets on the patterned anti-wetting fabric is similar to the dew
16
drops on green Oregon grape leaves shown in the inset of (e)
photography by Brent Vanfossen. .....................................
Copyright and
86
Figure 4-1. Schematic illustration of the experimental setups for breakdown anodization (BDA) (a),
and electrophoretic deposition (EPD) (b). The water temperature is controlled to
maintain constant electrolyte conditions during BDA. TiO 2 nanoparticles are dispersed
in acetic acid solvents with 1 wt% concentration for EPD. The solvents of both methods
are stirred with magnetic bars.....................................................................................
95
Figure 4-2. Schematic illustration of the capillary rise measurement (CRM) system. Capillary
height is recorded by a digital camera and estimated with customized image processing
software (Labview). Evaporation from the sample surface is prevented by encapsulating
the sample in a glass colum n....................................................................................
96
Figure 4-3. SEM images of superhydrophilic surfaces fabricated by breakdown anodization (BDA)
(a)-(c), electrophoretic deposition (EPD) (d)-(f), and the hybrid BDA/EPD method (g)(i). BDA was conducted at the electric potential 90 V for 30 min with an acidic
electrolyte (pH 3) at 10 'C. EPD was conducted with the electric potential 30 V for 90
sec with 1 wt.% TiO 2 in an acetic acid solvent at ambient temperature. The surface
produced by BDA consists of several entangled micro-porous structures while the
surface deposited with TiO 2 nanoparticles by EPD shows uniformly distributed nanoporous structures. The hybrid BDA/EPD method yields hierarchical micro- and nanoporous structures.................................................................................
....... .
......... 98
Figure 4-4. Square of experimentally derived capillary rise height is linearly proportional to time,
as predicted by Washburn's equation (a). The samples produced by BDA and EPD
show different capillary pressures and spreading speeds (b). The sample produced by
the hybrid BDA/EPD method shows slightly lower spreading speed than the sample
produced by BDA at the same conditions. In BDA, electrolyte temperatures were
maintained at 10 'C and electric potentials were supplied for 30 min. EPD was
conducted at the electric potential 30 V for 90 sec. Hydraulic diffusivity, Dcap, of the
surface can be obtained from the slope of each curve as shown in equation (4-2). The
capillary pressure is calculated from equation (4-3) using the maximum rise height.. 100
Figure 4-5. Changes in capillary pressure (a) and spreading speed constant (b) with respect to
electric potential and electrolyte temperature during BDA. Four different electric
potentials (30 V, 60 V, 90 V, and 120 V) and four different electrolyte temperatures
17
(10 *C, 25 *C, 50 'C, and 75 "C) were used to obtain the surfaces. The error bars
indicate
one standard deviation resulting from four measurements..........................
101
Figure 4-6. Sample SEM images of surfaces produced by BDA. At low electrolyte temperature and
low electric potential (a), initiation of BDA is not facile; therefore, partially burst
structures are observed on the surface produced at 30 V and 10 "C. When the electrolyte
temperature was maintained at 75 "C during BDA, the highly interconnected porous
structures shown in Figure 4-3a-c dissolve in the electrolyte, leaving smooth surfaces
w ith large pores (b)......................................................................................................102
Figure 4-7. Capillary rise measurements of surfaces modified by EPD. EPD processes was
conducted on bare titanium substrates (a) and on surfaces augmented by BDA (b).
Pcap/P cap and Deap/D*cap are the ratios of capillary pressure and spreading speed
constant before and after EPD, respectively. EPD was conducted at 30 V and the BDA
conditions were 120 V, 30 min, and 25 'C. Porosity of the deposits by EPD was
calculated using the deposition weight per unit area and the deposition height (c). The
error bars indicate
one standard deviation resulting from three measurements........ 104
Figure 4-8. XRD patterns of the surfaces produced by EPD, BDA, and the hybrid BDA/EPD
method. A bare titanium plate and the TiO 2 deposit surface were used as control XRD
substrates showing the spectra of titanium (a) and titanium dioxide (b). Surfaces
produced by variations of EPD and BDA shows aspects of both Ti and TiO 2 spectra.
Sediments obtained after BDA shows very weak peaks (j), which are indicative of
amorphous titanium oxide [174, 175]. After heat treatment, the surface used in (i) and
the sediments used in (j) show the spectra of anatase TiO 2 as shown in (k) and (1).... 108
Figure 4-9. Plots of the pore radius (a), the capillary pressure (Pcap) (b), and hydraulic diffusivity
(Dcap) (c) with respect to surface roughness. The pore radius obtained by equation (4-4)
with Pcap and Dcap shown in (b) and (c) is linearly proportional to the surface roughness
(a). The box, circle, triangle, and diamond symbols indicate the electric potentials of 30
V, 60 V, 90 V, and 120 V, respectively, used in the BDA processes. The fill colors
indicate the electrolyte temperature, 10 "C (white) and 25 "C (red). Morphological data
was obtained with a profilometer (Measurement system: Tencor P-16 Surface
Profilometer (TM)). The error bars indicate
one standard deviation resulting from four
m easurem ents. ......... ...................................................................................................
18
110
Figure 4-10. Schematic illustrations of electrode gap-profiles and electrode shapes used to
demonstrate capillary transport modification with BDA and EPD. Case 1 was used as a
reference with a constant gap-distance (10 mm) and a rectangular electrode shape (10
mm x 70 mm). In Cases 2 and 3 the electric potentials vary with gap distance between
anode and cathode electrodes, with identical electrode cross sectional area as Case 1. In
Case 3, TiO 2 nanoparticles were partially deposited on the surface produced by BDA
using EPD. In Cases 4 and Case 5, triangular electrodes were used with the same
electrode gap-distance as Case 1 (10 mm). ..................................
112
Figure 4-11. Square of measured capillary rise height with respect to time for superhydrophilic
surfaces produced by the BDA and EPD methods presented in Figure 4-10. In the BDA
processes, two different electrolyte temperatures (10 'C and 25 'C) and one electric
potential (90 V) were used. In the EPD process, 30 V was supplied for 5 min to deposit
TiO 2 nanoparticles. In Cases 2-4 the square of capillary height is nonlinear in time,
unlike conventional capillary flows. With augmentation via EPD, the spreading speed
can be discontinuously changed, as shown in Case 3. .......................
113
Figure 5-1. SEM images of prepared surfaces; (a) superhydrophobic surface by EPD, (b)
superhydrophilic surface by BDA, and (c) mixed wetting surface by the combined
B D A /EPD process.......................................................................................................
120
Figure 5-2. Boiling behavior on the prepared surfaces. Images of the superhydrophobic surface of
sample 1 at the saturation temperature (a), the boiling inception temperature (b), and the
nucleate boiling region (c). Images of the superhydrophilic surface of sample 2 at the
saturation temperature (d), the boiling inception temperature (e), and the nucleate
boiling region (f). Images of the hybrid wetting surface of sample 3 at the saturation
temperature (g), the boiling inception temperature (h), and in the nucleate boiling region
.... .................. 12 3
(i). ........................................................................................................
Figure 6-1. Schematic illustration of the conceptual model for wettable porous films with varying
cross sectional area. The porous film has the constant height, He, and varying half width,
R. The porous film can be modeled as multi-layered capillary tubes vertically oriented
in the capillary height, y. The number of the capillary tubes in x-direction and ydirection is varied according to the radius of a single capillary tube, re, and the width of
R .. . ...............................................................................................................................
19
132
Figure 6-2. Schematic illustrations of control volumes depending on the shapes of wicking surfaces.
The wicking surfaces can be conceptually modeled as vertically packed capillary tubes.
(a) The control volume covers the whole wetted area when the capillary width increases
with respect to the capillary height. (b) The wet area that has the same column width as
the top wetting line is considered as the control volume when the wicking surface has
decreasing width.............................................
136
Figure 6-3. Droplet spreading on the surface produced by breakdown anodization (BDA). BDA
was conducted with 90 V for 30 min in pH 3.0 electrolytes at 25 *C. The droplet
suspended from the needle is immediately separated into two parts after contacting to
the surface, finally showing almost zero contact angles. The scale bars in the images
indicate 1 mm length. .............................................................................
.....................
138
Figure 6-4. SEM images of surfaces fabricated by breakdown anodization (BDA). BDA was
conducted at the electric potential 120 V for 30 min with an acidic electrolyte (pH 3.0)
at 10 'C. The surface shows highly irregular micro porous structures (a)-(b) that have
submicron scale-like structures on the surface. The cross sectional area of the surface is
composed of multi-layers of amorphous titanium oxide, which have micro-scale
w icking channels (c)-(e) ...............................................................................................
139
Figure 6-5. Results of the capillary rise measurements with highly wettable porous films produced
by breakdown anodization (BDA). As expected from Washburn's equation, the square
of capillary height is linear to time at initial region of rising time. The maximum
capillary diffusivity is 155 mm2 /s and the maximum capillary pressure is 1.75 kPa.
These values are ten times and three times higher than the commercial wicking sheet
composed of micron Si0 2 particles (200 tm thickness of 25 pm silica particles).
Samples were produced by BDA with titanium plates (10 mm
x
250 mm) in pH 3.0
electrolytes. The gap distance between anode and cathode electrodes was 10 mm. The
error bars indicate
one standard deviation resulting from four measurements. ........ 140
Figure 6-6. Shapes of the BDA surfaces and the chromatography papers (Genesee Scientific) used
for the capillary rise measurements. Type A and B have linearly changed shape
functions, and Type C and D have exponentially changed shape functions. All BDA
processes had the same condition of electrolyte (pH 3.0 and 25 *C), electrode gap
distance (10 mm), and electric potential (90 V for 30 min)...................... 142
20
Figure 6-7. Capillary flows on the BDA surfaces and the chromatography papers with the surface
shapes shown in Figure 6-6 and Table 6-1. The symbols and the lines indicate the
experimental data and the theoretical expectations calculated by equation (6-10). The
gray small dots and solid-line show the reference capillary rise on a constant width
surface..........................................................................................................................
144
Figure 6-8. Capillary pressure (Pcap) and capillary diffusivity (Dap) with respect to surface
roughness (Ra) and electric potential (V) of breakdown anodization (BDA) at the
electrolyte temperature of 25 'C. The box, circle, triangle, and diamond symbols
indicate the electric potentials of 30 V, 60 V, 90 V, and 120 V, respectively. The red
and the white colors inside the symbols correspond to the capillary pressure and the
capillary diffusivity, respectively. When the electrolyte temperature is 25 *C, the
capillary pressure and the capillary diffusivity are linearly proportional to the surface
roughness, which is linearly enhanced by the electric potential of BDA. The error bars
indicate
one standard deviation.....................................
145
Figure 6-9. Capillary pressure and surface roughness produced by breakdown anodization (BDA)
with varying electrode gap distance, x. (a) Two parallel electrodes were used with
varying the electrode gap distance (x) in BDA processes. (b) The capillary pressure and
the surface roughness are inversely proportional to the electrode gap distance. The
electric potential of 120 V and an electrolyte temperature of 25 0C were used to produce
the BDA surfaces. The error bars indicate
one standard deviation. ..........................
147
Figure 6-10. Electrode distance profiles used in breakdown anodization (BDA) processes. The
constant gap distance profile was used to produce a reference surface. Four different
gap profiles, which linearly change (a)-(b) and quadratically change (c)-(d), were used
in BDA processes. All BDA processes had the same condition of electrolyte (pH 3.0
and 25 *C), electrode width (10 mm), and electric potential (120 V and 30 min). The
left side electrodes (the red lines) in each image indicate the anode electrodes converted
to highly wetting porous surfaces. The anode electrodes have different surface heights
(H).......................................................................................
..............
.... .......... ... 14 8
Figure 6-11. Capillary flows on surfaces produced by breakdown anodization (BDA) with the
electrode gap profiles shown in Figure 6-10 and Table 6-2. The solid lines and the
symbols indicate the theoretical data and the experimental data, respectively. The solidcircle, solid-box, circle, and box symbols are obtained with the electrode configurations
21
shown in Figure 6-1 0a, (b), (c) and (d), respectively. BDA surfaces were produced with
different electrode gap profiles but the same BDA conditions: 120 V for 30 min in pH
3.0 electrolyte at 25 0C. ............................................
150
Figure 6-12. Surface roughness changes with respect to the non-dimensional height of surfaces
produced by the electrode profiles shown in Figure 6-10 and Table 6-2. The surface
height (H) shown in Figure 6-10 was used to obtain the non-dimensional capillary
height in the x-axis. The surface roughness (Ra) is fimctionally varied according to the
profiles of electrode gap distance. The symbols and the dashed-lines indicate the
measured data and the predictive data, respectively. The predictive data were obtained
from the relationship between the surface roughness and the electrode gap distance. 151
Figure 7-1. SEM images of as-prepared surfaces show micro-scale and nano-scale porous structures
produced by breakdown anodization (BDA) (a) and electrophoretic deposition (EPD)
(b), respectively [198]. The combined BDA/EPD process yields highly wetting
micro/nano scale hierarchical porous structures......................
...............................
156
Figure 7-2. Droplets show four different impingement modes depending on the WashburnReynolds number after impacting highly wetting porous surfaces. The WashburnReynolds number can be expressed as Rew = U0precos9/p, where U is the impact
velocity, p is the liquid density, r, is the effective capillary radius, 0 is the surface
contact angle, and p is the liquid viscosity. Mode-Al: compressing-oscillating, ModeA2: necking and spreading, Mode-B: spreading, and Mode-C: radial jetting and
spreading. A high-speed camera (Photron) was used to record the behavior of liquid
droplets on the surfaces. The scale bar in each image is 1 mm.....................
157
Figure 7-3. Schematic diagram of the cylindrical droplet impact model with time dependent radius,
R(t), and height, H(t). The model cylindrical droplet has the same volume and impact
velocity as the real droplet......................................
....
........................................
. 160
Figure 7-4. Schematic diagram of capillary flow for the assumed cylindrical droplet geometry. The
porous region can be considered as several cylindrical capillaries in parallel, each
having a height, 2rc. The porous region has height, H,, and the flow velocity, vr, at a
distance, R(t), from the center, assuming the ratio of the height of the porous region to
the initial droplet diameter, He/D, is small. , is the sliding contact angle, the contact
angle of the droplet on the top surface of the porous layer during spreading. ............. 166
22
Figure 7-5. Schematic illustrations of droplet spreading on highly wetting porous surfaces. At high
capillary-Weber numbers (Wee > 103), the kinetic energy determines droplet expansion,
while the contact line and viscous effects dissipate mechanical energy (a). At low
capillary-Weber numbers (Wee < 10), the capillary energy governs droplet spreading,
and viscous dissipation is most prominent inside the porous region (b)......................
169
Figure 7-6. Theoretical and experimental droplet spreading for multiple liquids after impact on
highly wetting porous surfaces. Solid lines represent spreading radii obtained from
equation (7-9) while circles are experimental data. The impact velocities are selected
such that Wec exceeds 10 3 . The table provides the surface and liquid properties and the
dimensionless parameters of the energy equation for each data set. Viscous dissipation
inside the porous layer, which is the column highlighted in gray in the table, is not
considered when Wec > 103. Here we only considered impingement Mode-Al and
Mode-B because the droplet mass is not conserved in Mode-A2 and Mode-C due to
necking and jetting behavior, respectively. ..................................
174
Figure 7-7. Experimental results for droplet spreading at low capillary Weber number for the
liquids shown in Table 7-1. The symbols and the black solid line indicate the
experimental data when Wec < 100 and the theoretical data obtained from equation
(7-13), respectively. Viscous dissipation inside the droplet and line dissipation, which
are the columns highlighted in gray in the table, are not considered in the energy
equation because Wec is low. The square of the dimensionless radius change is linearly
proportional to the dimensionless time. The table provides the surface and liquid
properties and the dimensionless parameters of the energy equation for each data set.
The impingement modes are confined to Mode-Al and Mode-A2 because Rew < 0.2
when W ec < 100.....................................
..........................
..................... 175
Figure 7-8. Impingement mode transitions correlate with the Washburn-Reynolds number, as
shown in the log-log plot of Rew vs. cos/Oh2 , where Oh is the Ohnesorge number and
,
9 is the Young's contact angle of the surface. Dcap/u has the same form of cos/0h 2
where o is the kinematic viscosity of liquids used. Both dimensionless parameters can
be used to distinguish wetting properties of the surfaces. Droplets fall from heights
ranging from 0.003 m to 1 m prior to impact. Symbols:
, LI, A
and 0 indicate
Mode-Al, Mode-A2, Mode-B, and Mode-C, respectively. The capital letter under each
23
vertical line indicates the surface name shown in Table 7-1. The inset shows the mode
transitions in a narrow Dca,/lu region of 1 to 100. ........................................................
179
Figure 8-1. Aerosol generation from droplets hitting soils and porous surfaces. a, The clay soil has
irregularly rough surfaces and a droplet falls with an impact speed of 2.0 m/s. b, Tiny
bubbles are formed under the droplet. The bubbles are inside the white circles in the
image. c, Tiny water-jets are ejected from the droplet during impact. The white circles
and arrows in the image highlight aerosols and jets ejected from the droplet. d-g, Highspeed images of the process of generating aerosol when a single bubble breaks inside
the droplet. d, A bubble is trapped inside the droplet. e, The bubble breaks at the
interface of water and air. f, A water pillar is jetted from the droplet. g, The water pillar
breaks up into tiny droplets. h, Many simultaneous water-jets and aerosols are generated
on a thin layer chromatography plate within a specific range of drop impact speeds.. 185
Figure 8-2. Bubble generation, growth, and breaking inside droplets hitting porous surfaces. a-c,
High-speed images of bubble formation inside water-droplets on a thin layer
chromatography plate with respect to impact velocity. Bubble size and distribution
become uniform with impact velocity, resulting in simultaneous water-jets on the
droplet surface. d-g, The schematic illustration of the process of water-jet generation. d,
A droplet impacts a porous layer and the droplet radius is expanded. e, After it reaches
the maximum radius, tiny bubbles are inflated at the interface of the droplet and the
porous surface. f, The droplet height thins due to the absorption of water into the porous
layer and the bubble size grows due to the inflation with air squeezed from the porous
layer. g, Finally, the tops of the bubbles meet the interface of air and water, and they are
ruptured, generating tiny water jets. The maximum number of bubbles inside the droplet
increases with impact velocity. The scale bars in a-c indicate 1 mm...........................
186
Figure 8-3 Characteristics of droplets and bubbles generated after the droplets hit the three TLC
plates. The hydraulic diffusivities of TLC-A, TLC-B and TLC-C are 9.5, 20.4, and 22.4
MM /s respectively. (a) The average bubble diameter does not change significantly by
impact velocity U 2 but the average droplet film thickness is inversely proportional to
U. (b) The maximum number of bubbles inside the droplet linearly increases with
respect to U0 . (c) The time it takes to observe the first jet is affected by the surface
wettability at low impact velocity but by the droplet film thickness at high impact
velocity since the droplet film thickness governs the maximum bubble size at high
24
impact velocity. (d) The droplet film thickness h,,, after hitting the surfaces is the
highest on TL C -B
...................................................................................
................. 196
Figure 8-4. Characterization of aerosol generation when droplets hit soils and porous surfaces. The
x-axis indicates a modified Peclet number (Pe
(U -Do)/Dcap), where U and D, are the
impact velocity and the diameter of the droplet. The y-axis indicates the Weber number
(We
pD0 U 2/a), mainly varied by the impact velocity. We and Pe represent the
impact condition and the surface property, respectively. The Da, values of the soils
were measured by the capillary rise experiments. The red symbols indicate the
observation of aerosol dispersion from the droplets at the corresponding We and Pe.
The blue circle named "aerosol generation region" highlights the group of the data
points where aerosols are generated. The yellow symbols inside the aerosol generation
region show the data points of frenetic aerosol generation. Rainfalls on soils are placed
on the upper part of the characterization map, and clay and sandy-clay soils have
concentrated regions in the sparling zone. a-c, the reprehensive images of drop
impingements in the regions classified with We...........................
199
Figure 9-1. Fabrication processes for micro/nano hierarchically structured surfaces and Scanning
Electron Microscopy (SEM) images (a)-(f). For micro-porous structures, breakdown
anodization (BDA) is used with different electric fields, (a)-(c). For nano porous
structures, electrophoretic deposition (EPD) is used with different nanoparticles, (d)-(f).
The hierachical micro- and nano-porous structures are produced by a series of BDA and
EPD, (g)-(i). The electrolyte temperature and the nanoparticles affect the surface
morphology and the surface energy, respectively ..........................
205
Figure 9-2. Functional surfaces produced by electro-fabrication. (a) Anti-wetting fabric with biomimicked coating-layers for water harvesting. Each fiber of the fabric was uniformly
coated with hydrophobic silica nanoparticles, resulting in high static contact angle and
low roll-off angle. The fabric maintains its original flexibility and breathability after the
modification. The water droplets were growing with a regular pattern similar to tlhose on
a real leaf during condensation. (b) Hierarchical surfaces for critical heat flux
enhancement. The micropillars, created on a silicon wafer, were coated with hydrophilic
silica nanoparticles, enhancing hydrophilicity. The coatings prevent vapor-blankets on
25
the heater surface and dramatically enhance critical heat flux and heat transfer
efficiency in pool boiling [255]......................................
206
Figure 9-3. Aerosol generation from droplets hitting porous surfaces. Frenzied aerosol dispersion
can be observed in a specific region of the Weber number of droplets and the hydraulic
diffusivity of surfaces.........................................
207
Figure 9-4 Schematic comparison between (a) a conventional microfluidic device and (b) the
porous thin film m icrofluidic device. .................................................
...................... 208
Figure 9-5. Fabrication process. A photoresist layer is patterned using photolithography.
Breakdown anodization is conducted with the patterned Ti electrode in an acidic
electrolyte ....................................................................................................................
209
Figure 9-6. Porous thin film microfluidic channels produced by BDA. (a)-(c) Patterned Ti sheets
after BDA with different electric potentials. (d)-(f) Thin channels generated by BDA.
....................
...... . ........................................................................................................
2 09
Figure 9-7. Wettable area and wicking speeds of different porous media with a one microliter
sample of 1 g/L Rhodamine B in deionized water. The wetted area of the BDA surface
is significantly larger due to its high permeability and low thickness. ....................... 210
Figure 9-8. Fabrication procedure for the carbon nanotube and hydrogel composite layer and the
experiment setup for electrophoretic deposition with two immiscible liquids. Both water
and oil are added to a container and the electrode assembly is placed into the container.
The oil-water interface must be positioned at the middle of both electrodes. During an
electric potential is applied to the electrodes, the crosslink solution is added to the top of
the oil phase. After the polymerization, the oil phase is extracted and then the composite
hydrogel film is gently lifted up. Experiment setup for electrophoretic deposition at the
oil-water interface................................................
212
Figure 9-9. Schematic illustrations of carbon nanotube and surfactant assemblies. The surfactant is
composed of a hydrophilic head, which has the cross sectional area of A, (the head
radius is R,) and a hydrophobic tail, which has length L,. (a) In reality, multiple
surfactants are attached on the surface of the CNT. (b) In the simplified model, the
surfactant heads are considered a single cylinder.......................................................
213
Figure 9-10. Total interaction potentials between two CNT-surfactant assemblies. The total
interaction potential can be obtained by the summation of van der Waals force,
electrostatic force, and osmotic pressure. The total interaction potentials of (a) and (b)
26
are obtained with the surfactant coverage ratio of 30 % and the tail stretching ratio of
100 %.
Different bulk surfactant concentrations of CMC (8.7xO1
mol/L) and 2xCMC
are used in (a) and (b) to compare the effect of micelle formation .................. 214
27
28
List of tables
Table 4-1. Changes in capillary pressure for five superhydrophilic surfaces 30 days after fabrication.
...... . . .................................................................................................
................. .......... 10 7
Table 5-1. Evaluation of prepared surfaces with BDA and/or EPD methods.................................
120
Table 5-2. CHF results for modified surfaces. Reference: an untreated titanium surface. Sample 1: a
superhydrophobic surface produced with EPD. Sample 2: a superhydrophilic surface
produced by BDA. Sample 3: a hybrid surface produced by the coupled BDA and EPD
m ethod .........................................................................................................................
12 1
Table 6-1. Shape functions of the BDA surfaces and the chromatography papers used to verify the
alternation of capillary flows. As a reference, a BDA surface was produced with two
parallel electrodes, which have a constant width of 10 mm and an electrode gap distance
o f 10 mm ................................................................................................
.....................
143
Table 6-2. Profile functions of electrode gap distance shown in Figure 6-10. In Type A and B,
linearly changed gap distance was employed. Circular shape electrodes were used in
Tape C and D. The reference BDA surface was produced with a constant electrode gap
distance of 10 mm . .............................................................................
.........................
149
Table 7-1. Liquid and surface properties used in the drop impingement experiments and numerical
simulations. The properties of the glycerol and water mixture were obtained from the
literature [208]. Highly wetting porous titania (TiO 2) surfaces were produced by an
electrochemical fabrication method [198]. The porous titania surfaces showed wide
variations in capillary pressure and spreading speed. The thin layer chromatography
(TLC) plates were obtained from Sigma-Aldrich. The Gel-Blotting paper is a
chromatography paper (grade 230) obtained from Genesee Scientific. The coffee filter
is a commercial product made by Melitta USA, Inc. The symbols correspond to the
symbols in the plot of drop impingement modes (Figure 7-8) .................
... 158
Table 7-2. Simplified energy conservation equation and dimensionless droplet radius at different
physical regimes. The line dissipation in equation (7-9) is considered dominant and the
other dissipation terms are ignored to obtain simplified energy conservation equations
as functions of common dimensionless parameters. The dimensionless droplet radius
can be expressed as a function of the Reynolds number and another dimensionless
29
parameter; therefore, we can characterize the droplet radius change with respect to the
relative influence of the Reynolds number...................................................................
171
Table 8-1. Characteristics and wetting properties of the media used to examine aerosol generation.
.. . ......... ..... ................................................................................................................
30
19 3
Chapter 1. Introduction: Electrophoretic
Deposition and Breakdown
Anodization
Reproduced in part with permission from
Young Soo Joung, Cullen R. Buie, "Electrophoretic Deposition of Unstable Colloidal Suspensions
for Superhydrophobic Surfaces," Langmuir, 2011. 27(7): pp. 4156-4163.
Copyright 2011 American Chemical Society.
Young Soo Joung, Cullen R. Buie, "A Hybrid Method Employing Breakdown Anodization and
Electrophoretic Deposition for Superhydrophilic Surfaces," JournalofPhysical Chemistry B, 2013,
117 (6), pp. 1714-1723.
Copyright 2013 American Chemical Society.
31
1.1.
Introductory remarks
Over the past decade, superhydrophobic surfaces have been explored due to their promising
applications in diverse areas such as self-cleaning surfaces [1, 2], drag reduction [3, 4], microfluidics [4, 5], heat transfer [6, 7], and anti-wetting textiles [8, 9]. To date, dozens of fabrication
methods have been investigated to produce superhydrophobicity. The key properties to achieve
superhydrophobicity are low surface energy and high surface roughness. The techniques to make
high surface roughness can be classified as either top-down (machining) or bottom-top (molding)
methods. Top-down methods transform a flat surface to a roughened surface. Lithography and
etching [10-191, soft-lithography [3, 20-22], and micro-machining [23-25] can be classified as topdown. These methods typically provide precise control of surface roughness, and consequently,
wettability. However, these processes tend to be complicated, toxic, or relatively expensive. In
addition, top down techniques are often difficult to scale to large areas (i.e. order m 2 ). Alternatively,
bottom-up approaches add materials to a flat substrate in order to increase surface roughness.
Coating methods such as dip-coating [26-28], layer-by-layer [29-32], sol-gel processes [8, 33],
chemical
vapor
deposition
electrohydrodynainics
[6,
7,
34-36],
electrochemical
deposition
[37-41],
and
[42] are considered bottom-up techniques. Advantages of bottom-up
approaches include cost, and scalability but they often suffer from reduced control of surface
roughness. Methods to reduce surface energy can be categorized in two ways; those that use lowsurface-energy materials during the roughening process [42-48], and those that reduce surface
energy after surface roughening such as via chemical vapor deposition [19, 20, 49-52], or the
application of self-assembled monolayers [16, 39, 53, 54]. Regardless of the type of surface
roughening process, most fabrication methods use additional surface treatments to reduce surface
32
energy since the raw materials used for the fabrication rarely have sufficiently low surface energy.
This tends to add additional complexity to the fabrication process.
In addition to superhydrophobic surfaces, superhydrophilic surfaces offer great opportunities to
provide unique surface functionality for practical applications such as anti-fogging glass, heat sinks
in pool boiling, heat pipes, evaporators, fuel spreaders, and micro-fluidic devices [55-59].
Classically, superhydrophilic surfaces have been defined as surfaces with contact angles less than
five
degrees
[60].
However,
this
criterion
is not sufficient to precisely characterize
superhydrophilicity since superhydrophilic surfaces can show diverse behaviors in the above
applications, even though all have similar static contact angles. Indeed, a definition of
superhydrophilic
surfaces has remained elusive [61]. Therefore, appropriate parameters to
characterize superhydrophilic surfaces and fabrication methods to control those parameters are
necessary.
To realize superhydrophilicity two key features, highly porous (rough) structures and high surface
energy, are necessary [60]. From Wenzel's equation [62], it is well known that contact angles on a
surface decrease with increasing surface roughness when the flat surface has a static contact angle
less than ninety degrees. Thus, it is necessary to achieve highly rough structures with nanomaterials or micro-fabrication techniques to produce superhydrophilic surfaces [58, 63-67]. In some
cases, additional surface modifications with high surface energy materials are necessary [41]. In
most studies of superhydrophilic surfaces, the surfaces show nearly zero contact angle, but they are
rarely evaluated in terms of transport properties such as capillary pressure or spreading speed.
Given the importance
of transport properties
it is impossible to distinguish between
superhydrophilic surfaces utilizing contact angle alone.
Manufacturing demands for superhydrophobic and superhydrophilic surfaces include process
simplicity, low manufacturing cost, environmental compatibility (i.e. non-toxic), scalability, and
33
potential for mass production. With these considerations, this thesis presents electrophoretic
deposition
(EPD)
and breakdown
anodization
(BDA)
as
potential
tools
to
produce
superhydrophobic and superhydrophilic surfaces. EPD employs electrophoresis of charged particles
in dielectric solvents to created dense porous films and structures [68]. When a sufficient electric
field is supplied to a colloidal suspension, charged particles are attracted to and deposit upon the
oppositely charged electrode. Among many applications, EPD has been investigated to fabricate
microscale and nanoscale structures [69, 70]. EPD has also been explored to develop novel
electrodes and catalyst layers for electrochemical systems [71, 72], since EPD is considered as an
effective technique to control porosity, surface area, and density of porous films. Superhydrophobic
surfaces, composed of coated SiO 2 nanoparticles, have been produced using electrophoretic
deposition (EPD) [73]. In this study low surface energy PDMS (Polydimethylsiloxane) coated
silicon dioxide (SiO 2) nanoparticles were employed while controlling suspension stability to
produce highly rough surfaces. To produce superhydrophilic surfaces, we can use the same
mechanism to achieve high porosity/roughness but while using high surface energy particles. TiO 2
nanoparticles or nanotubes have been used to achieve high surface energy [63, 67, 74]. However, it
is challenging to simultaneously obtain high capillary pressure and fast spreading speed due to high
viscous resistance in small nano-structures, even though they show contact angles near zero. In this
work, we suggest a novel fabrication method to produce superhydrophilic surfaces with high
capillary pressure and fast spreading speed. We show that the method can be utilized to control
capillary pressure and spreading speed independently. EPD is utilized to obtain nano-structures
composed of TiO 2 nanoparticles, while breakdown anodization method (BDA) was employed to
produce micro-porous structures. During anodization, the oxidization film thickness linearly
increases with respect to applied electric potential [75]. However, when the electric potential is
higher than a critical value, the film thickness abruptly increases, resulting in a number of micro-
34
scale irregularities. The critical electric potential is called the breakdown point [76, 77]. At electric
potentials exceeding the breakdown point, micro-scale porous structures are created on the anode
surface.
1.2.
1.2.1.
Fundamental of electrophoretic deposition
Electrophoresis
When the surface of a particle in an electrolyte is electrically charged, the particle has an
electrophoretic mobility p. Under an applied electric field, E, the charged particle moves towards an
oppositely charged electrode with the velocity, v, expressed by,
v = pE
The mobility, p, is a function of zeta potential,
(1-1)
, permittivity,
, and viscosity, , of the fluid as is
shown in Henry's equation [78],
(1-2)
317
This equation assumes spherically shaped particle with small r/AD, where
AD-
is the Debye-HUckel
length and r is particle radius [78].Particles transported to the electrode agglomerate on the surface
of the electrode if the electric field is sufficiently high to induce deposition [79].
35
1.2.2.
Suspension stability
In EPD, suspension stability is critical since the morphology of the deposition layer is
significantly affected by particle flocculation. A stable suspension results in well-dispersed
particles, devoid of serious flocculation. In contrast, fast particle sedimentation is observed in
unstable suspensions due to particle agglomeration. Interfacial forces between particles determine
suspension stability. Two opposing forces are induced between particles in close proximity. The
attraction force is commonly known as the van der Waals force and the repulsive force is due to the
electrical double layer. The net interaction potential, D,,t, is the summation of the attractive
potential, (DA, and the repulsive potential, (DR, between two particles. Assuming spherical particles
of identical size, the interaction potential can be expressed as [80],
DA +
R=64kB
ke
A 2
12vd
(1-3)
where A is the Hamaker constant, d the distance between particles, kB the Boltzmann constant, T the
absolute temperature, and n,, the bulk ionic concentration expressed as the number of ions per cubic
meter. ;o is a function of the surface potential,
defined as [80]
ii,
e zo
12 kBT
-I
2
4; ezwIol kjT+
(1-4)
where c is the elementary electric charge, and z the valence number. Surface potential is directly
proportional to the zeta potential such that we can consider the electric repulsion a function of the
36
zeta potential. To evaluate suspension stability experimentally, the stability ratio, W, is employed
and expressed by [811
net
W
K
Kr
KS
2
fo
.
oo e
^D S
0
Here,
Kr
(skBT
oo e -ds
is the rate constant for rapid coagulation,
(1-5)
kBT
2
K3 ,
the rate constant for slow coagulation, and s is
the ratio of the particle radius to the distance between two-particle centers. Equation (1-5) assumes
that fast coagulation occurs when the attraction force dominates and electric double layer repulsion
is negligible.
From equations (1-2) and (1-5), it is notable that the zeta potential, which can be determined
experimentally, influences both deposition rate and stability. In general, higher zeta potential leads
to higher deposition rate and improved stability. The effects of pH [82], ionic concentration [83],
surfactants [84], and solvent composition [85] on suspension stability have been investigated by
others. In this work, we chose to vary stability by varying suspension pH at a specified ionic
concentration, since the zeta potential is a strong function of pH.
1.2.3.
Stability ratio
Suspension stability can be quantitatively evaluated from the change of optical absorbance with
respect to time [86, 87]. A stable suspension shows moderate change of absorbance due to slow
flocculation and sedimentation. In contrast, unstable suspensions feature fast sedimentation,
attributable to the low net interaction potential between particles, as shown in the equation (1-3).
37
This results in a steep gradient in absorbance versus time. Change of absorbance, a, versus time is
directly proportional to the initial rate constant, ,, for coagulation when time, t, is small, and can be
expressed by [86, 87]
KKNO2 2
(1+INt)2
da
dt
(1-6)
Here No is the initial number of particles, A, the wavelength of incident light, and K, is a
proportionality constant. Experimental stability ratio can be acquired by dividing the maximum rate
of change of absorbance by the rate at a particular pH, as in the following equation,
_[ dcd dtL
l
Kc
afbs(17
S
dt
(-7
H
As an alternative, changes in particle size can be measured using dynamic light scattering (DLS)
to assess stability [83, 88]. The average hydrodynamic particle diameter, Dh, can be calculated by
the Stokes-Einstein equation,
D= kBT
B
3,TriD
(1-8)
In equation (1-8), D is the average translational diffusion coefficient of colloidal particles in dilute
suspension, which can be determined by the temporal evolution of intensity fluctuations in dynamic
light scattering measurements. The change of particle size, Dh, with respect to time is a function of
38
the initial aggregation rate constant
K
and the initial particle concentration, Co, when time, t, is small,
as
h
'ArCo
dt-
(1-9)
where, 8 is a constant that depends on scattering angle and material properties of particles. Noting
the presence of coagulation rate in equation (1-7) and equation (1-9), the experimental stability ratio
can be expressed in terms of the ratio of the fast coagulation rate to the slow coagulation rate,
W
-
=
(dDh I dt)max
(dDh /dt)pH
If we know the initial particle size, Dhj, and the maximum particle size, Dh..'ax at a specific time t,
the stability ratio based on size, Wize, can be calculated as
sD
-h.i
The size based stability ratio, Wsze, calculated by equation (1-11) should be comparable with the
absorbance stability ratio, Wabs, obtained through the absorbance measurement as in equation (1-7).
Notably, the initial particle size can be estimated by comparing both stability ratios.
1.3.
Fundamental of breakdown anodization
39
1.3.1.
Anodization process
On the Pourbaix diagram of titanium-water systems [89], cathode and anode potentials during
breakdown anodization correspond to immunity and passivity regimes, respectively. The chemical
reaction processes on the anode and the cathode electrodes we consider are. as follows:
<Anode>
(1-12)
Electrolysis: 2H 20 -+02() + 4H + 4e
Corrosion: Ti
-+
Ti43 + 3
Oxidation: Ti+ 2H 2 O(0
Oxidation: Ti +02
-+
-+
(1-13)
Ti02+ 4H + 4e-
(1-14)
TiO2
(1-15)
Dissolution: TiO 2 -x+ H 2 0(0 1-+ TiO 26xH 2 O(s)
(1-16)
Dissolution: TiO 2 + H 2 0 + H+ -+ Ti(OH) 3
(1-17)
<Cathode>
Electrolysis: 4H2 0+ 4e
Electrodeposition:Ti
+ 3e
2
H2(g) + 40HW
+
(1-18)
Ti
(1-19)
Electrolysis (1-12) and dissolution (1-16) are continuously observed during the anodization process.
Corrosion and electrodeposition can be expected in the initial stage of the anodization process but
these processes quickly terminate because the oxide layer prevents further corrosion (1-13). At
40
steady state, the electrolysis, oxidation, and dissolution processes continue. Therefore, the overall
anodization reaction in aqueous electrolytes can be expressed as
'/ 2Ti+ 2H 2 0(0
'/2Ti02+ 2 H2(g)+ 2O2(g)
(1-20)
considering both oxidation and electrolysis processes. Given this, two dissolution processes (1-16)
and (1-17) can be taken into account on the anode electrode. Through the dissolution process (1-16),
hydrated titanium oxide sedimentations are observed in the electrolyte after the anodization process.
Then, the increase of electrolyte pH during the anodization process can be explained by the
dissolution process (1-17).
1.3.2.
Breakdown potential
The general breakdown phenomenon was theoretically investigated by Sato [90]. He suggested
that the surface pressure, P, of the electrode during the anodization process can be estimated by the
summation of the electrostriction effect and the interfacial tension effect as follows:
P=Pe+
0
87r
ha
(1-21)
with ambient pressure P0 , electric field E, surface tension of the anodic oxide film y, and the anodic
oxide film thickness ha. When an electric field is applied to dielectric materials, the electrostriction
stress is induced due to the effect of deformation on permittivity [91]. When the surface pressure is
higher than the critical compressive stress of the film ao, the breakdown process takes place during
41
anodization. If surface tension effects are considered, the electrochemical properties of the
electrolyte and electrode must be taken into account to estimate the breakdown conditions because
ion adsorption under the film surface influences surface tension. The breakdown electric field, Ec,
on the oxide layer can be expressed as a function of the electric potential, E= (# -#fz)/ha where
# is
the electrode potential and o is the equilibrium potential at the interface between the oxide layer
and the electrolyte. Finally, when breakdown is initiated, the electrode potential, 0*, can be
expressed by [90].
do*
dIna
8xkBTPa
-87ro -e (6+1)E
(1-22)
1-22,
where a is the anion activity in the electrolyte and pa is the anion adsorption density. From equation
(1-22), we expect that high temperature electrolytes and high anion adsorption under the film
surface lower the critical potential.
1.3.3.
Effect of electrolyte temperature on oxide films
For identical electrolytes, the maximum oxide film thickness is governed mainly by the
electrolyte temperature and electric potential during the anodization process. The dissolution
process (1-16) expresses the dissolution reaction governing the total oxide film thickness. This
reaction is the hydration of the titanium oxide, which is soluble in acidic solutions. Electrolyte
temperature affects the rate of this hydration step. In other studies, it has been generally accepted
that with increasing electrolyte temperature, the hydration rate also increases [92, 93]. This behavior
can be verified by investigating the oxide film thickness with respect to electrolyte temperature. The
42
oxide film thickness can be measured using the capacitance, C, of the oxide layer. The inverse
capacitance, C
is proportional to the oxide film thickness [94]. An empirical relationship
between the capacitance and electrolyte temperature was suggested by Bockris et al. [95]:
_A
C7
1
AH
-l -RT
(1 -2 3
)
dIn d(C;)
l-dt
I10.5 kJ/mol
where
and the
R isactivation
the universal
energy
gas constant.
AH 1From equation
(1-23) we find that the rate at which the oxide film thickness increases is inversely proportional to
the electrolyte temperature.
1.4.
Thesis objective and outline
The first objective of this thesis is to develop new fabrication methods employing
electrophoretic deposition (EPD) and breakdown anodization (BDA) for producing micro and nano
structures with various surface-functionality. The second objective is to understand liquid transport
and droplet spreading on micro and nano porous surfaces produced by EPD, BDA, and
combinations thereof. The third objective is to apply the electro-fabrication methods and the liquid
transport properties to real world applications such as superhydrophobic and superhydrophilic
surfaces, anti-wetting fabric, capillary flow devices, and anti-biofouling surfaces. The following
paragraphs outline the organization of this thesis.
In Chapter 2, a new method to fabricate superhydrophobic surfaces using electrophoretic
deposition (EPD) is presented. Low surface energy materials with high surface roughness are
achieved using EPD of unstable hydrophobic SiO2 particles suspensions. The effect of suspension
stability on surface roughness is quantitatively explored with optical absorbance measurements (to
43
determine suspension stability) and atomic force microscopy (to measure surface roughness).
Varying suspension pH modulates suspension stability. Contrary to most applications of EPD,
superhydrophobic surfaces favor mildly unstable suspensions since they result in high surface
roughness. Particle agglomerates formed in unstable suspensions lead to highly irregular films after
EPD. After only one minute of EPD we obtain surfaces with low contact angle hysteresis and static
contact angles exceeding 1600. This thesis also presents a technique to enhance the mechanical
durability of the superhydrophobic surfaces via co-deposition of a polymeric binder added to the
suspension prior to EPD.
In Chapter 3, electrophoretic deposition is used for fast modification of polyester fabric with
silica nanoparticles and polymer networks for highly durable coatings To date, electrophoretic
deposition (EPD) has been utilized on electrically conductive substrates due to its dependence on
electrical sources. Even though EPD on non-conductive materials such as ion conductive polymers
has been attempted, weak adhesion, cracks, and irregular deposition have remained drawbacks [96,
97]. To resolve these problems, thin polymer layers were coated first on a polyester fabric using an
electrostatic self-assembly technique. Then, the silica nanoparticles were uniformly seeded on the
polymers. Finally, polymer stabilized silica nanoparticles were deposited by EPD on the silica
nanoparticles, followed by heat treatment. As a result, the modified polyester fabric shows high
static contact angle and low contact angle hysteresis, while keeping its original color, flexibility,
and breathability.
In Chapter 4, a new fabrication method is presented for superhydrophilic surfaces with high
capillary pressure and fast spreading speed. The fabrication method consists of electrophoretic
deposition (EPD) and breakdown anodization (BDA). Nanopores and micropores were produced on
titanium plates by EPD and BDA, respectively. In EPD, TiO 2 nanoparticles were used to enhance
the surface energy and create nano-porous structures; while BDA was employed to produce micro-
44
porous
structures.
Capillary
rise
measurements
(CRM)
were
utilized
to
characterize
superhydrophilic surfaces in terms of capillary pressure and spreading speed. From CRM, it was
revealed that micro-porous structures play a dominant role in determining transport properties, and
nano-porous structures affect local wettability without significantly reducing spreading speed. By
combining BDA and EPD into a hybrid method, dual-scale (nano and micro) porous structures were
produced on titanium plates. The methods presented offer the potential to vary the transport
characteristics of superhydrophilic surfaces by altering the nano-scale and micro-scale features
independently. As an example, surfaces with unconventional capillary flows were produced by the
hybrid method. This method provides additional opportunities to investigate wetting phenomena,
while offering a potentially low cost process for industrial applications.
In Chapter 5, superhydrophilic surfaces with hydrophobic layers are used to enhance critical
heat flux (CHF) and to reduce boiling inception temperatures (BIT). The novel surfaces were
fabricated by a hybrid electrophoretic deposition (EPD) method coupled with break down
anodization (BDA). With the BDA process, microporous superhydrophilic surfaces were created on
titanium substrates. Subsequently, nanoporous hydrophobic particles were deposited with EPD on
the superhydrophilic surfaces. The hydrophobic layers provide numerous nucleation sites, lowering
BIT while the superhydrophilic layers prevent film boiling, resulting in increased CHF. The
resulting surfaces exhibit higher CHF with lower BIT than untreated titanium surfaces.
In Chapter 6, breakdown anodization (BDA) is employed to present various capillary flows
that can be expressed as functions of capillary height. Capillary transport properties can be
controlled by varying the electric field and electrolyte temperature. Furthermore, they can be
expressed as functions of capillary height when customized electric fields are used in BDA. To
predict capillary flows on BDA surfaces, a conceptual model of highly wettable porous films is
developed, the model assumes the porous films consist of multiple layers of capillary tubes oriented
45
in the flow direction. From the model, a general capillary flow equation of motion was derived in
terms of capillary pressure and capillary diffusivity, which can be expressed as functions of
capillary height. The theoretical model was verified by comparison with experimental capillary
flows and showed good agreement. From the investigation of the surface morphologies, it is found
that the surface structures were also functionally graded with respect to the capillary height. The
fabrication method and the theoretical model suggested offer novel design methodologies for
devices requiring passive control over liquid propagation speeds.
In Chapter 7, drop impingement is investigated on highly wetting porous films and paper.
Experiments reveal previously unexplored impingement modes on porous surfaces designated as
necking, spreading and jetting. Dimensional analysis yields a new non-dimensional parameter,
denoted the Washburn-Reynolds number, relating droplet kinetic energy and surface energy. The
impingement modes correlate with Washburn-Reynolds number variations spanning four orders of
magnitude and a corresponding energy conservation analysis for droplet spreading shows good
agreement with the experimental results. The simple scaling laws presented inform the investigation
of dynamic interactions between porous surfaces and liquid drops.
In Chapter 8, it is shown that artificial aerosol particles can be generated on porous surfaces.
Aerosols have their significant impact on the environmental and global warming. To date, bubbles
breaking on the sea and fossil fuel combustion have been considered the main origins of aerosol
dispersion. However, this thesis reports that rainfall hitting soil can also generate aerosol. Use of
high-speed imaging technologies provides visual evidence of aerosol generation. Interesting droplet
behaviors are observed when simulated rainfall impinges upon engineered porous surfaces. Within a
specific range of impact velocity, we observe frenzied ejection of tiny droplets, which produce
aerosol clouds above the surface. Knowledge of surface properties and impact conditions can be
used to predict when frenzied aerosol generation will occur.
46
In Chapter 9, we will show on-going efforts to develop additional applications using electric field
based fabrication methods. First, highly wettable thin porous films, produced by breakdown
anodization, are utilized to produce thin porous film based microfluidic devices. Second, conductive
hydrogel membranes are produced by electrophoretic deposition of carbon nanotubes at the
oil/water interface. Third, dispersion of carbon nanotubes in aqueous solutions is investigated to
understand the role of surfactants on the dispersion.
47
48
Chapter 2. Electrophoretic Deposition of
Unstable Colloidal Suspensions for
Superhydrophobic Surfaces
Reproduced in part with permission from
Young Soo Joung, Cullen R. Buie, "Electrophoretic Deposition of Unstable Colloidal Suspensions
for Superhydrophobic Surfaces," Langmuir, 2011. 27(7): pp. 4156-4163.
Copyright 2011 American Chemical Society.
49
2.1.
Introduction
EPD is a well-established process, but wettability of structures fabricated with EPD has largely
been overlooked. In one particular study, the wettability of thin films produced by EPD with titanate
nanotubes was investigated [74]. In their work, the surface of the titanate deposition layer was
switched from superhydrophilic
to superhydrophobic
after a surface modification
with
1H,lH,2H,2H-perfluorooctyltriethoxysilane. The porous structure of the titanate deposition layer
was considered the primary factor to produce superhydrophobicity, but EPD itself was not
investigated as a tool to control wettability. Recently, Ogihara et al. demonstrated the possibility of
using EPD to fabricate superhydrophobic surfaces [98]. Several hydrophobic particles including
carbon black, activated carbon, vapor-grown carbon nanofibers, titanium dioxide, beta-type copper
phthalocyanine, and phthalocyanine green were used to produce superhydrophobic surfaces.
However, they did not explore mechanisms to control wettability with EPD or address the relatively
weak adhesion of EPD surfaces.
The purpose of this work is to illuminate how EPD can be utilized to control surface roughness
and achieve superhydrophobicity. Prior EPD studies have used suspension stability, the electric
field, and deposition time as variables to control surface roughness of deposited films [99, 100].
This work is a significant extension beyond the study of Ogihara et al. as we elucidate the role of
suspension stability and deposition time to enhance surface roughness for the purposes of antiwetting. The effect of colloid stability on surface wettability is explored experimentally, resulting in
superhydrophobic surfaces with static contact angles exceeding 1600.
2.2.
Experimental
50
2.2.1.
Suspension preparation
For all experiments in this study, hydrophobic SiO 2 particles (polydimethylsiloxane (PDMS)
coated, average particle diameter 14 nm [PlasmaChem, Berlin, Germany]) were used without
additional purification or modification. A mixture of 90% methanol (ACS Reagent, Baker analyzed)
and deionized (DI) water (by volume) was used as the solvent. The PDMS coated SiO 2 particles are
hydrophobic, making dispersion in aqueous solvents impractical. Therefore, non-aqueous solvents
were used and methanol was chosen since its refractive index (n
=
1.33 at 25 *C) is similar to water.
However, we note that our technique to create superhydrophobic surfaces is not limited to PDMS
modified hydrophobic SiO 2 particles and methanol based solvents as presented here. We have also
successfully produced superhydrophobic surfaces with both hydrophobic TiO 2 particles and SiO 2
particles modified by octylsilane (unpublished results). For our colloid stability, zeta potential, and
particle size measurements we use particle concentrations of 0.1 g/L. Following initial dispersion,
potassium nitrate (ACS reagent, > 99 %, Sigma-Aldrich) was added to the suspension in order to
adjust the salt concentration to ~10-6 M. The purpose of the salt is to vary the gradient of the zeta
potential curve [86]. After 5 minutes of sonication (all sonication was conducted with the amplitude
0.25 pm/mL, Sonicator 400, Qsonica, LLC.), the SiO 2 particles were well dispersed in the
suspension. Next, the suspension pH was adjusted with acid (Nitric acid, 70 % ACS reagent, SigmaAldrich) or base (Potassium hydroxide, 45 wt.% solution in water, Sigma-Aldrich). Ten different
pHs; 3.0, 4.0, 5.0, 6.0, 7.0, 7.4, 7.6, 7.9, 8.0, and 8.3, were prepared for the measurements. Five
minutes after the pH was adjusted, the suspension was sonicated again for 5 min. After the
suspension settled for 30 s, zeta potential and particle sizes were measured with a zeta potential
meter (Zetasizer Nano ZS, Malvern Instruments, Inc.) and absorbance vs. time was recorded with a
spectrophotometer
(Wavelength
450 nm,
Spectrophotometer
51
UV-1800,
Shimadzu).
Each
measurement at a given pH was conducted three times with independently prepared suspensions in
order to acquire average values.
The suspensions used for EPD were prepared using the procedure indicated above except that the
SiO 2 particle concentration was 1 g/L. Figure 2-1 shows a schematic of the EPD system. Two
titanium plates (Purity > 99.6 %, Annealed, Goodfellow Corporation), with identical dimensions of
thickness (0.5 mm), width (10 mm), and length (50 mm), were used as working and counter
electrodes. In each experiment 10 V was applied between two electrodes separated by 15 mm. The
EPD process was conducted at ambient temperature and without mechanical stirring. Deposition
times were 30 s, 60 s, 90 s, 120 s, and 180 s. After completing EPD the sample was dried in ambient
temperature air.
DC Power Supply
Substrate
Particle
Suspension
Counter
electrode
<-
Figure 2-1. Schematic illustration of the EPD cell. The cell consists of two titanium electrodes with
a 15 mm of gap, a DC power supply (10 V applied), and a suspension consisting of hydrophobic
SiO 2 particles dispersed in a mixture of 90% methanol and 10% DI water by volume.
52
To improve the adhesion of deposits, two part conductive epoxy (CW2400, Chemtronics) was
added into the suspension. After the 1 g/L SiO 2 suspension was prepared with the same way
mentioned above, the concentration 10 g/L of each epoxy was separately mixed into the suspension
with 5 min sonication. After mixing both epoxies, the EPD process was instantly conducted. A
stirrer (7 x 7 in ceramic top plate, 1xO.5 in Teflon magnetic stirring bar, VWR) was used at the
rotating speed of 1000 rpm during the EPD process in order to maintain well dispersed epoxy in the
suspension. The electric potential was 30 V/cm and the deposition time was 10 min. Other
conditions for the EPD process were the same to the case of the non-epoxy suspensions.
2.2.2.
Surface characterization
The morphology of deposited films was characterized with a scanning electron microscope (SEM,
JEOL 6320FV Field-Emission High-resolution SEM). Surface roughness was measured by atomic
force microscopy (AFM, DI Nanoscope) at three distinct points on each sample. The area scanned
for AFM measurements was 40 x 40 pm and the average root mean square (RMS) surface
roughness was calculated using commercial software provided by the AFM manufacturer. A
goniometer (Kyowa, DM-CE1) was used to dispense and image a 3 pL drop of DI water at four
different points on each sample. Static contact angles (CA) were calculated using the tangential
curvefitting method.
2.3.
2.3.1.
Results and Discussion
Zeta potential and particle size
53
The first suspension property measured was zeta potential since it is the key characteristic of a
colloidal suspension. Zeta potential measurements were conducted at ten pH values: 3.0, 4.0, 5.0,
6.0, 7.0, 7.4, 7.6, 7.9, 8.0, and 8.3. Figure 2-2a shows zeta potential as a function of suspension pH.
The isoelectric point (IEP) is roughly pH 3 for the PDMS coated SiO 2 particles, and zeta potential
generally decreases with increasing pH. From equations (1-4) and (1-5), one would expect that
particles in lower pH suspensions (< pH 7) show lower stability ratios. In addition, the deposition
rate during EPD should be higher in the basic region than the acidic region due to increased zeta
potential. It is worth noting that the maximum absolute value of zeta potential measured occurs at
pH 8. Further, zeta potential directly affects the size of particle agglomerates in the suspension.
Figure 2-2b shows the average particle diameter as a function of pH in the suspension after
sonication. As expected, particle agglomerate size decreases with higher absolute value of zeta
potential due to electric double layer repulsion. Particle size at pH 8.3 was larger than pH 8.0,
indicating a slightly reduced stability ratio.
2.3.2.
Optical absorbance and stability ratio
Optical absorbance as a function of time was measured with the suspensions prepared in the zeta
potential and size measurements. Figure 2-3 shows the change of absorbance for each pH. A
moving average filter was used to remove random fluctuations. The window of the moving average
filter was 300 seconds. The absorbance results qualitatively agree with the particle size
measurements since suspensions with larger particle sizes showed steeper absorbance changes in
time. With equation (1-4), this result can be explained by the high absolute zeta potential. High zeta
potential leads to high electrostatic repulsion, (DR, and the net interaction potential, (D, between
54
particles becomes high, resulting in slow agglomeration. The slow agglomeration reduces both the
rate of change of absorbance and the rate of particle coagulation.
0
-
>
E
C-10
-20
0
> -30
2
3
4
5
3
4
5
67
pH
8
9
8
9
3.5
3
2.5
1.5
0.5
$1
pH
6
7
Figure 2-2. Characterization of PDMS coated SiO 2 particles as a function of pH. (a) Average zeta
potential showing the isoelectric point (IEP) at pH 3. (b) Average agglomerate diameter, indicating
smaller agglomerates at high pH. The error bars shown in (a) and (b) represent two-standard
deviations of three measurements.
55
.0
- -pH 3.0
-QpH 4.0
-0-pH 5.0
-V-pH 6.0
,-r-pH 7.0
-0-pH 7.4
CV)
VII
o -10a
I
-5
<-15
215
C
0
-0-pH 7.6
-)-pH 7.9
-V-pH 8.0
,--V
-ApH 8.3
-0.5
-0.75
'
-1.25
2,200
2,500
2,800
2000
Time (sec)
1000
3000
Figure 2-3. Change in suspension optical absorbance as a function of time for ten different pH
suspensions with 0.1g/L PDMS coated SiO 2 particle concentration. The inset shows absorbance
curves for higher pH values (7.4 to 8.3). The low pH curves show fast change of absorbance, which
is attributed to rapid coagulation.
From the absorbance curves, experimental stability ratios were calculated with equation (1-10).
The maximum absorbance slope occurs at pH 4.0, which was used for the numerator (fast
coagulation rate) of equation (1-8). By dividing the maximum absorbance slope by the slope at each
pH, the stability ratio, Wabs, was determined, as shown in Figure 2-4. For comparison, a second
stability ratio based on agglomerate size, Wsize, and calculated using equation (1-11) is given in
Figure 2-4. The measured particle size of 304 nm was used as the initial particle size, Dhj, in
equation (1-8). Both stability curves are in good agreement, as expected from equations (1-8) and
(1-11).
56
16
14 *W bs
.W.
12
size
0 10
422
3
4
5
pH
6
7
8
9
Figure 2-4. Stability ratio as a function of suspension pH. Wabs and Wsize are the absorbance based
and size based stability ratios, respectively, calculated by equations (1-8) and (1-11), respectively.
The measured particle size of 304 nm was used as the initial particle size, D.,, to obtain Wsize with
equation (1-11).
Films consisting of PDMS coated SiO 2 particles were produced by EPD using four suspensions
with pH 7.4, 7.6, 7.9, and 8.3. The pH values were chosen to span a wide range of stability ratios
(c.f.
Figure 2-4 and Figure 2-4). Stable deposition layers were not produced with suspensions
having pH lower than 6.5 due to rapid coagulation and sedimentation during EPD. Since the
stability ratio curve showed a steep slope at around pH 7.5, we expected the effect of stability on
EPD to be most apparent in this pH region. In addition, pH 8.3 was considered due to its unexpected
lower stability value after the maximum stability at pH 8.0 (see Figure 2-4). For EPD, the
suspensions were prepared using the same procedure employed for the zeta potential and stability
tests. However, the concentration of PDMS coated Si0 2 particles was increased to 1 g/L in order to
reduce deposition time. Stability ratios at higher particle concentration (not shown) displayed
similar trends to the 0.1 g/L data shown in Figure 2-4.
57
(a)
170!FC
-- 160~
--
---
'51
CTS
0
150:
- ..pH 7.4, W abs =6
(D)
0D
c 140
.-- pH 7.6, Wa =8
a~H7.9, Wabs =1s
.D-pH 8.3, W
130
()
30
=10
60 90 120 150
Deposition Time (sec)
170rI
I
180
I
-C1- Advancing contact angles
-0- Receding contact angles
165
1 160
30
c02
-
S)155
S150
2
?10
o
145
rot
0
60
120 180
Deposition Time (sec)
30
60
90
120 150
Deposition Time (sec)
180
Figure 2-5. Contact angles on films deposited via EPD. (a) Static contact angle as a function of
deposition time for four suspensions with varying pH. (b) Advancing and receding contact angles
on the surfaces created at suspension pH 7.6. The inset in (b) shows roll-off angles calculated from
the advancing and receding contact angles. The error bars shown in (a) represent two-standard
deviations of twelve measurements at each point. The maximum contact angle was achieved at pH
7.6, corresponding to a stability ratio of
Wabs
= 8 and deposition time of 60 s.
58
2.3.3.
Contact angle
Figure 2-5a shows static contact angle on EPD modified surfaces as a function of deposition time
and suspension pH. Contact angles on the films produced were calculated by the tangential method
with 3 pL water droplets. The maximum contact angles for each pH were 1600 at pH 7.4, 1660 at
pH 7.6, 1610 at pH 7.9, and 1630 at pH 8.3. The highest contact angle was produced with the pH 7.6
suspension after 60 s of EPD. Suspensions with higher stability ratios were unable to obtain higher
contact angles than the pH 7.6 suspension. It is interesting to note that the pH 8.3 suspension
produced higher contact angles than the pH 7.9 suspension. This is further evidence that contact
angle is highly dependent upon suspension stability. Dynamic contact angles were measured on the
films produced with pH 7.6 suspension as a function of deposition time, as shown in Figure 2-5b.
The difference between advancing and receding contact angles is considered a more reliable method
to evaluate superhydrophobicity since water-repellant surfaces can be evaluated strictly by the
contact angle hysteresis rather than static contact angles [101]. The roll-off angle, aR, of water
droplets can be calculated with the equation
aR =sin
{yLv'm 'g 'w-( cos OR - cos OA)}, where m
and w are the mass and width of the droplet, yLvthe surface tension of water, g the gravitational
acceleration, and OA and OR are advancing and receding contact angles, respectively. In the surfaces
prepared with pH 7.6 suspensions, the calculated roll-off angles shown in the inset of Figure 2-5b
were 30, 20, and 70 for 30 s, 60 s, and 90 s deposition times, respectively. Roll off angles less than
100 indicate that the surfaces can be regarded as having superhydrophobicity in terms of both static
and dynamic contact angles.
Surfaces produced with the pH 7.4 suspension showed the highest standard deviation in measured
contact angle over the range of deposition times. This could be explained by the zeta potential and
particle size measurements shown in Figure 2-2, which also displays high variation at pH 7.4. In
59
addition, each suspension has a maximum contact angle as a function of deposition time.
Interestingly, there is an optimal deposition time to acquire maximum contact angle for a specific
suspension pH. The film produced by the pH 7.4 suspension has the slowest increase of contact
angle with deposition time due to its low deposition rate compared to the higher pH suspensions. To
explain the observed optimum deposition time we consider the influence of microscale and
nanoscale features on surface energy. Lee et al. [11] presented the role of microscale and nanoscale
features on wettability. Their work showed that contact angle increases with longer nanofibers but
there was an optimal microstructure length scale to maximize the contact angle. Their observed
results resemble the present study, given that suspension stability and deposition time affect
nanoscale and microscale features, respectively. With EPD, nanoscale surface features are
controlled by suspension stability since the agglomerate particle size (order 100 nm) increases with
decreasing stability, as shown in Figure 2-2b. Meanwhile, the role of the deposition time is shown
in Figure 2-6. Here, EPD surfaces produced with pH 7.9 suspensions are observed as a function
deposition time (30 s to 30 min). Patterns on the substrate grow with deposition time, indicating that
deposition time influences the micro/macro length scales of the surface. A similar phenomenon has
been reported in the EPD process to produce thin and porous alumina membranes [102]. They
found that the 'porosity of deposited films decreased after a specific deposition time. In their
experiments, the pore structures became smaller and denser after a critical deposition time as the
deposition mechanism changed from vertically stacked particles to horizontally organized
structures, resulting in decreased pore size. Porosity and surface roughness are comparable with one
another and we attribute both decreases after a specific deposition time to the increased length scale
of deposits.
60
Figure 2-6. Patterns of EPD films produced by the pH 7.9 suspension with different deposition
times. All images have the same scale bar in the top and most left picture. Deposition features grow
with deposition time, resulting in a decrease in contact angle when deposition time exceeds 60 sec.
2.3.4.
Surface roughness
To reveal the mechanism underlying the varying contact angles, surface roughness of the
deposited films were measured for each pH. Figure 2-7 shows contact angles with respect to surface
roughness for the EPD samples. As shown, contact angle tends to increase with increasing surface
roughness. The relation between contact angles and surface roughness is given by the Cassie
equation [103], cos=ficos9E- fa. The contact angle on a rough surface, 0, is a function of the
native contact angle, OE, of the flat surface, the solid area fraction, fs, and the vapor area fraction, fa,
on the rough surface, respectively. The Cassie model assumes that the droplet is positioned on the
roughened surface without wetting the porous structure. This function can also be expressed as
cos 0= -l + f, (cos OE + 1) since fs + fa = 1 [60]. This means that higher surface roughness leads to
higher contact angle when the contact angle on the flat surface is exceeds 90'. The native contact
angle of PDMS, the material encapsulating the SiO 2 particles, is 100-112' [24], therefore the result
of Figure 2-7 is consistent with Cassie's equation. As expected, the deposition layer created with the
61
pH 7.6 suspension had the highest surface roughness and contact angle, while the pH 7.4 suspension
showed the lowest values. This behavior is qualitatively explained in
Figure 2-8. In the case of pH 7.4, the large coagulated particles prevent the creation of thick films
due to the low electrophoretic force compared to sedimentation, limiting surface roughness. In the
case of pH 7.6, coagulated particles, which are smaller than pH 7.4 agglomerates, are reasonably
well dispersed in the suspension and have sufficient concentration to produce thick layers. Multiple
layers of randomly oriented coagulated particles provide high surface roughness. However, with the
pH 7.9 suspension, the deposition layer results in lower surface roughness than the pH 7.6 case
because smaller coagulates yield a more ordered deposition surface. Though the thickest deposition
layers are achieved with the pH 7.9 suspension, the increased stability leads to reduced surface
180
U
170-
,
.
-
roughness.
pH 7.4, W =6
0 pH 7.6, W =8
A pH 7.9, W=11
1
pH 8.3, W,=101
SV
A
~V
A
B 150C
0
130 1
,
250
.
300
350
.
400
,
140
450
500
Surface Roughness (nm)
Figure 2-7. Contact angle as a function of RMS surface roughness. In surface roughness
measurements, the measured area was 40x40 pm2 and three point values were averaged in each
sample. The contact angle is roughly proportional to the surfaces roughness, as can be expected by
the Cassie mode.
62
To verify the mechanism explained in
Figure 2-8, SEM images were taken of EPD sample surfaces (Figure 2-9). From the SEM images,
we find that the most uniform deposition layer, with full substrate (black area) coverage, is
produced at pH 7.9. At pH lower than 7.9, large islands of deposited particles appear in a random
orientation on the substrate. For example, the pH 7.4 sample in Figure 2-9a showed the largest
coagulated-particles and the least surface coverage.
Unstable
M
Quasistable
+
Stable
4E0Q *Q
_fN_
-,a,<-Q
r*
*QQ<-0
<-Q
<_<-0 0
<-Q*
Flocculated
particles
Irregular thindeposition layer
Flocculated
particles
Irregular thickdeposition layer
Dispersed
particles
Well ordered
deposition layer
Figure 2-8. Qualitative schematic of deposition behavior with respect to suspension stability. In
unstable suspensions, particles flocculate and thick deposition layers cannot be formed due to
sedimentation. In contrast, well dispersed (i.e. stable) particles form uniform films with low surface
roughness. At moderate stability ('quasistable') EPD of particle agglomerates yields high surface
roughness.
2.3.5.
Mechanical durability
A sample superhydrophobic surface produced by EPD with contact angle exceeding 1600 is
shown in Figure 2-10. In most EPD applications, weak adhesion between particles and the substrate
must be addressed in order to obtain robust surfaces. Here, conductive epoxy was used to enhance
63
mechanical durability without degrading the low energy surfaces obtained during EPD of PDMS
modified SiO 2 particles. In other EPD studies, various polymers have been used as binders in order
to enhance adhesion and avoid cracks in the film, resulting in high mechanical stability [79, 104,
105]. However, longer deposition time were required due to the high suspension conductivity
obtained after adding the conductive epoxy [106].
of
(b)
(C)
10pm10n
1~,,p
10S
(d)--
Figure 2-9. SEM images at two different magnifications of deposited films yielding maximum
contact angles at pH 7.4 (a), 7.6 (b), 7.9 (c), and 8.3 (d). As pH increases the film become
increasingly uniform, consistent with the stability measurements of Figure 2-4.
64
Figure 2-1 Oa shows a representative image of a water droplet on the surface of a substrate
modified with EPD, augmented with conductive epoxy. In this case, the average contact angle on
the surface is 1690 and the average RMS surface roughness obtained via AFM is 640 nm (Figure
2-10b). In the SEM images of Figure 2-10c-e, irregular porous structures composed of coagulated
SiO 2 particles were observed, from hundreds of nanometers to tens of micrometers, providing high
surface roughness.
(a)
U1
(b)
Figure 2-10. Characteristics of EPD films with suspensions including conductive epoxy. (a) Image
of liquid water droplet on EPD modified surface with contact angle of 1680. (b) 40x40 Pm2 AFM
image of the deposition surface and SEM images [(c)-(e)] at three magnifications. In (c) Several ten
micron scale features composed of flocculated SiO 2 particles were observed under the SEM. In
image (d), micron scale porous structures are visible on the surface, and (e) shows ten nanometer
scale SiO 2 particles mechanically connected by the epoxy additive.
65
The mechanical stability of two different superhydrophobic surfaces, one with epoxy and one
without, were compared using the peel test [27]. Briefly, in the peel test, the contact angle on a
surface is measured before and after an adhesive tape (in this case 1 x 1 cm 2, 1 N/cm 2, PTFE
adhesive tape, Cole-Parmer) is attached and subsequently removed from the surface. Changes in
contact angle on the two surfaces were measured as a function of the number of peel tests, as shown
Figure 2-11. While the surface produced without epoxy lost its superhydrophobicity after the fourth
peel test, the surface produced with the epoxy maintained its superhydrophobicity after ten
iterations. Clearly, the mechanical stability of the deposition layer was dramatically enhanced with
the addition of conductive epoxy.
-
170
160
150
4,140
<130120
S110100
0-"- EPD without Epoxy
-O- EPD with Epoxy
0
2
4
10
Peel Test Iteration
Figure 2-11. Contact angle on EPD surfaces obtained with epoxy (circles) and without epoxy
(squares), after successive 'peel' tests. The static contact angle produced without epoxy decreases far
faster due to the destruction of the deposition layer after each test. However, the surface obtained
with epoxy maintains its superhydrophobicity after successive peel tests.
66
2.4.
Conclusions
In this study superhydrophobic surfaces were produced by EPD. PDMS modified Si0 2 particles
were used to acquire low surface energy and high surface roughness and increase the apparent
contact angle. Suspension stability was identified as a key factor to control surface roughness and
stability was varied using suspension pH. Two independent techniques were employed to
quantitatively compare suspension stability. For the PDMS modified SiO 2 particles, stability ratio
increases with higher pH, showing steepest increase at around pH 7.5. Four different pH values, 7.4,
7.6, 7.9, and 8.3 were chosen for EPD to compare surface wettability as a function of suspension
stability. The deposited films created with pH 7.6 suspensions and a deposition time of 60 s showed
the highest average surface roughness (500 nm) and the highest average contact angle (1660).
Surface roughness measurements demonstrate that higher surface roughness leads to higher contact
angles, as expected. To explain the results, we suggest that coagulated particle size and mobility are
the main factors affecting wettability. EPD of small coagulated particles in stable suspensions leads
to low surface roughness and low contact angle. On the other hand, the low surface contact angles
produced by unstable suspensions are attributed to sedimentation and low particle mobility,
prohibiting thick deposition layers. We conclude that unstable suspensions with sufficient mobility
to achieve multi-layer coatings are required to produce superhydrophobic surfaces with EPD. In
addition, irregular microscale and nanoscale features on the deposited film increase in size as a
function of deposition time, ultimately decreasing contact angle. With regards to durability,
conductive epoxy was employed to enhance the adhesion between particles and the surface.
Deposition layers with suspensions including conductive epoxy exhibit contact angles over 160*
with significantly improved mechanical stability. As shown, conductive epoxy enhances adhesion
without degrading the surface properties of the PDMS modified Si0 2 particles. However, more
67
investigation is required to clearly elucidate the function of the conductive epoxy. In this work, we
show that by optimizing suspension stability and deposition time, superhydrophobic surfaces can be
produced in a one-step process. Ultimately EPD may be an attractive option for manufacturing
superhydrophobic surfaces due to its low cost and scalability compared to other fabrication
techniques.
68
Chapter 3. Anti-wetting Fabric Coatings
Produced by Electrophoretic
Deposition of Polymer Stabilized
Hydrophobic Nanoparticles
69
3.1.
Introduction
Cost-effective, scalable fabrication methods for anti-wetting fabric are in high demand because
not only can it be used for clothing but also it can replace expensive membranes and filters for
water purification and oil-water separation [107-110]. Furthermore, promising fabrication methods
can be employed for developing other types of functional fabric including anti-microbial, UVabsorbing, fire retardant and conductive [111-118]. Given the numerous potential applications,
many coating techniques have been reported for functionalizing fabric [119, 120]. Among these
methods, the use of nanoparticles has generally been accepted as the most promising because
various types of functionality can be achieved with different nanoparticles [115-118, 121-126].
Furthermore, the use of nanoparticles is effective to maintain the original fabric properties (e.g.
tactility, flexibility, color, and permeability) except the desired properties after coating.
Various coating methods have been investigated to implement nanoparticle-based-coatings for
anti-wetting fabric. Spray coating, bar-coating, and deep-coating are considered simple methods,
but it is challenging to obtain durable and uniform coatings and to control wettability [117, 118,
127-133]. Surface functionalization utilizing chemical vapor deposition, or sol-gel processes have
shown good hydrophobicity but the intrinsic characteristics of the fabric are more likely to be
distorted during processing [134-141]. Recently, electrostatic assembly techniques have been
investigated, demonstrating uniform superhydrophobic fabrics [142-144]. Advantages of this
technique include coating uniformity and precise control of coating thickness. However,
electrostatic assembly is limited by its considerable processing times, increasing manufacturing
costs.
Another challenge in coating nanoparticles is to produce patterned functionalized fabrics. For
example, in the past decade, patterned superhydrophobic surfaces have been widely investigated to
70
enhance the efficiency of harvesting water from fog [145-147]. To maximize the efficiency, the
patterns and wetting properties must be optimized. Conventional micro-fabrication techniques such
as photolithography [146, 148], dewetting polymers [149], selective deposition of chemicals and
polymers [150, 151], spatial photocrosslinking [147, 152], and patterned imprinting [153, 154] have
been employed to produce the patterned superhydrophobic surfaces. However, there have been few
attempts to produce patterned anti-wetting fabrics because these conventional microfabrication
techniques are difficult to apply to soft and permeable materials. Therefore, we need a new
fabrication technique to effectively design the patterns of wetting property on fabric. Furthermore,
the technology for patterned anti-wetting fabric can be utilized for other functional fabrics such as
conductive fabrics with customized electric circuits [116, 155].
In our previous work, superhydrophobic surfaces were produced by electrophoretic deposition
(EPD) with polydimethylsiloxane (PDMS) modified SiO 2 nanoparticles on steel plates [73]. This
method provides fast and customizable deposition of superhydrophobic surface coatings. The
coating thickness can be controlled by the electric field intensity and deposition time. Furthermore,
the morphology on the modified surface can be altered by changing the suspension stability during
EPD [73]. Additionally, the durability was dramatically enhanced by co-deposition of nanoparticles
with polymeric adhesives. EPD has tremendous potential to overcome the drawbacks of existing
methods for coating fabric with nanoparticles. However, to date most EPD processes have been
employed on electrically conductive substrates due to the necessity of electric field lines
perpendicular to the deposition substrate in order to achieve sufficient adhesion [68, 79, 106].
Some studies have explored the possibility for EPD on electrically non-conductive substrates [96,
97]. Among these investigations, ionic conductive films and porous-substrates show deposits after
EPD [156-158]. Fabrics are a promising candidate for EPD because they are permeable to solvents
and can be penetrated by electric fields after swelling. However, weak adhesion, poor deposition
71
quality, and limited control of deposition thickness have been plagued previous attempts due to the
high electric fields employed [159-161]. The high electric fields result in significant irregularity
because concentration polarization near the substrate results in large, weakly adhered nanoparticle
agglomerates on the non-conducting substrate.
In this work, we suggest a hybrid method employing electrostatic deposition and EPD for coating
nanoparticles on fabric. First, using electrostatic deposition, thin polymer-layers are deposited on
fabric and then covered by a uniform dispersion of nanoparticles. Next, EPD is conducted with
polymer stabilized nanoparticle suspensions. The first polymer layer enhances the adhesion between
nanoparticles and the substrate after heat treatment. The initial layer of nanoparticles provides
deposition nucleation sites, preventing aggregation on the substrate during EPD. The suspension is
stable enough to yield uniform deposition on the substrate due to the steric repulsion between
nanoparticles. Our hybrid technique employing electrostatic assembly and EPD results in durable,
uniform nanoparticle deposits on fabric. Furthermore we demonstrate anti-wetting fabrics with
properties (e.g. color, flexibility, permeability) very similar to the initial fabric.
In addition,
hydrophobicity can be spatially altered on fabrics modified by EPD with customized electric fields.
To verify the patterned wetting property, we demonstrate that water droplets can be coalesced in
regular patterns on the fabrics.
3.2.
3.2.1.
Experimental
Preparation of materials and suspensions
In this study we used two types of polyester fabric (Patagonia, Fabric A: brown, 100% polyester,
20 denier in warp and 20 denier in fill direction, and Fabric B: red, 100% polyester texturized fiber
72
without any coating/treatment, 10 CFM in air porous, and plain weave face and twill weave back).
Two kinds of polymers, poly(dimethyl-diammonium chloride) (PDDA) (Aldrich, 30 wt.% solution
in water) and poly(sodium 4-styrenesulfonate) (PSS) (Aldrich, 35 wt.% solution in water), were
used as positively and negatively charged polymers, respectively, for the electrostatic coating
process. Both polymer concentrations were 8 g/L in deionized (DI) water. These two polymers have
been widely used for layer-by-layer techniques because they can be electrically charged in dielectric
solvents, resulting in high electrostatic attractive and repulsive forces.[67, 162] Two kinds of
nanoparticle suspensions were prepared; in the first suspension: PDMS modified SiO 2 nanoparticles
(PlasmaChem, 14 nm) and polyvinylidene fluoride (PVDF, Sigma-Aldrich) are dispersed into a
mixture of methanol (90 vol.%) and water (10 vol.%) with concentrations of lg/L and 0.5 g/L,
respectively; and in the second suspension: PDDA is added to the SiO 2 and PVDF suspension
described above until the PDDA concentration reaches 3.75x 10- g/L. Finally, the pH of both
suspensions is adjusted to 8.5 with a basic solution (Potassium hydroxide, 45 % for HPLC, SigmaAldrich).
73
(a)
Step 1: Electrostatic deposition of polymers
(b)
Cathode
Fabric
Anode
Suspension
Power supply
Step 2: Electrostatic deposition of particles
Step 3: Electrophoretic deposition of
particle-polymer assemblies
1000
Fabric
PDDA
PSS
Step 4: Heat-treatment of the fabric
Particle
PDDA + Particle
Figure 3-1. Schematic illustrations of the fabrication process suggested for anti-wetting fabric
coating. (a) Step 1: multi-layered polymers are electrostatically deposited on the fabric. Step 2:
nanoparticle are electrostatically deposited on the polymer layers of the fabric. Step 3: the polymer
and nanoparticle assemblies are deposited by electrophoretic deposition (EPD). Step 4: heat
treatment is conducted on the fabric for enhancing mechanical durability. (b) The EPD cell for Step
3 in (a). The cell consists of two stainless steel electrodes and a fabric sheet is wrapped around the
cathode electrode.
3.2.2.
Electrophoretic deposition for fabric coating
The fabrication process for anti-wetting fabric consists of four steps, as shown in Figure 3-1. First,
a steel plate (type 316 Stainless steel foil, full hard temper, .004" Thick, 10 cm x 30 cm, Trinity
Brand Industries, Inc.) is wrapped with a sheet of fabric (20 cm x 30 cm). In this step, slightly
curved steel plates make good contact with the fabric by providing a small amount of tension. Next,
74
the steel plate and fabric assembly is immersed into the PSS solution (8 g/L concentration in DI
water) for 1 min and then the fabric is washed with DI water for 10 sec. Afterwards, the assembly is
immersed into the PDDA solution (8 g/L concentration in DI water) for 1 min and then washed with
DI water for 10 sec. These two immersion-washing steps are conducted twice (Step 1). Next, the
fabric-plate assembly is immersed into the nanoparticle suspension (the first suspension) for 5 min
and then washed with DI water for 20 sec (Step 2). For EPD in the second suspension (Step 3), the
fabric-electrode assembly and a similarly sized stainless steel plate are used as the cathode and the
anode, respectively. During EPD, an electric potential difference of 120 V is applied to the
electrodes, which are separated by 20 mm. After EPD, the fabric is dried in the laboratory
atmosphere, and then heat-treated at 150 - 220 'C for 2 min with a heat-press apparatus (Clamshell,
Model PRO-3804X) (Step 4).
Zeta potential of polymers and nanoparticles dispersed in solution were measured by a zeta
potential meter (Zetasizer Nano ZS, Malvem Instruments, Inc.). Two scanning electron microscopes
(SEM, JEOL 6320FV Field-Emission High-resolution SEM and He-Ion microscope, Zeiss) were
used to observe the morphologies of modified fabric surfaces. Static and dynamic contact angles
were measured with a goniometer (Kyowa, DM-CE1) with a 3 pL drop of DI water. Water droplet
behaviors on the fabric were recorded using a digital camera (J2, Nikon). Color changes before/after
coating were evaluated by RGB comparison with an image processing program (Adobe photoshop
CS4 extended). A customized skin friction generator was used for durability tests.
3.3.
3.3.1.
Result and discussion
Suspension Zeta potential
75
Surface charge is necessary for electrostatic self-assembly and electrophoresis, and the amount of
charge is estimated by zeta potential measurements. Figure 3-2 shows the zeta potential of the
suspensions of SiO 2 nanoparticles and polymers used in this work.
(b)
(a) 30
20
10
0
-10
N
(c)
-20
-30
Polymer
@ pH 8.5
Polyester
Zeta potential
-45
PSS
D
-40
2
3
4
O PDDA
PSS
5
6
7
pH
8
<SO 2
9
10
-25
PDDA SiO, SiO,+PDDA PVDF PVDF+PDDA
+20
[my]
11
-PDDA:
Particle suspension
solution
-25
10
-19
24
poly(dimethyl-diammonium chloride), PSS: poly(sodium 4-styrenesulfonate),
SIO2: PDMS modified SiO 2 nanoparticles, PVDF: poly(vinylidene fluoride)
Figure 3-2. Zeta potentials of the polymers and the SiO 2 nanoparticles. (a) Zeta potentials of
poly(sodium 4-styrenesulfonate)
(PSS), poly(dimethyl-diammonium
chloride) (PDDA),
SiO 2
nanoparticles with respect to pH. (b) Digital image of the suspensions of SiO 2 , polyvinylidene
fluoride (PVDF), PDDA, and PSS. (c) The table summarizes the zeta potentials at pH 8.5. The zeta
potential of non-treated polyester fiber was obtained from a reference.[163] The solvent for the SiO 2
nanoparticle and PVDF suspensions is composed of methanol 90 vol. % and water 10 vol. %. The
others are deionized water. The concentrations are 8 g/L PSS and PDDA and 1 g/L SiO 2 and 0.5 g/L
PVDF with and without 3.75x 10~3, g/L PDDA polymers. The error bars indicate
one standard
deviation from three measurements.
The zeta potentials of poly(sodium 4-styrenesulfonate) (PSS) and poly(dimethyl-diammonium
chloride) (PDDA) solutions (8 g/L for each) are -25 mV and +20 mV at pH 8.5, respectively. The
zeta potentials of SiO 2 nanoparticles, dispersed in the water (10 vol. %) and methanol (90 vol. %)
mixtures, were -25 mV without PDDA polymers and +10 mV with 3.75x 10-3 g/L concentration of
PDDA polymers. The sign change of the zeta potential of SiO 2 nanoparticles indicates the formation
76
of SiO2-PDDA assemblies, as shown in Figure 3-1. As a reference, the polyester fibers have a zetapotential of -45 mV at pH 8.5 in water, and the isoelectric point (IEP) is pH 2.3 [163].
Based on the zeta potentials measured, the fabrication process, as shown in Figure 3-1, is
suggested. The PDDA polymers naturally deposit on the polyester fabric due to electrostatic
attraction because the polyester fiber and PDDA have opposite surface charge. Then, PDDA and
PSS layers can be produced by alternating immersions of each polymer solution due to their
opposite surface charge. Next, immersing the polyester fabric pre-treated by PDDA and PSS into a
suspension with 1.0 g/L SiO 2 and 0.5 g/L polyvinylidene fluoride (PVDF) leads to self-assembly of
the nanoparticles on the PDDA. Finally, on the SiO 2 -PVDF layer, PVDF-PDDA-SiO 2 assemblies
are uniformly deposited by EPD with the suspension composed of 1.0 g/L SiO 2 , 0.5 g/L PVDF, and
3.75x10 3 g/L. The use of EPD leads to rapid fabrication, much faster than the multiple immersions
required for thick electrostatic assemblies. To enhance mechanical durability of the modified fabrics,
annealing processes are conducted at temperatures slightly lower than the melting points of the
polymers after EPD.
3.3.2.
Wettability of coated fabric
Through the fabrication process shown in Figure 3-1, we produced anti-wetting fabric coated by
hydrophobic SiO 2 nanoparticles, as shown in Figure 3-3a. Even though the original fabric instantly
absorbed water droplets (Figure 3-3b), droplets on the modified fabric show static contact angles
higher than 1500 and roll-off angles less than 20 when EPD was conducted for 90 sec. The modified
fabric is still flexible with minimal color change (Figure 3-3a and c). This method results in uniform
anti-wetting performance on the entire area modified. The modified surface area is entirely
77
dependent on the electrode size and the electrolyte volume during EPD. Therefore, the fabrication
method is easily scalable to large areas of fabric.
t=0
t=l10me
t=340ms
t=8l0ms
Figure 3-3. Images of water droplets on polyester fabrics modified by the fabrication process
shown in Figure 3-1. Two different fabrics, which color red and yellow, were used to produce antiwetting fabrics. Electrophoretic deposition was conducted for 90 sec in Step 3. (a) The modified
fabric does not lose its original color but the droplets show high contact angles and low roll-off
angles. Flexibility of the original fabric is maintained after modification while wettability changes
dramatically from hydrophilic to superhydrophobic. (b) A water droplet is rapidly absorbed into the
original polyester fabric. The scale bars indicate 1 mm. (c) The brown fabrics do not show
significant difference in their colors before and after the modification. Water droplets show contact
angles higher than 1500 and roll-off angles lower than 5*.
The fabric wettability can be altered by the duration of EPD. Static contact angle and roll-off
angle were measured on the fabric produced as a function of deposition time during EPD (Figure
3-4). The contact angle of water droplets on the fabric before EPD (time is zero in Figure 3-4) was
approximately 1300. This shows that the electrostatic assembly was not sufficient to achieve a
superhydrophobic surface due to inadequate surface coverage (the inset of Figure 3-5a). After EPD,
the static contact angles were significantly enhanced and low contact angle hysteresis was achieved.
With increasing EPD time, the static contact angle increased and the roll-off angle decreases. The
maximum static contact angle and minimum roll-off angle were achieved at 90 sec deposition time.
78
A similar relationship between the contact angle and deposition time was found in our previous
work on steel plates [73].
170
140
120
-
160
100
4)0
150
80-O8
08
OContact angle
oRoll-off angle
ts140
04
130
60
740
5
20
120
0
,0
30 60
90 120 150 180 210 240
Time (sec)
Figure 3-4. Static contact angle and roll-off angle of fabric produced with different deposition times
for EPD. Contact angles were measured after heat treatment. Water droplets instantly absorbed into
the original fabric resulting in and effective static contact angle of zero degrees. The static contact
angle is 1360 on the fabric coated with polymer and thin layers of hydrophobic SiO 2 nanoparticles
(after Step 2). Static contact angle is dramatically enhanced after EPD process (after Steps 4). The
maximum contact angle of 1590 and the minimum roll-off angle of 2' are achieved at 90 sec
deposition time. The error bars indicate
3.3.3.
one standard deviation from five measurements.
Scanning Electron Microscopy
The morphology of the modified fabric was investigated using SEM images, as shown in Figure
3-5. The original fabric has a twill wave pattern composed of 15 micron polyester fibers (Figure
3-5a). After Step 2 in Figure 3-1, Si0 2 nanoparticles are uniformly deposited on the fabric (the inset
of Figure 3-5a). The coatings on the fabric become thicker with increasing duration of EPD (Figure
79
3-5b-c) after Step 3. The SiO 2 particles are partially deposited on the fibers after 30 sec of EPD
(Figure 3-5b) but fully covered after 60 sec of EPD (Figure 3-5c-).
Figure 3-5. SEM images of fabrics produced by electrophoretic deposition (EPD) with different
deposition times. (a) Original polyester fabric has twill weave patterns. The inset shows a fabric
fiber with SiO 2 nanoparticles deposited on the surface (after Step 2 in Figure 3-1). (b) After 30 sec
of EPD, SiO 2 nanoparticle layers are observed on the fabric but do not fully cover the surface. (c)
After 60 sec of EPD, the fabric fibers are uniformly and densely coated with SiO 2 nanoparticles.
This surface exhibits the maximum contact angle of 1570 and minimum roll-off angle less than 5*.
3.3.4.
Color change test
Colorfast tests were conducted by comparing the RGB values of the coated fabric with respect to
the duration of EPD, as shown in Figure 3-6. The relative RGB values (R*, G*, and B*) were the
ratios of the RGB values at a specific EPD time to the original fabric. It is known that thin SiO 2
nanoparticle layers, uniformly deposited, are highly transparent [14, 27, 55]. For instance, Cebeci et
al. showed that transparent superhydrophilic glass can be achieved using thin layers of SiO 2
nanoparticles [55]. The colors do not change significantly even after the static contact angle with
80
water reaches 1500 (Figure 3-6a-b). It is worth to noting that dense SiO 2 nanoparticle coatings
deposit on polyester fibers, which are not electrically conductive, with the help of the Si0 2
nanoparticles and polymer film coated prior to EPD. Without the pre-treatment processes large,
irregularly spaced particle aggregates are deposited rather than uniform thin films, as shown in
Figure 3-6d. When the polymerically stabilized SiO 2 suspension was not used, the fabric color
changed significantly after EPD (Figure 3-6e).
(a)
aOR* +G*
4
+B*
(b)
0
Q3
33
EPD time (sec)
30
60
90
120
150
180
210
00
30
60 90 120 150 180 210
EPD time (sec)
Figure 3-6. Color difference tests using RGB comparison and real images of the modified fabrics.
(a) R*, G*, and B*, which are the relative RGB values to the original fabric, with respect to
deposition time in electrophoretic deposition (EPD). The error bars indicate
one standard
deviation from five measurements. (b) RGB values are obtained by using image software (Adobe
Photoshop CS4) with captured images of fabric produced with varying EPD time. (c)-(e) Captured
images of fabrics produced with three different fabrication processes and with the same EPD time
of 90 sec: (c) Fabric produced with Steps 1-4 in Figure 3-1, (d) Fabric produced without Steps 1-2.
(e) Fabric without polymeric stabilization of the particles in Step 3.
3.3.5.
Air permeability testing
81
To evaluate the breathability of the anti-wetting fabric, water vapor transmission (WVT) rates
were measured according to the standard method for water vapor transmission of materials (ASTM
E 96, Procedure B, 1999) [164]. The WVT rate can be calculated as WVT = AM/(A -t), where AM is
the weight change of liquid water, A is the fabric surface area, and t is the time elapsed to obtain
AM. We filled 80 ml of liquid water into 100 ml media bottles and capped the bottles with vented
caps sealed with fabric having 9.1 x 10- m 2 test-area. The WVT rates were measured every 5 hours
and the average WVT rates were calculated from five measurements at a specific water temperature.
The water temperature was controlled from 35 'C to 65 "C at intervals of 10 'C. The test
environmental conditions were 24
1 'C and 30
5 % relative humidity with negligible air flow on
the fabric during testing. Interestingly, slightly higher WVT rates were obtained from the antiwetting fabric than the original fabric across the entire temperature range. The difference becomes
greater at higher temperatures, as shown in Figure 3-7. At the least we can say that the coating does
not reduce breathability but the data suggests it may be enhanced. We hypothesize that the
hydrophobic nanoparticles can prevent condensation, enhancing direct vapor transport through
voids of the fabric.
82
1.6
1.4
-
E
OOriginal fabric
OAnti-wetting fabric
1.2
1.0
0.8
0.6
0.4
0.2
0.0*.............................
30
40
50
60
Water temperature (*C)
70
Figure 3-7. Water vapor transmission (WVT) rate tests for the original fabric (box symbols) and the
anti-wetting fabric (circle symbols). The anti-wetting fabric was produced with 90 sec of EPD at
120 V. The WVT rate experiments were conducted with water temperatures ranging from 35 *C to
65 'C. The error bars indicate
3.3.6.
one standard deviation from four measurements.
Coating durability
Durability of the fabric coatings was evaluated by a skin friction resistance test using boundary
layer flow. A circulating pump continuously generated water flows at 10 m/s on the anti-wetting
fabric attached to a steel plate. The flow speed was chosen to imitate the environment on the surface
of a ship, which is stressed from water friction during operation. We measured the static contact
angle with respect to test time on the fabric. The fabric was fully dried on a hot plate at 50 'C and
cooled down to the environment temperature before the measurement. Figure 3-8 shows the change
of the contact angle on the anti-wetting fabric during the test. The fabric maintained contact angles
higher than 1100 over 100 hours. Even though the static contact angle decreased, the coatings were
83
not completely eroded. Future work will involve further enhancements to the fabrication process in
order to maintain superhydrophobicity in harsh environments.
180
160
140
0)M
~~O'--
120
100
80
0
60
40
20
t =0
t=35hr
t=70hr
t=100hr
0
0
20
40
60
80
100
120
Test time (hr)
Figure 3-8. Contact angles on the anti-wetting fabric with respect to test time. The durability test
was conducted with a customized skin friction generator. The skin friction was induced by
boundary layers on the fabric with flows circulated by a water pump. The flow speed was 10 m/s.
The contact angles were measured after the fabric was fully dried on a hot plate. Each data point is
the average contact angle. The error bars indicate
3.3.7.
one standard deviation from five measurements.
Patterned anti-wetting fabric
One advantage of utilizing EPD for fabric coatings is the ability to produce patterned surfaces.
We demonstrate this by producing patterned anti-wetting surfaces using honeycomb-shaped
electrodes (Figure 3-9a). As shown in Figure 3-3, the fabric wettability can vary with the duration
of EPD. In addition, the electric field during EPD can be utilized to control wettability [73]. When
84
shaped electrodes are used, the electric field on the fabric varies spatially. The weakest electric
fields are induced at the center of the holes while the highest electric field occurs at the steel
features. The sample fabric coated using the shaped electrode is shown in Figure 3-6a. Even though,
the fabric has non-uniform deposits on its surface, there is no discernable color difference on the
surface. To test the locally varying wettability, water was sprayed on the fabric at a speed of 0.6
ml/cm 2 -min. The water spray results in droplets growing with time as they merge with the spray
droplets .(Figure 3-6b-c). Interestingly, the growing droplets have regular patterns similar to the
patterns of the electrode holes (Figure 3-9c). This result shows that designing the electric field using
customized electrodes can be used to alter the fabric wettability. This allows us to control fabric
characteristics with respect to location as well as deposition time. In nature, one can observe regular
distribution of dew drops on leaves, as shown in the inset of Figure 3-9e. The uniform patterns
prevent the mass concentration caused by large drops and the subsequent deflection of the surface.
This same feature can be obtained on the anti-wetting surfaces with regularly patterned wettability.
85
Figure 3-9. Patterned anti-wetting fabric using a patterned electrode. (a) An electrode with
honeycomb shaped holes (left) was used to coat hydrophobic nanoparticles on polyester fabric
(right). The fabric coated by the patterned electrode does not show significant color difference
relative to the original fabric. (b)-(e) Water was continuously sprayed on two different fabrics,
which are uniform anti-wetting fabric and patterned anti-wetting fabric, and the resulting droplets
on the surfaces were imaged with respect to time. (a) Droplets grow irregularly on the uniform antiwetting fabric. (c) Droplets grow with regular patterns and ultimately show similar patterns as the
electrode. (d) The pattern of coalescent droplets on the patterned anti-wetting fabric is similar to the
dew drops on green Oregon grape leaves shown in the inset of (e) - Copyright and photography by
Brent Vanfossen.
3.4.
Conclusions
We have presented a novel method employing electrophoretic deposition to create anti-wetting
polyester fabric. Advantages of this method include of scalability, durability, and control of
wettability, showing great potential for commercial use. These features have been achieved by a
hybrid method employing electrostatic assembly and electrophoretic deposition for coating three
86
different constituents (polymers, nanoparticles, and polymeric nanoparticles) on fabric surfaces. The
first polymer layer and the second nanoparticle layer are electrostatically deposited on the fabric
surface. The first polymer layer provides strong mechanical networks between the fabric and the
polymeric nanoparticles after heat treatment. The second nanoparticle layer provides nucleation
sites for the subsequent EPD. The polymeric nanoparticles show low zeta potential but they were
highly stable in the suspension because of steric repulsion between particles. As a result, this
method simultaneously provides both advantages of EPD and electrostatic deposition: it is fast,
cost-effective, and scalable as well as precisely controllable.
Water droplets on the modified polyester fabrics show static contact angles exceeding 1500 and
contact angle hysteresis less than 20. SEM images of the fabric show uniformly and densely
deposited nanoparticles on the polyester fibers. An optimal EPD time of 90 sec was shown to
produce highly anti-wetting fabric without significant color distortion. The anti-wetting fabric
maintained its hydrophobicity over 100 hours during an aggressive skin friction resistance test.
Furthermore, fabric wettability of can be controlled by EPD time and electrode geometry.
We expect that this method can be directly employed to develop commercial functionalized fabric.
Large areas can be modified by our method in a time and cost effective manner. In addition, the
resultant fabric has sufficient durability for practical applications, but more work must be conducted
for more aggressive applications. Perhaps the most unique advantage of this method is that patterns
of wettability can be implemented using varying electrode geometries. Considering these
advantages, we believe that this method can be widely utilized to functionalize fabric with
nanoparticles for various purposes.
87
88
Chapter 4. A Hybrid Method Employing
Breakdown Anodization and
Electrophoretic Deposition for
Superhydrophilic Surfaces
Reproduced in part with permission from
Young Soo Joung, Cullen R. Buie, "A Hybrid Method Employing Breakdown Anodization and
Electrophoretic Deposition for Superhydrophilic Surfaces," Journalof Physical Chemistry B, 2013,
117 (6), pp. 1714-1723.
Copyright 2013 American Chemical Society.
89
4.1.
Introduction
In this work, we suggest a novel fabrication method to produce superhydrophilic surfaces with
high capillary pressure and fast spreading speed. We show that the method can be utilized to control
capillary pressure and spreading speed independently. EPD is utilized to obtain nano-structures
composed of TiO 2 nanoparticles, while breakdown anodization method (BDA) was employed to
produce micro-porous structures. During anodization, the oxidization film thickness linearly
increases with respect to electric potential [75]. However, when the electric potential is higher than
a critical value, the film thickness abruptly increases, resulting in a number of micro-scale
irregularities. The critical electric potential is called the breakdown point. At electric potentials
exceeding the breakdown point, micro-scale porous structures are created on the electrode. This
phenomenon was reported a few decades ago but has not been exploited to produce
superhydrophilic surfaces [76, 77]. Similar breakdown anodization methods have been used to
produce nano-scale titanium structures such as nanotubes and nanowires on titanium substrates
[165-171]. These methods have typically used strong etchants in the electrolytes to locally etch the
titanium substrate at the breakdown locations. The final nano-structures result from the balance
between the etching rate and the oxidation rate. However, in our method, only mildly acidic
electrolytes were used to make micro-scale titanium porous structures. This forces the need for
higher electric potentials to initiate breakdown behavior. In addition, a balance between the
dissolution rate of the oxide layer and the oxidation rate control the resulting structures because
weak electrolytes do not locally etch the titanium substrate.
EPD and BDA offer independent control of nano-scale and micro-scale features, respectively,
resulting in a wide variety of superhydrophilic surfaces. We characterize these surfaces in terms of
capillary pressure and spreading speed using CRM. The roles of nanopores (nano-scale spaces
90
created by the nanoparticles and micropores (micro-scale spaces existing between micro structures)
are investigated to understand the mechanisms governing capillary transport. Further, we
demonstrate specially tailored superhydrophilic surfaces with spatially varying pore radii which
result in unconventional capillary flows.
4.2.
Theory
Capillary flows can be characterized by Washburn's equation. Following this equation, the square
of capillary height is linear with rising time. From this relation, two characteristic parameters,
capillary pressure and spreading speed constant, can be semi-empirically obtained. These
parameters can be utilized to characterize superhydrophilic surfaces. EPD and BDA can be used to
produce superhydrophilic surfaces with various capillary pressures and spreading speed constants.
In EPD, suspension stability is important to control nano-scale structures [73]. In BDA, micro-scale
porous structures are created on anode electrodes when the anodization electric potential is higher
than a critical value. The following sections outline the theoretical considerations necessary to
control transport in surfaces produced with BDA and EPD.
4.2.1.
Capillary flow
If the capillary forces exceed the gravitational force, the wetting line can rise. Washburn's
equation has been widely used to predict the speed of capillary rise and can be expressed by [172]
91
-= r-2 F2YCOS9pgh1,
dt8iyh
r
(4-1)
where h is the height of the wetting line; t is the time after contact between with liquid; r is the pore
radius; qy, y, and p are the dynamic viscosity, surface tension, and density of liquid, respectively; 9
is the native contact angle of surface material; and g is the gravitational constant.
If the effect of gravity is negligible and the pore radius is constant, the relation between the
capillary rise height and time can be expressed by
h2rcos
2t7
I
2
(4-2)
where Dcap is hydraulic diffusivity. From CRM, the change of capillary height with respect to time
can be obtained and hydraulic diffusivity can be calculated by curve fitting.
Capillary pressure can be calculated from the maximum capillary height since at this condition
the capillary force balances the gravitational force, assuming liquid evaporation is negligible. Thus,
the capillary pressure can be expressed by
P
r
H
(4-3)
where H,,x is the maximum capillary height. From equations (4-2) and (4-3), we can semiempirically calculate the capillary pore size, r, and the contact angle, 0, as follows
92
r
21C.
=
and
Pca,
jD
2y 2
Pca
f(4
(4-4)
If the pore radius is not constant but a function of h, we can obtain various profiles of contact line
propagation.
4.2.2.
Electrophoretic deposition
The electrophoretic mobility, p, is linearly proportional to the zeta-potential,
C,
and the
permittivity, c, of the medium, and is inversely proportional to the viscosity of the medium, 17, as
expressed by [78]
2c4-
(4-5)
317
assuming spherical particles where the Debye length is small relative to the particle radius.
During EPD, the deposition rate, A, is a function of the mobility, the particle concentration, C,
and the electric field, E, subjected to the electrodes as follows
M=p-C-E
(4-6)
Thus, if the concentration and the electric field are fixed during the EPD process, the deposited
mass can be altered by the deposition time.
93
4.3.
4.3.1.
Experimental
Suspension and electrolyte preparation
EPD and BDA were used to produce superhydrophilic surfaces. By combining both methods, we
were able to make three different types of superhydrophilic surfaces; EPD only, BDA only, and a
hybrid BDA/EPD method. Schematic illustrations of BDA and EPD are shown in Figure 4-la and
Figure 4-lb, respectively. For EPD, TiO 2 nanoparticles (Sigma-Aldrich, titanium oxide, anatase,
nanopowder, < 25 nm particle size, ;> 99.7% purity) were used. Acetic acid was used as solvent to
prepare 1 g/L concentrations of TiO 2 suspensions. Titanium plates (Ultra-Corrosion-Resistant
Titanium Grade 2, 0.020" thick) were used as anode and cathode electrodes. An electric potential of
-
30 V was subjected to the electrodes (the gap distance between the electrodes was 10 mm) for 30
120 sec to deposit thin films on the substrate. During BDA, the DI water was adjusted to pH 3 by
adding acid (Nitric acid, 70 % ACS reagent, Sigma-Aldrich). Two titanium plates (same material
used for EPD) were used as cathode and anode electrodes (the gap distance between electrodes was
10 mm), and electric potentials were supplied in the range of 30 - 120 V for 30 min.
During BDA, the electrolyte temperatures were maintained at 10 - 75 'C because breakdown
initiation is affected by electrolyte temperature, as shown in equation (1-22). Furthermore, it has
been reported that electrolyte temperature affects the resulting electrode morphology [76, 173].
Therefore, the temperatures were adjusted using a circulating bath (polystate, Cole-Parmer) in order
to investigate the effect of electrolyte temperature on wetting properties. Throughout BDA
experiments the electrolyte was rigorously stirred with a magnetic bar.
94
To produce nano- and micro- scale hierarchical structures on the titanium substrates, we used a
hybrid BDA/EPD method. In this method, BDA was conducted first and then the anodized
electrode was re-used as the substrate for EPD. The EPD process in the hybrid method was
conducted with the same operating conditions as the surfaces modified solely by EPD.
(a)
DCPower Supply
SDC
Power Supply
Electrodes
Nanoparticle
Magnetic bars
Solvent
Water bath
Acidic
electrolyte
[00
Stirrer
1
Stirrer
Figure 4-1. Schematic illustration of the experimental setups for breakdown anodization (BDA) (a),
and electrophoretic deposition (EPD) (b). The water temperature is controlled to maintain constant
electrolyte conditions during BDA. TiO 2 nanoparticles are dispersed in acetic acid solvents with 1
wt% concentration for EPD. The solvents of both methods are stirred with magnetic bars.
4.3.2.
Capillary rise measurement (CRM)
CRMs were performed to evaluate the capillary pressure and the spreading speed of the
superhydrophilic surfaces. Figure 4-2 shows a schematic illustration of the CRM setup. During
CRM the sample is enclosed in a glass column to prevent evaporation from the surface during the
test. The sample is fixed vertically and the height of water bath is gradually increased to make
contact between the bottom of the sample and the water surface. Capillary rise through the substrate
95
is recorded with a digital camera (Canon, PowerShot S90). A ruler fixed adjacent to the substrate is
used to estimate the capillary rise height with respect to time.
Sample
Ruler
Watr bath
Stage
Figure 4-2. Schematic illustration of the capillary rise measurement (CRM) system. Capillary
height is recorded by a digital camera and estimated with customized image processing software
(Labview). Evaporation from the sample surface is prevented by encapsulating the sample in a glass
column.
4.3.3.
Characterization
Morphologies of the deposited films were characterized with a scanning electron microscope
(SEM, JEOL 6320FV Field-Emission High-resolution SEM). Static contact angles (CA) were
calculated using the tangential curvefitting method. A goniometer (Kyowa, DM-CE1) was used to
dispense and image a 3 uL drop of DI water on each sample. X-ray diffraction (XRD) data were
collected from the PANalytical X'Pert Pro Multipurpose Diffractometer with Cu anode material at
96
45 kW and 40 mA to investigate the material composition and atomic structure of the resulting
surfaces. The step size and the scan step time are 29= 0.0 17 and 42.55 sec, respectively.
4.4.
4.4.1.
Results and discussion
Surface morphology
Figure 4-3 shows SEM images of the fabricated surface structures under different magnifications.
Highly irregular and entangled microstructures appear on the titanium electrode after BDA in
Figure 4-3a-c. In the samples prepared by EPD with a 30 sec deposition time, well ordered TiO 2
nanoparticles were observed, as shown in Figure 4-3d-f. Hierarchical structures, as shown in Figure
4-3g-i, were observed in the case of the hybrid BDA/EPD method. Here the micro structures were
highly curved and entangled while TiO 2 nanoparticles were well dispersed on the surface. This
suggests that the anodized surfaces do not completely lose their electrical conductivity.
Static contact angles were measured on each of the modified substrates. Each surface exhibited
contact angles near zero degrees. Therefore, following the classical definition of superhydrophilic
surfaces [60], the three fabrication processes resulted in superhydrophilicity. However, the time
required to achieve zero contact angle differed amongst the samples. This reveals that the samples
in fact have differing wettability, which is not evident from static contact angle measurements.
97
Figure 4-3. SEM images of superhydrophilic surfaces fabricated by breakdown anodization (BDA)
(a)-(c), electrophoretic deposition (EPD) (d)-(f), and the hybrid BDA/EPD method (g)-(i). BDA was
conducted at the electric potential 90 V for 30 min with an acidic electrolyte (pH 3) at 10 'C. EPD
was conducted with the electric potential 30 V for 90 sec with I wt.% TiO 2 in an acetic acid solvent
at ambient temperature. The surface produced by BDA consists of several entangled micro-porous
structures while the surface deposited with TiO 2 nanoparticles by EPD shows uniformly distributed
nano-porous structures. The hybrid BDA/EPD method yields hierarchical micro- and nano- porous
structures.
98
4.4.2.
Capillary pressure and hydraulic diffusivity
To further evaluate the superhydrophilic surfaces, spreading speed and capillary pressure were
measured with CRM, as shown in Figure 4-2. As can be expected from equation (4-2), the square of
capillary rise height is linearly proportional to time (Figure 4-4a). The slope of each linear fit line
represents hydraulic diffusivity, %2 Dcap. Capillary pressures were calculated from equation (4-3)
using the maximum capillary rise height of each surface. The surfaces produced by BDA show
higher capillary pressure and spreading speed constant than the surfaces produced by EPD. This is
attributed to the pore sizes of each surface. The BDA surfaces have micro-scale pores as shown in
Figure 4-3a-c, while the EPD surfaces are composed of nano-scale pores as shown in Figure 4-3d-f.
From equation (4-2), hydraulic diffusivity is linearly proportional to the effective pore radius.
Therefore, it is reasonable to expect the BDA surfaces to show higher spreading speed constants
than the EPD surfaces. However, unlike hydraulic diffusivity, capillary pressure is inversely
proportional to the pore radius. Viscous drag through smaller pores reduces capillary speed at low
heights. For time scales on the order of days, the capillary rise height of the EPD surfaces can be
considered as quasi-static. Therefore, the EPD surfaces have lower effective capillary pressures than
the BDA surfaces even though the pore size is significantly smaller. Interestingly, the surfaces
produced by the hybrid BDA/EPD method maintained both high capillary pressure and spreading
speed constant. From this result, we conclude that the overall transport characteristics are governed
by micro-scale structures and only locally influenced by the nano-scale structures.
99
40
0
O
A
0
BDA: 120 V
BDA: 90 V
BDA: 60 V
BDA: 30 V
*BDA: 120 V + EPD
35
30
25
E20
E20
-
(a)
00
%%0 15
---
10
-A
--
1---
-5
0
5
10
15
20
25
30
35
40
Time (sec)
(b)
BDA: 120 V
BDA: 90 V
BDA: 60 V
BDA: 30 V
BDA: 120 V+ EPD
EPD
H,,, (cm)
P,8 p (kPa)
D,.p (mm 2 /s)
16.1
14.2
9.2
7.2
13.4
1.2
1.6
1.4
0.9
0.7
1.3
0.12
145
118
47
38
79
6.6
Figure 4-4. Square of experimentally derived capillary rise height is linearly proportional to time,
as predicted by Washburn's equation (a). The samples produced by BDA and EPD show different
capillary pressures and spreading speeds (b). The sample produced by the hybrid BDA/EPD method
shows slightly lower spreading speed than the sample produced by BDA at the same conditions. In
BDA, electrolyte temperatures were maintained at 10 'C and electric potentials were supplied for 30
min. EPD was conducted at the electric potential 30 V for 90 sec. Hydraulic diffusivity, Dcap, of the
surface can be obtained from the slope of each curve as shown in equation (4-2). The capillary
pressure is calculated from equation (4-3) using the maximum rise height.
Different electric potentials and electrolyte temperatures during BDA were investigated to control
wettability and capillary transport properties. Capillary pressure and spreading speed constant with
respect to electric potentials and electrolyte temperatures are shown in Figure 4-5a-b. Interestingly,
for a given temperature the electric potential to achieve the maximum capillary pressure was not
always consistent with the value to obtain the maximum spreading speed. This highlights why both
100
the capillary pressure and the spreading speed are necessary to evaluate and optimize
superhydrophilic surfaces. For electrolyte temperatures less than 50 'C, the capillary pressure and
hydraulic diffusivity increased with increasing of electric potential. However, all surfaces showed
similar capillary pressure and spreading speed at electrolyte temperatures greater than 50 'C (Figure
4-5). This behavior can be explained from the mechanisms of breakdown initiation and oxide layer
dissolution. The electric potential to initiate breakdown is inversely proportional to the electrolyte
temperature, as shown in equation (1-22). Therefore, high electrolyte temperatures are favorable for
BDA at low electric potential. In contrast, because the dissolution rate of the oxide layer is
low electrolyte
proportional to the electrolyte temperature as shown in equation (1-23),
temperatures promote thick and rough surfaces at high electric potential. At electrolyte temperatures
exceeding 50 *C, both capillary pressure and spreading speed constant decrease due to significant
dissolution of the oxide film into the electrolyte.
(a)
(b)
2.0
1.8
1.6
-*-30 V
--
1.4
1.2
rk
oV
120V
160
140
-0-30 V
120
90V
- A -120V
a)
1.0
EA
0.8
0.6
0.4
0.2
E
0.0
10
20
I
30
I
40
I
50
60
60Q
40
20
0
I0
70
Temperature (C)
.
-*
10
20
30
40
*
50
I ....
60 70
Temperature (*C)
Figure 4-5. Changes in capillary pressure (a) and spreading speed constant (b) with respect to
electric potential and electrolyte temperature during BDA. Four different electric potentials (30 V,
60 V, 90 V, and 120 V) and four different electrolyte temperatures (10 'C, 25 *C, 50 'C, and 75 'C)
were used to obtain the surfaces. The error bars indicate
four measurements.
101
one standard deviation resulting from
Figure 4-6. Sample SEM images of surfaces produced by BDA. At low electrolyte temperature and
low electric potential (a), initiation of BDA is not facile; therefore, partially burst structures are
observed on the surface produced at 30 V and 10 'C. When the electrolyte temperature was
maintained at 75 'C during BDA, the highly interconnected porous structures shown in Figure 4-3ac dissolve in the electrolyte, leaving smooth surfaces with large pores (b).
This theory is supported by SEM images of the surfaces at different electrolyte temperatures. The
surfaces produced at an electrolyte temperature of 10 *C and electric potential of 30 V do not have
porous structures, as shown in Figure 4-6a. Instead they feature small cracks that could not develop
into pores. This suggests that high electric potentials are necessary to initiate BDA at low
electrolyte temperatures. Conversely, the surfaces produced at high electrolyte temperatures show
large porous structures, as shown in Figure 4-6b. This SEM image further suggests that dissolution
at high electrolyte temperatures facilitates pore formation. The final weight of each substrate after
BDA is further evidence of the influence of dissolutions. When the electrolyte temperatures were
lower than 50 *C the weight of the substrate increased due to oxidation. However, for temperatures
exceeding 50 'C the substrate weight decreased due to the influence of dissolution. The relative
amount of dissolution can be qualitatively measured by the amount of sediment in the electrolyte
after the BDA processes. The sediments result from oxidized titanium through the dissolution
process (equation (1-16)) and are the same color as the porous oxide titanium structures shown in
Figure 4-3a-c. As the electrolyte temperature increases, more sediment is observed.
102
4.4.3.
Relationship between wetting properties and surface
structure
To understand the role of nano-porous structures on capillary transport, TiO 2 nanoparticles were
deposited on both bare titanium substrates and micro-porous surfaces by EPD. The capillary
pressure and spreading speed were significantly affected by the deposition time (Figure 4-7). On the
bare titanium substrate, the capillary pressure was linearly proportional to the deposition time while
the spreading speed decreased for deposition times longer than 90 sec. To explain this result, the
porosities were obtained from the deposition weights and the deposition heights. The porosity of the
EPD surface can be estimated by.
Porosity =1
Deposition weight
Deposition volume x TiO 2 density
The density of TiO 2 nanoparticles is 3.9 g/cm 3 (Sigma-Aldrich, titanium oxide, anatase,
nanopowder, < 25 nm particle size, ;> 99.7% purity). The deposition weight increases with EPD
time, as shown in Figure 4-7c (red-circles). The deposition volumes were calculated with the
average deposition-heights measured using a profilometer (Measurement system: Tencor P-16
Surface Profilometer (TM)). The average deposition-height increases with the EPD time (blackboxes in Figure 4-7c). The porosity calculated by equation (4-7) shows a minimum at the deposition
time of 90 sec (blue-diamonds in Figure 4-7c). It is clear that hydraulic diffusivity is inversely
proportional to the porosity and the capillary pressure is proportional to the deposition height. A
similar result, namely increasing spreading speed with deposition thickness, was also observed in
Cebeci et al. [55].
103
(a)
0.150.14-
-10
-*-PCW
-8
0.13'
-6
0.12-
-4 E
S0.11CL0.10-
-2 0
0.09-
P
1%
-
0.08 - - - - - - - - - - - - - - - - - - - 2 340
100
60
80
Time (sec)
(b)
0.920.88-
120
PCap/F Cap
D ID
COP Cap
0.84
od 0.80
%0.76
0.72
----------
20
35
30
25
60
80
Time (sec)
160
120
00
r%^
+0-Weight
-85
Height
-0-
-
.80
SPoroty
20
-75
15
-70
10
ES
.
(c)
40
-65&
25
-60
40
60
80T16m
Time (sec)
120
Figure 4-7. Capillary rise measurements of surfaces modified by EPD. EPD processes was
conducted on bare titanium substrates (a) and on surfaces augmented by BDA (b). PCaIP*cap and
Dcap/D*cap are the ratios of capillary pressure and spreading speed constant before and after EPD,
respectively. EPD was conducted at 30 V and the BDA conditions were 120 V, 30 min, and 25 *C.
Porosity of the deposits by EPD was calculated using the deposition weight per unit area and the
deposition height (c). The error bars indicate
measurements.
104
one standard deviation resulting from three
For EPD on micro-porous surfaces produced by BDA, the capillary pressure shows opposite
tendency as the bare substrate, decreasing with increasing deposition time. Hydraulic diffusivity
behaves similarly to the case of EPD on flat substrates. The nano-porous structures produced by
EPD increase the viscous drag resistance; thus, hydraulic diffusivity displays a maximum
irrespective of the initial substrate condition. However, micro-porous surfaces with thicker nanoporous layers (longer deposition time) show lower capillary pressures because the capillary pressure
is affected by the additional viscous drag through the nano-porous structures.
4.4.4.
Surface chemical composition and atomic structure
The material compositions and atomic structures of the surfaces were investigated with X-ray
diffraction (XRD) (Figure 4-8). The XRD patterns of a bare titanium substrate and TiO 2 deposits
were measured (Figure 4-8a-b) to serve as reference surfaces. Notably, the surface produced by the
hybrid BDA/EPD method show a combination of titanium and TiO 2 patterns (Figure 4-8c). Further,
the amount of oxidized titanium produced by BDA affects the intensity of the peaks shown in
Figure 4-8e-i. It is interesting to note that the surface produced at 120 V and 10 C shows nearly no
peak (Figure 4-8i), identical to the spectra of the sediment obtained after BDA (Figure 4-8j).
According to other studies, the sediment can be assumed to be amorphous titanium oxide which
lacks crystal structure [174, 175]. To confirm this hypothesis, we heat treated the BDA surfaces and
the sedimentation at 450 *C for 2 hours to initiate crystallization. After heat treatment, the spectra of
both samples (Figure 4-8k and 1) are similar to anatase TiO 2 (Figure 4-8b). This result reveals that
the porous structures created by BDA are composed of amorphous titanium oxide.
At electrolyte temperatures higher than 50 *C, oxidized titanium quickly dissolves into the
electrolyte through the reactions in equation (1-16). As a result, titanium peak patterns are observed
105
on these surfaces, as shown in Figure 4-8e and f. It is worth noting that the BDA surfaces produced
with high electrolyte temperature show different spectra after prolonged exposure to air (Figure
4-8d). This indicates that the surface titanium slowly oxidizes to titanium oxide. In addition, we
found that the wettability is degraded by these transitions. EPD of high surface energy nanoparticles
such as TiO 2 and SiO 2 alleviates the effect of surface oxidation in air. We believe that the
nanoporous TiO 2 structures contribute to the higher durability of the BDA/EPD surfaces relative to
the BDA surfaces. As explained in Cebeci et al. [55] and Drelich et al.[61], superhydrophilic
surfaces can be achieved even with materials that have native contact angles higher than 65 - 700 if
the surface roughness is extremely high. The nanoporous TiO 2 structures on the BDA surfaces
greatly enhance the surface roughness. Therefore, the nano/micro porous structures can maintain
their superhydrophilicity longer than the BDA surfaces alone. In addition, we hypothesize that the
enhanced durability is due to reduced oxidation of Ti relative to the BDA fabricated structures. To
investigate this, we compared XRD data of the BDA/EPD and EPD surfaces immediately after they
were produced and again 30 days later. The XRD patterns of the EPD surface did not change after
30 days. This suggests that the chemical composition and atomic structure of TiO 2 nanoparticles are
relatively fixed. Therefore, the change in wetting properties of the BDA/EPD surface originated
from property changes of the BDA surface underneath the EPD layer. Since the BDA/EPD surface
shows higher durability than the BDA surface, we believe that the EPD layer on the BDA surface
helped to retard the degradation of wetting properties.
We compare the degradation rates of five superhydrophilic surfaces that were produced by BDA
with 120 V electric potential at 10 'C, 25 *C, 50 'C, and 75 'C electrolyte temperature. We also
examined the BDA/EPD method with BDA at 120V and 10 'C and EPD at 30 V for 90 sec. The
five samples were maintained in laboratory air under ambient conditions for 30 days. The
degradation rates were calculated by
106
P
Deraaiate=1-
4,
where Pap.i and Pcap.2 are the initial and the final capillary pressures, respectively, of the surface.
Table 4-1 shows the degradation rates of the prepared surfaces. The BDA surfaces produced with
different electrolyte temperatures show similar degradation rates and the average degradation rate is
20 %. As expected, the lowest degradation rate was observed from the BDA/EPD surface due to the
nanoporous structures, as mentioned above.
Table 4-1. Changes in capillary pressure for five superhydrophilic surfaces 30 days after fabrication.
10*C
Degradation
rate
23%
I
BDA BDA
25*C
50*C
75*C
17%
21%
21%
aIII
107
BDA/EPD
7%
Ti
Tro
Ti
Ti
TrI
T
lii
t4
I
Titanium plate
T42
T2
T10 2
a)
Ti
(a)
~Ti
Ti0 2
TiO_
EPD with T2
.1
( C)
I
ODA + EPD
(d)
(d)
II
BDA 90V SI
at 75GC in 30 days
I
(b)
I
i
1- (e)
BDA 90V at 75 OC
MDA
9WV at 50 OC
BOA
10V
at 10OC
Amorphous Titanium
(k)
Heat treated BDA 120V at 10 GC
A(1)
I
Heat treated amophoua Titanium
10
20
30
40
50
60
70
80
90
Position (20) (Copper (Cu))
Figure 4-8. XRD patterns of the surfaces produced by EPD, BDA, and the hybrid BDA/EPD
method. A bare titanium plate and the TiO 2 deposit surface were used as control XRD substrates
showing the spectra of titanium (a) and titanium dioxide (b). Surfaces produced by variations of
EPD and BDA shows aspects of both Ti and TiO 2 spectra. Sediments obtained after BDA shows
very weak peaks (j), which are indicative of amorphous titanium oxide [174, 175]. After heat
treatment, the surface used in (i) and the sediments used in (j) show the spectra of anatase TiO 2 as
shown in (k) and (1).
108
4.4.5.
Relationship between the effective pore radius and
surface roughness
From equations (4-2) and (4-3) we know that the pore size strongly influences capillary pressure
and spreading speed constant. To determine the role of electric potential in BDA, surface roughness
was measured using the profilometer. Surface roughness was measured for the substrates used in
Figure 4-5 with the exception of the 50 'C and 75 *C electrolytes. At these high electrolyte
temperatures BDA resulted in highly interconnected pores as shown in Figure 4-6b; therefore, it is
not appropriate to compare with other surfaces. To show the correlations between the wetting
properties of the BDA surfaces and the surface structure, first we compare the effective pore radius
with the surface roughness, as shown in Figure 4-9a. The effective pore radius can be considered a
key parameter to characterize the surface structure. The pore radius can be calculated by equation
(4-4) with the values of Pcap and Deap obtained from capillary rise measurements (CRM). In Figure
4-9a, we confirm that the pore radius is roughly linearly proportional to the surface roughness.
Capillary pressure asymptotes with surface roughness (and therefore pore radius), as shown in
Figure 4-9b. However, hydraulic diffusivity is linear with surface roughness and pore radius (Figure
4-9c). This result reveals that capillary pressure and spreading speed can be tuned with both electric
potential and electrolyte temperature because the surface roughness and pore radii are changed.
109
14
-
(a)
12
0 30 V. 10 *C
* 30 V, 25 -C
060V, 10*c
0 60 V, 25 *C
a 90 V, 10 *C
A 90 V, 25 *C
0 120 V, 10 *C
* 120 V, 25 *C
10
:.
0
8
13
6
0
10
20
3
2
(b)
1.5
030 V, 10 *C
/30 V, 25 *C
060 V, 10 *C
l60 V, 25 *C
A90 V, 10 *C
A90 V, 25 *C
0*120 V, 10 *C
0 120 V, 25 *C
................................
....
I
1
0.5
0
0
10
0 30 V,
(C)140
20
3C
10 -C
* 30 V, 25 *C
0 60V, 10 *C
@ 60 V, 25 @C
0 100
a
E 80
E
E60
90 V, 10
25
A 90 V,
:c
*
120
+
0~
* 120 V, 10 -C
*120 V, 25 *C
40
20
n
5
1~p0)
r(Atm)
15
Figure 4-9. Plots of the pore radius (a), the capillary pressure (Pcap) (b), and hydraulic diffusivity
(Dcap) (c) with respect to surface roughness. The pore radius obtained by equation (4-4) with Pcap
and Dcap shown in (b) and (c) is linearly proportional to the surface roughness (a). The box, circle,
triangle, and diamond symbols indicate the electric potentials of 30 V, 60 V, 90 V, and 120 V,
respectively, used in the BDA processes. The fill colors indicate the electrolyte temperature, 10 'C
(white) and 25 'C (red). Morphological data was obtained with a profilometer (Measurement
system: Tencor P-16 Surface Profilometer (TM)). The error bars indicate E one standard deviation
resulting from four measurements.
110
4.4.6.
Modification of capillary flows
From the relation between electric potentials and spreading speed constants (Figure 4-9), we
developed superhydrophilic surfaces that have unconventional capillary flows. To vary the electric
potentials continuously through an electrode used in BDA, various profiles of electrodes were used
as shown in Figure 4-10 from Case 1 to Case 3. In addition, triangle substrates were used to
demonstrate unconventional flows can be achieved with different shapes of electrodes (Case 4 and
Case 5 in Figure 4-10). Same size (10 mm x 70 mm) of rectangular electrodes was used in Case 1-3.
Constant electrode gap distance (10 mm) was used in Case 1 and 4-5. To show the effect of nanoporous layers on capillary flows, TiO 2 nanoparticles were partially deposited by EPD with constant
electric potential (30 V) for 5 min on the surface produce by BDA with the electrode profile given
in Case 3.
With the electrodes designed in Figure 4-10, various unconventional capillary flows were
obtained (Figure 4-11). The results of CRM show superhydrophilic surfaces where square of
capillary height can be non-linear in time. Case 2 shows faster spreading speeds than Case 1 for
short times but becomes slower over time. We attribute this result to pore radius changes resulting
from the varying electrode gap distance. Notably in Case 3, the surface with partial TiO 2 deposit via
EPD, there is a discontinuous change of spreading speed. This shows that the nano-porous
structures produced by EPD can locally change the spreading speed. Cases 4 and 5 show that
capillary flows can depend on the electrode shapes and orientation. For Case 4, hydraulic diffusivity
increases with time, while Case 5 is nearly identical to Case 1. The trend lines in Figure 4-11 are
linear and quadratic fitting lines of the experimental data. However, theoretical predictions for the
capillary flows are possible but beyond the scope of this paper. We are now preparing a follow up
paper investigating the effects of electrode configurations and shapes on capillary flows. The
111
approach to predict the capillary flows is as follows. The capillary pressure and hydraulic diffusivity
are functions of the rise height (h shown in Figure 4-10) depending on the configuration and shape
of the electrode in the BDA method. As a result, we can formulate the general capillary flow
equations in terms of the capillary pressure and spreading speed constant.
Case I
Case 2
Case 3
Case 4
Case 5
10 mm
Triangle
electrode
Triangle
electrode
55 mm
50mm
quadratic
E
E
E
E0
a.
E
E
E
E
E
so
CO
linear
h
10m
M
10mm
55mm
50mm
Figure 4-10. Schematic illustrations of electrode gap-profiles and electrode shapes used to
demonstrate capillary transport modification with BDA and EPD. Case 1 was used as a reference
with a constant gap-distance (10 mm) and a rectangular electrode shape (10 mm x 70 mm). In Cases
2 and 3 the electric potentials vary with gap distance between anode and cathode electrodes, with
identical electrode cross sectional area as Case 1. In Case 3, TiO 2 nanoparticles were partially
deposited on the surface produced by BDA using EPD. In Cases 4 and Case 5, triangular electrodes
were used with the same electrode gap-distance as Case 1 (10 mm).
112
25
p
foPP
15
0'
-
20
10
Dca 1: eMA (sOW, 25-C)
5
dV
OCMs 1: BDA (9w., 10*C)
2: BOA (sOW, 26*C)
*Case 3: BDA (OWV, 250C)
#Case 3: BOA (OW., 250C) + EPD
80we
*Case 4: 4M (90V, 10*C)
*Case 5: BOA (qDv, 10-C)
0
0
20
40
so
so
100
Time (sec)
Figure 4-11. Square of measured capillary rise height with respect to time for superhydrophilic
surfaces produced by the BDA and EPD methods presented in Figure 4-10. In the BDA processes,
two different electrolyte temperatures (10 C and 25 C) and one electric potential (90 V) were used.
In the EPD process, 30 V was supplied for 5 min to deposit Ti02 nanoparticles. In Cases 2-4 the
square of capillary height is nonlinear in time, unlike conventional
capillary flows. With
augmentation via EPD, the spreading speed can be discontinuously changed, as shown in Case 3.
4.5.
Conclusions
Superhydrophilic surfaces with hierarchical micro- and nano-scales pores were produced a hybrid
BDA/EPD method. BDA creates micro-scale porous structures on titanium substrates. BDA
morphology is a function of electric potential and electrolyte temperature in constant pH
electrolytes. We found that there were optimal values of electric potential and electrolyte
temperature to obtain high capillary pressure and spreading speed. The electrolyte temperature
affects both the breakdown potential and the thickness of the resulting oxide layer. High electrolyte
113
temperatures decrease the breakdown potential but also decrease the oxide layer thickness due to
dissolution. These opposing contributions result in an optimal electrolyte temperature for a given
electric potential. Amorphous titanium oxide layers provide high surface energy to the micro-porous
structures, resulting in highly wetting surfaces.
Nano-porous titanium dioxide layers were deposited on the micro-porous structures produced by
BDA using EPD. With the EPD process, capillary pressure and spreading speed were precisely
controlled by the deposited mass. The nano-porous films offer stability to the BDA surfaces. The
surfaces produced by the hybrid method showed significantly higher capillary pressure and
spreading speed than the surfaces produced by EPD alone. Ultimately the characteristics of the
superhydrophilic surfaces are mainly controlled by BDA but the EPD films can offer various
surface energies and nano-structures to micro-porous surfaces produced by BDA.
We have also presented various methods to achieve unconventional capillary flows. These
capillary flows showed varying spreading speed constants at different locations on the substrate.
The methods presented can be used to create low-cost superhydrophilic surfaces with specially
tailored transport properties. Furthermore, the hybrid BDA/EPD method has great potential to be
used for various applications requiring high surface area or a large number of reacting sites.
Numerous material compositions and nano-structures can be effectively altered by EPD with
different kinds of nanoparticles, depending upon the desired application.
114
Chapter 5. Hybrid Electrophoretic Deposition
with Anodization Process for
Superhydrophilic Surfaces to Enhance
Critical Heat Flux
Reproduced in part with permission from
Young Soo Joung, Cullen R. Buie, "Hybrid Electrophoretic Deposition with Anodization Process
for Superhydrophilic Surfaces to Enhance Critical Heat Flux," Key EngineeringMaterials,Vol. 507
(2012) pp. 9-13.
Copyright 0 2012 Scientific.net. All rights reserved.
115
5.1 .
Introduction
Pool boiling is a heat transfer method with high heat transfer rates attributed to phase change and
high mass transfer through bubble generation. In pool boiling, enhancement of critical heat flux
(CHF) has been considered the most important issue to not only enhance the heat transfer efficiency
but also escape from burn out incidents [176]. At high superheat temperatures, liquid vapor covers
the entire heater surface and abruptly increases the thermal resistance, resulting in system failure.
Another challenge is to reduce the boiling inception temperature (BIT) in order to achieve high heat
transfer rates at temperatures closer to the liquid saturation temperature. In heat exchanger systems
operating near liquid saturation temperature, BIT has a stronger influence on heat transfer efficiency
than CHF enhancement.
Methods to enhance CHF can be classified in two categories. The first is modification of the
working fluids [177]. For instance, CHF can be enhanced with nanofluids, which are mixtures of
liquids and nanoparticles. Different CHF values are shown during pool boiling depending upon the
specific nanoparticles utilized. The mechanism of CHF enhancement is the deposition of
nanoparticles on the heater surface, resulting in changes in the wettability and porosity of the heater
surface [57]. This approach can provide an easy way to enhance CHF but it exhibits limited control.
The second method is the direct modification of the heater surface. Theoretically, CHF is the
function of roughness and surface energy of the heat transfer surface. Porous structures and various
wetting surfaces have been investigated to improve CHF [178]. Both approaches rely upon altered
wettability to enhance CHF and it has been shown that hydrophilic surfaces typically show higher
CHF values than hydrophobic surfaces. However, to date porous superhydrophilic surfaces with
high capillary pressure have not been investigated and BIT has rarely been considered in previous
work related to CHF.
116
In this work, electrophoretic deposition (EPD) and break down anodization (BDA) were utilized
to produce surfaces with varying wettability from superhydrophilic to superhydrophobic surfaces in
order to enhance CHF and reduce BIT. Recently, we have developed novel methods to produce
superhydrophobic surfaces with EPD and superhydrophilic surfaces with BDA [73, 179].
Superhydrophilic surfaces produced by BDA show high CHF with high BIT values. To reduce the
BIT of the superhydrophilic
surfaces, hydrophobic nanoparticles were deposited on the
superhydrophilic surfaces in order to provide nucleation sites. With the hybrid method,
unconventional surfaces with mixed wettability are obtained, resulting in higher CHF and lower
BIT.
5.2.
5.2.1.
Experimental
Hybrid method of electrophoretic deposition of TiO 2
nanoparticles and breakdown anodization of titanium
plates
BDA and EPD were used to prepare heat transfer surfaces. In the BDA process, the pH of DI
water was adjusted to pH 3 with acid (Nitric acid, 70 % ACS reagent, Sigma-Aldrich). Two
titanium plates (Titanium foil (99.7%), 0.05 mm Thickness) were used as cathode and anode
electrodes and electric potentials up to 90 V were applied for 10 min. For the EPD method, PDMS
modified Si0 2 nanoparticles (14 nm, PlasmaChem) in a mixture of 90% methanol and 10% DI
water by volume were used to make 1 g/L concentration Si0 2 suspensions. Titanium plates were
again used as anode and cathode electrodes. An electric field of 30 V/cm was subjected to the
electrodes for 30 seconds to deposit nanoparticles on the substrate. Ultimately three kinds of heat
117
transfer surfaces were prepared, superhydrophobic, superhydrophilic, and mixed wettability
surfaces. Superhydrophobic surfaces and superhydrophilic surfaces were produced by the EPD and
BDA processes, respectively. Both BDA and EPD were employed to create the mixed wettability
surface.
5.2.2.
Capillary rise measurement
Capillary rise experiments were used to evaluate the superhydrophilicity of the prepared surfaces
in terms of capillary pressure and spreading speed [179, 180]. In summary, the capillary pressure,
Pap, can be calculated from the maximum capillary height using the equation of Pcap = [2ycosOIR]=
H,,xgp, where H.,x is the maximum capillary rise height, y is liquid surface tension, 0 is a native
contact angle, and p is the liquid density. Hydraulic diffusivity, Dap, can be obtained from the
equation h 2 = (Rycos/27)t = Dcapt, where h is the rise height, I is the liquid viscosity, and t is time.
The morphologies of prepared surfaces were characterized with a scanning electron microscope
(SEM, JEOL 6320FV Field-Emission High-resolution SEM). A goniometer (Kyowa, DM CEl) was
used to dispense and image 3 pL drops of DI water on each sample. Static contact angles (CA) were
calculated using the tangential curve-fitting method. A digital camera was used to record bubble
dynamics on the heat transfer surfaces.
5.2.3.
Critical heat flux in pool-boiling
CHF tests were conducted with a custom built pool-boiling experimental system composed of a
heater assembly, a water bath, and a temperature control unit. The heater assembly includes
thermocouples positioned on three different distances from the top in order to calculate heat flux
118
and uncertainty [181]. The heat flux, q ", can be calculated with the equation q" = kA T/Ax, where k
is the thermal conductivity of heat transfer surface, AT is the temperature difference between
thermocouples with a separation distance Ax. The uncertainty in heat flux can be estimated by the
equation Eq" = q"[(Ex/Ax)
where ex is the distance uncertainty between the
thermocouples and ET is the temperature uncertainty. The water bath was maintained at the
saturation temperature, 100 'C, during CHF tests and the water level was kept constant with a
condenser to recycle water vapor.
5.3.
Results and discussion
Table 5-1 shows the wetting characteristics of the superhydrophobic, superhydrophilic, and
mixed wettability samples including untreated titanium as a reference. Sample 1, produced by EPD
of PDMS modified Si0 2 particles showed a very high contact angle of 168*, confiming it's
superhydrophobicity. Sample 2 was prepared by the BDA process and it showed a contact angle
near zero with a high capillary pressure and spreading speed constant. As expected, sample 3
displayed mixed wettability. The average contact angle on the surface was 280 but the capillary
pressure and hydraulic diffusivity were 538 Pa and 9.36 mm2/s, respectively. This suggests that the
layer of hydrophobic SiO 2 particles increased the contact angle while still allowing liquid transport
along the surface.
119
Table 5-1. Evaluation of prepared surfaces with BDA and/or EPD methods.
Reference
Method Bare Ti plate
Sample 1
EPD
Sample 2
BDA
Sample 3
BDA and EPD
Contact angle
550
1680
00
280
Capillary pressure (Pa)
Spreading speed constant (mm2/s)
n/a
n/a
n/a
n/a
851
31
538
9.36
SEM images in Figure 5-1 illuminate the mixed behavior of sample 3. Nanoporous layers in
Figure 5-la were observed with the samples produced by EPD while micro porous structures were
observed in the samples prepared by the BDA process, as shown Figure 5-lb. The dual scale micro
and nano porous structures in Figure 5-1c were produced by the hybrid method.
Figure 5-1. SEM images of prepared surfaces; (a) superhydrophobic surface by EPD, (b)
superhydrophilic surface by BDA, and (c) mixed wetting surface by the combined BDA/EPD
process.
120
Table 5-2 shows the CHF test results. The untreated titanium surface showed CHF and BIT of
441 kW/m 2 and 114*C, respectively. Conversely, BIT was 140 'C on the superhydrophilic surface
produced by the BDA process. The higher BIT could be explained with well-known boiling theory.
BIT can be estimated by the equation Psat(T) = Po+2a/R, with the assumption that the contact
angle is 90* on the surface and the gas pressure is ignored. Psat(T) is the saturation pressure inside a
bubble at the wall temperature Ts, P. is the ambient pressure around the vapor bubble, a is the liquid
surface tension, and R, is the critical bubble departure radius [176].
Table 5-2. CHF results for modified surfaces. Reference: an untreated titanium surface. Sample 1: a
superhydrophobic surface produced with EPD. Sample 2: a superhydrophilic surface produced by
BDA. Sample 3: a hybrid surface produced by the coupled BDA and EPD method.
Boiling Inception Superheat (AT)
Critical Heat Flux (kW/m2 )
Critical Superheat (AT)
Reference
14
441
81
Sample 1
5
598
78
Sample 2
40
536
148
Sample 3
10
507
176
On superhydrophilic surfaces (Sample 2), the contact angle is nearly zero; therefore the
assumption of 900 contact angle must be reconsidered. In this case the nucleation site becomes
smaller, resulting in a higher BIT. The higher CHF on the superhydrophilic surface can be
explained with the maximum heat flux equation, q,,x ~ hfgpVmax, where hfg is the liquid latent heat,
p, is the liquid density and Vmax is the maximum vapor velocity. V,,, can be approximated by V,,, ~
(u/pvL)'12, where Lc= [u/(pt-pv)g]112 is the characteristic length of heater assuming a 90* contact
angle on the surface [176]. Considering superhydrophilic surfaces, the characteristic length of Lc
become smaller, increasing the maximum velocity and resulting in increased maximum heat flux.
121
Conversely, the BIT of the superhydrophobic surface (Sample 1) was close to the water saturation
temperature at 105 *C. We believe that during boiling vapor bubbles trapped in the
superhydrophobic surface merge to find local energy minima, resulting in macro scale bubbles.
Therefore R, becomes on the order of a few millimeters so that the term 2a/Re can be neglected,
resulting in Psa,(T) ~ P. Interestingly, the CHF on the superhydrophobic surface was larger than
the superhydrophilic surface at the low superheat. This phenomenon is an ongoing area of research
in our group and we speculate that bubble generation on the superhydrophobic surface dramatically
enhanced the heat transfer coefficient at low superheat regions [182].
Sample 3, which had nano/micro porous structures with different wettabilities, showed a low BIT
of 110 *C but the film boiling was effectively delayed up to the high superheat of 176 *C, exhibiting
the high CHF value of 507 kW/m 2. Fast nucleate boiling was attributed to the hydrophobic
nanoparticles providing additional nucleation sites.
122
Figure 5-2. Boiling behavior on the prepared surfaces. Images of the superhydrophobic surface of
sample 1 at the saturation temperature (a), the boiling inception temperature (b), and the nucleate
boiling region (c). Images of the superhydrophilic surface of sample 2 at the saturation temperature
(d), the boiling inception temperature (e), and the nucleate boiling region (f). Images of the hybrid
wetting surface of sample 3 at the saturation temperature (g), the boiling inception temperature (h),
and in the nucleate boiling region (i).
The former descriptions can be verified by observing bubble generation during boiling. Figure
5-2 shows the bubble generation on the modified surfaces. On the superhydrophobic surface vapor
bubbles were generated at the water saturation temperature of 100 *C as shown in Figure 5-2a.
Boiling inception at 105 'C was observed on Sample 1 with vapor bubbles larger than other surfaces,
as shown in Figure 5-2b. On the superhydrophilic surface, Sample 2, bubbles were not be until 140
'C and boiling began abruptly as shown in Figure 5-2e. On the hybrid wetting surface, Sample 3,
small bubbles were observed at the water saturation temperature as shown in Figure 5-2g. This
123
confirms that the hydrophobic layer provides additional nucleation sites. Aided by hydrophobic
nanoporous structures, boiling inception occurred at the low temperature of 110 *C. We conclude
that on the hybrid wetting surface the nanoporous hydrophobic layers provide numerous nucleation
sites, reducing BIT, while the microporous hydrophilic layers enhance CHF by preventing film
boiling.
5.4.
Summary
A novel surface with low BIT and high CHF was produced by a hybrid EPD and BDA method.
The superhydrophobic surface displayed low BIT, which is attributed to numerous nucleation sites
on the nanoporous structures. The superhydrophilic surface fabricated by BDA did not generate
vapors even at superheats up to 40 *C due to limited nucleation sites on the surface. Low BIT and
high superheat at CHF were observed on the hybrid wetting surface produced by the hybrid BDA
and EPD process. The resulting mixed wettability surface was composed of a hydrophobic
nanoparticle layer on top of a superhydrophilic layer. The hydrophobic nanoparticle layer provides
nucleation sites while the superhydrophilic layer prevents film boiling, resulting in lower BIT and
higher CHF than untreated titanium surfaces. This work demonstrates the potential to use processes
based on EPD to enhance heat transfer surfaces.
124
Chapter 6. Design of Capillary Flows with
Functionally Graded Porous Films
Controlled by Anodization Instability
Reproduced in part with permission from
Young Soo Joung, Bruno Michel Figliuzzi, Cullen R. Buie, "Design of Capillary Flows with
Functionally Graded Porous Titanium Oxide Films Controlled by Anodization Instability," Journal
of Colloid and Interface Science, 2014.
Copyright C 2014 Elsevier B.V. All rights reserved.
125
6.1.
Introduction
Capillary flows through thin porous media have been widely utilized for small liquid
transportation systems such as chromatographic analyzers, biosensors, micro chemical reactors, and
paper-based microfluidic devices [183-190]. These devices are generally cheap and simple because
additional pumping systems are not necessary to make liquid transportations. Furthermore, the
capillary flows are predictable and effectively scaled down; therefore, they are appropriate to
develop small devices with precise liquid deliveries. To take these advantages of capillary flows,
many different porous media have been applied to the devices because capillary flows show
different characteristics depending on the media; examples include capillary tubes and wedges,
micro-fabricated structures, porous media composed of small particles or fibers, and sponges [61,
191]. However, in most media it is difficult to tailor the capillary flow for a given application
because it is challenging to realize arbitrary shapes and spatially functionalized micro-scale and
nano-scale structures. Therefore, the media mentioned above can only be used for conventional
capillary flows obeying Washburn's equation and the modifications thereof [180, 192, 193]. Given
background, new fabrication techniques and corresponding capillary flow equations of motion must
be developed for more demanding applications.
In the literature, equations of motion for capillary flows have been derived from the NavierStokes equations, or modifications thereof [172, 180, 192-194]. These approaches result in
Washburn's classical equation for one-dimensional capillary flows assuming uniform capillary
pressure, no inertial-effects, and constant channel cross section [172]. This equation can be used to
estimate capillary flows through wetting porous media with uniform porous structures and surface
energy. However, Washburn's equation cannot be used to estimate the capillary flows for porous
media with spatial variations in surface energy, pore radius, and cross sectional area. Eeyssat et al.
126
recently developed an imbibition model aimed at studying capillary flows for porous media with
varying circular cross-section, demonstrating that shape variations affect the dynamics of the
capillary rise [195].
Recently, we developed a method to produce highly wetting porous surfaces using anodization
instabilities [196]. During conventional anodization, oxide film thickness increases linearly with
time [75]. However, when the electric potential of anodization is higher than a critical value, the
anodized films burst due to ionic shear stress that exceeds the surface tension of the films, resulting
in irregular structures on the substrate [90]. This fabrication method is known as breakdown
anodization (BDA). Surfaces produced by BDA on titanium plates show extremely low effective
contact angles (nearly zero) and fast water spreading. These properties result from the highly porous
surface composed of amorphous titanium dioxide, which provides high surface energy. In addition,
we've shown that capillary flows on surfaces produced by BDA can be expressed by Washburn's
equation [196]. However, if porous structures of the surface are non-uniform, the capillary pressure
changes locally, resulting in varying propagation speeds. In this case, the capillary flows do not
follow Washburn's equation. Therefore, we modify the equations of motion to account for local
variations in capillary properties.
Capillary pressure and spreading speed are well-known parameters for characterizing porous
materials such as packed beads [180]. Both parameters can be obtained from capillary rise
measurements (CRM). Capillary pressure and spreading speed depend on the surface energy and
bead size and are not generally proportional to each other. Thus, we consider them separately for
evaluating superhydrophilic surfaces. In this study we utilize CRM to characterize superhydrophilic
surfaces. The surfaces can be considered as bundles of capillary tubes with various tube diameters
[172].
127
In this work, for the first time, an electrochemical fabrication method using anodization instability
is presented for the design of capillary flows with functionally graded porous films controlled by
electric fields. Additionally, we derive capillary flow equations of motion to predict the transport in
these systems. First, we suggest a simplified conceptual model of highly wetting porous surfaces.
Then, we derive a general capillary flow equation of motion from the conceptual model for
predicting capillary speeds on heterogeneous surfaces. Finally, the capillary flows are expressed as
functions of the local capillary properties of capillary pressure and capillary diffusivity, which are
functions of capillary rise height. With the fabrication method and the theoretical model, we show
that various capillary flows can be designed by BDA with spatially variable electric fields.
6.2.
Theory
From the Navier-Stokes equations, if inertial effects are negligible and the flow is laminar,
Poiseuille's law gives the average flow velocity in a single cylindrical tube:
r2
V,=
ap-
-+pg
8p o'y
(6-1)
where Vavg is the average flow velocity over the entire cross sectional area of the tube, r is the tube
radius, aP/Sy is the pressure gradient in the flow direction y, g is the gravitational acceleration
constant, and p and p are the liquid viscosity and density, respectively.
From equation (6-1), one-dimensional capillary flow in a uniform cylinder of radius r, can be
described by Washburn's equation [172],
128
-=
dt
-27cs
pgh
h 8p
r
(6-2)
where h denotes the height reached by the liquid in the capillary, t the time, 0 the surface contact
angle and y the air-liquid surface tension. From equation (6-2), when the height h of the liquid is
small enough, the hydrostatic pressure can be neglected, and we can obtain a simple expression of
the capillary rise height as a function of time,
=
2p
Dt
(6-3)
2
Here, we introduce the capillary diffusivity Dcap
=
rcycos9/p, which has units of m2/s. When the
properties of the material are uniform in the capillary, the surface contact angle remains constant
and Dcap remains constant. Similarly, the capillary pressure, Pcap, can be calculated from the
maximum capillary rise height, hmax. At equilibrium, the gravitational force on the liquid column
balances the capillary force. Thus, the capillary pressure can be calculated as
2ycos9
P=
r
hrgp
(6-4)
From equations (6-3) and (6-4), the capillary tube radius (re) and the surface contact angle (0) can
be obtained as follows: rc = (2puDcap/Pcap) and cosO= (2DcapPcap/yL).
We model highly wetting porous films as multi-layered capillary tubes oriented in the flow
direction, as shown in Figure 6-1. Similar capillary tube models have been employed to simplify
129
N
-
flows in porous media [197] but here we newly suggest a capillary tube model for wettable porous
films, which have varying surface width and capillary properties. The imaginary capillary tube has
the effective radius r. The number of capillary tubes (N,.y) present at the capillary height, y, can be
obtained using,
N
2R, HcRH
= 2r
2"2,2
(6-5)
where Ry and He are the half width and the thickness of the film, respectively, at the capillary height
of y. Therefore, the total cross-sectional area of capillary tubes (Ay) can be expressed as A =r 2 N.
The volumetric flow rate at a given cross-section of the porous film can be calculated as
(6-6)
2
-V,
Combining both equations (6-1) and (6-6), the relation between the pressure gradient and the
volumetric flow rate can be found to be:
8 Aiy
+p
)
=
2(6-7)
7rRHc
From mass conservation, we know that the volumetric flow rate is not a function of capillary height.
In addition, the local capillary radius can be expressed as a function of the capillary pressure and
capillary diffusivity as re., = (2pDcap./Pcap.y)"', where the subscript y indicates a function of capillary
130
height. Then, we can integrate both sides of equation (6-7) and derive the relation between capillary
pressure and volumetric flow rate:
16-V
IP~aP
dy + pgh
f0h
ca.=h
RH DaY
(6-8)
At y = h, the volumetric flow rate is
-= 7rRH dh
2
dt
(6-9)
Therefore, we can obtain the general capillary flow equation of motion in wettable porous films as
the following:
dh
dt
Pa,. - pgh
R
(6-10)
h
,, R, Dca,
If the porous material has uniform wetting properties and constant cross sectional area, equation (10)
becomes identical with Washburn's equation, as shown in equation (6-2).
131
77
T ube radius: r\
Y
II
\
'
I
I
\
Flow direction
Figure 6-1. Schematic illustration of the conceptual model for wettable porous films with varying
cross sectional area. The porous film has the constant height, He, and varying half width, R. The
porous film can be modeled as multi-layered capillary tubes vertically oriented in the capillary
height, y. The number of the capillary tubes in x-direction and y-direction is varied according to the
radius of a single capillary tube, re, and the width of R.
Equation (6-10) can be further modified when the surfaces have either a constant width or
uniform wetting properties throughout the volume. First, if we assume constant capillary pressure
2
,
and capillary diffusivity, but the surface width changes linearly in the flow direction: Ry=Ciy+C
where C1 and C2 are constants, equation (6-10) becomes
2cos 0pg
r 2Y
dh
dt
rC
8p
C1
(6-11)
1+ Eh In
C2 )(C2
I+ C'h
132
When C h << C2 , equation (6-11) can be simplified into
V
= dh = r2P
-P
C
- pg). (I- C'h
(6-12)
.
As a result, different capillary flow speeds can be obtained depending on the values of C1 and C2
When the surface width has an exponential form such as Ry= C2 ecrY, where C2 is the surface width
at y = 0 and C1 is a constant value, the capillary speed can be expressed as follows:
V
=
,P-pgh-
q
tc8Ai
8
Vh
eq'h-1
(6-13)
Therefore, the capillary flow can be altered by the constant C1 . When Clh << 1, equation (6-13)
simplifies to
V
dh
dt
r\
8 up
=-=-(P,-pgh)-
h(I +Ch)
(6-14)
Second, in the case of constant surface width, and varying capillary pressure and capillary
diffusivity, equation (6-10) becomes
dh _Pp,,hdt
4
Pgh
hPcapy
dy
0 D
133
(6-15)
Therefore, the flow velocity can be expressed as a function of both Pcap.y and Dcap.y. When the
capillary pressure and the capillary diffusivity vary linearly with rise height and have the forms of
Pcap.y=Pjy+P 2 and Dcap.y=Diy+D2 , respectively, equation (6-15) simplifies to
dh
dt
PJh+P2-pgh
+
(P
2 D 12
4f:' SD2
D.
YD2)y +1
-
(6-16)
dy
If Pjh <<P 2 and Djh << D2, equation (6-16) becomes
dit
= 1P P+-pg=
4 P2
P+-pg
h
(6-17)(2f
8p
h
here, D2 /P2 = rc2 /2p. As a result, we can control capillary flows by altering the capillary pressure
.
based on the constants P, and P2
In the conceptual model of porous wetting surfaces (Figure 6-1), it is assumed that the porous
surfaces behave like bundles of capillary tubes (Figure 6-2). Therefore, the control volume for
equation (6-10) can be determined depending on the surface shapes, as shown in Figure 6-2. The
rule of determining the control volume is that the conceptual capillary tubes that have been fully
filled with water are excluded from the control volume. As a result, wettable porous surfaces that
have decreasing width show the same capillary rising behaviors as constant width surfaces if we can
ignore evaporation on the surfaces.
134
Evaporation must be considered when the surfaces have varying cross sectional area and the rise
height is high. If a surface has an evaporation rate of e [kg/s-m 2 ], mass conservation can be
expressed as
V
pA, -f
y=h
4 -2Rdy=pKAh
(6-18)
Therefore, the capillary flow speed V can be expressed as follows:
V =V Rh
y
,,
4Qf-IR,,dy
+
_yy
prRH,
(6-19)
Equation (6-19) can be used instead of V.g in equation (6-6) to derive the capillary flow equation
(equations (6-10)) from equation (6-7) when accounting for evaporation. However, the use of
equation (6-19) complicates calculation of the rise height; therefore, commercial mathematics
software (Maple 16) was used to solve equation (6-10) when equation (6-19) was applied.
135
(a)
FTF
Partially filled
capillary tubes
(b)
Partially filled
capillary tube
V-
Wicking
surfaces
Fully filled
capillary tube
Control volume
Capillary rise
height
rWater
Capillary rise
height
Figure 6-2. Schematic illustrations of control volumes depending on the shapes of wicking surfaces.
The wicking surfaces can be conceptually modeled as vertically packed capillary tubes. (a) The
control volume covers the whole wetted area when the capillary width increases with respect to the
capillary height. (b) The wet area that has the same column width as the top wetting line is
considered as the control volume when the wicking surface has decreasing width.
6.3.
6.3.1.
Experimental
Fabrication method
Breakdown anodization (BDA) was used to produce highly wetting porous surfaces [196, 198].
For the BDA electrolyte, DI water was adjusted to pH = 3.0 with nitric acid (70 % ACS reagent,
Sigma-Aldrich). Electric potentials up to 120 V were applied for 30 min during the anodization
process. The electrolyte temperature was maintained at a constant value during the BDA process
using a water-circulating bath (Polystate, Cole-Parmer). Titanium plates (Ultra-Corrosion-Resistant
Titanium Grade 2, 0.020" thick, McMaster) were used as anode and cathode.
136
6.3.2.
Sample characterization
Capillary rise measurements (CRM) have been used to determine wetting properties of BDA
surfaces including capillary diffusivity and capillary pressure. Static contact angles (CA) were
calculated using the tangential curve-fitting method. A goniometer (Kyowa, DM-CE1) was used to
dispense and image a 3 pL drop of DI water on each sample. Droplet spreading on the surfaces was
recorded with a high speed camera (FASTCAM SA5, Photron USA, Inc.). The surface roughness
(Ra) was obtained with a profilometer (Tencor P-16 Surface Profilometer (TM)). Morphologies of
BDA surfaces were characterized with a scanning electron microscope (SEM, JEOL 6320FV FieldEmission High-resolution SEM).
6.4.
Results and discussion
Contact angles were measured on surfaces produced by BDA under the following conditions;
anodization potential of 90 V, 30 min duration, and electrolyte temperature of 25 *C. When a
droplet contacts the surface, the bottom of the droplet rapidly expands in the radial direction the
droplet is separated into two distinct volumes (Figure 6-3). The liquid in contact with the surface
spreads rapidly, illustrating the near zero effective contact angle.
137
Figure 6-3. Droplet spreading on the surface produced by breakdown anodization (BDA). BDA
was conducted with 90 V for 30 min in pH 3.0 electrolytes at 25 'C. The droplet suspended from
the needle is immediately separated into two parts after contacting to the surface, finally showing
almost zero contact angles. The scale bars in the images indicate 1 mm length.
Surfaces produced by BDA showed highly irregular and porous structures, as shown in Figure
6-4a. Interestingly, the micro-porous structures have fish-scale like sub-micron features (Figure
6-4b). Notably, inside the amorphous titanium oxide layers, we can observe multiple layers of
sponge-like capillary channels in the cross-sectional SEM images (Figure 6-4c-e). We found that
the porous structures are composed of amorphous titanium oxide, [198] which has high surface
energy [199], so the micro- and nano-structured surface can greatly enhance the wetting properties.
138
Figure 6-4. SEM images of surfaces fabricated by breakdown anodization (BDA). BDA was
conducted at the electric potential 120 V for 30 min with an acidic electrolyte (pH 3.0) at 10 'C.
The surface shows highly irregular micro porous structures (a)-(b) that have submicron scale-like
structures on the surface. The cross sectional area of the surface is composed of multi-layers of
amorphous titanium oxide, which have micro-scale wicking channels (c)-(e).
From the results of CRMs (Figure 6-5), we can confirm that the square of capillary height is
linearly proportional to time for the BDA surfaces, as expected from Washburn's equation.
Therefore, we can obtain the capillary pressure (Pcap) and the capillary diffusivity (Dcap) from the
CRM data of each BDA surface using equations (6-3) and (6-4). It is worth noting that the BDA
surfaces show approximately ten times higher capillary diffusivity and three times higher capillary
139
pressures than the commercial TLC plate, which is composed of 25 ptm silica particles with 200 ptm
thickness. The relatively large micro-scale pores and the channel-like nanostructures (Figure 6-4)
contribute to the high spreading speed and capillary pressure.
(b)
120 V at 10 *C
40
35
O 120Vat 25
30
25
8 60 V at 25 *C
C
o
15
0o
10
111"
a' "0.
U
0
0
5
15 20 25
Time (sec)
30
35
025 C
+506C
475 *C
-+75*C
1
100
0.5
50
0
10
010 *C
..- 15
&500C
d
cv.
(C) 200
*C
1.5
* TLC plate
20
*10 OC
2
-25
30
60
90
Poenil0
Potential
120
150
0
30
60
90
Potential
120
150
15
(
(a)
Figure 6-5. Results of the capillary rise measurements with highly wettable porous films produced
by breakdown anodization (BDA). As expected from Washburn's equation, the square of capillary
height is linear to time at initial region of rising time. The maximum capillary diffusivity is 155
mm2/s and the maximum capillary pressure is 1.75 kPa. These values are ten times and three times
higher than the commercial wicking sheet composed of micron SiO 2 particles (200 tm thickness of
25 ptm silica particles). Samples were produced by BDA with titanium plates (10 mm x 250 mm) in
pH 3.0 electrolytes. The gap distance between anode and cathode electrodes was 10 mm. The error
bars indicate
one standard deviation resulting from four measurements.
These high capillary pressure and fast capillary diffusivity are obtained when the anodization
potential is high and the electrolyte temperature is low, as shown in Figure 6-5b and c. This is due
to the correlation between the capillary properties (capillary pressure and capillary diffusivity) and
the surface roughness. The surface roughness decreases at high electrolyte temperature due to an
increased oxide dissolution rate. Therefore, the capillary pressure and capillary diffusivity are
relatively constant when the electrolyte temperature exceeds 50 'C (Figure 6-5b and c). However,
the capillary pressure is increases with anodization potential when the electrolyte temperature is less
140
than 25 *C. The capillary diffusivity also increases with anodization potential at low electrolyte
temperatures, except for 120 V at 10 *C. This deviation is due to the decrease in effective pore
radius resulting from the low oxide dissolution rate. This mechanism has been verified in our
previous work [198].
We explore two ways to alter capillary flows; surface width (e.g. cross sectional area) and the
electrode gap profiles. BDA surfaces produced by parallel electrodes have uniform capillary
pressure and capillary diffusivity on their surfaces due to the uniform electric field. However, to
alter capillary flows, the capillary pressure and capillary diffusivity must vary with rise height, as
shown in equation (6-10). We also see that the capillary flow can be manipulated by changing the
surface width. Under given options, first, we demonstrate capillary flows through surfaces produced
by BDA with various electrode shapes but uniform electrode spacing. In this case, the capillary
properties are constant but the surface width can be expressed as a function of the rise height. Next,
we use varying gap distance between electrodes instead of parallel electrodes to vary the local
electric field, resulting in spatially dependent capillary properties. The distance profile between
anode and cathode electrodes is expressed as a function of the capillary rise height.
6.4.1.
Case 1: Capillary flows with constant capillary
properties and varying surface width
Capillary flows were investigated on BDA surfaces with varying surface width. In addition,
chromatography papers (Gel-Blotting paper, 340
tm in thickness, Genesee Scientific) were
compared with BDA surfaces to show the general use of the conceptual model suggested. When the
electrode shape is a linear function of the rise height (R(h) = Clh + C 2 ), as shown in Figure 6-6a-b,
the capillary flows can be expressed with equation (6-12). If the electrode shapes vary exponentially
141
with rise height, e.g. R(h) = C2 eC
(Figure 6-6c-d), the capillary speed can be found from equation
h
(6-14). In both cases the capillary speed can be controlled by the constants C1, and C 2 . As shown in
Table 6-1, various electrode shapes with different values for Ci and C2 were used for surface
modification via BDA. Certain anodization conditions were held constant: electrolyte pH 3.0 and
temperature of 25 'C, 10 mm electrode spacing, and 90 V electric potential applied for 30 min.
Therefore, all BDA surfaces had the same capillary pressure and capillary diffusivity of 1.2 kPa and
133 mm 2 /s, respectively. For comparison, the chromatography papers were cut to the same shapes
as the electrodes shown in Figure 6-6 and Table 6-1. The capillary pressure and the capillary
diffusivity of the chromatography paper are 1.4 kPa and 18.7 mm 2 /s, respectively.
Refere nce
Type A
Type B
Type C
TY pe D
R(h)
R(h)
Th
R(h)
R(h)
_
-
R(h)=Clh+C
R(h)=Cc,"
2
Figure 6-6. Shapes of the BDA surfaces and the chromatography papers (Genesee Scientific) used
for the capillary rise measurements. Type A and B have linearly changed shape functions, and Type
C and D have exponentially changed shape functions. All BDA processes had the same condition of
electrolyte (pH 3.0 and 25 *C), electrode gap distance (10 mm), and electric potential (90 V for 30
min).
142
Table 6-1. Shape functions of the BDA surfaces and the chromatography papers used to verify the
alternation of capillary flows. As a reference, a BDA surface was produced with two parallel
electrodes, which have a constant width of 10 mm and an electrode gap distance of 10 mm.
Parameter
Function
[mm]
Reference
Type A-a
Type A-b
Type B-a
Type B-b
Type C-a
Type C-b
Type D-a
Type D-b
R(h)=Clh+C 2
R(h)=C 2 eCh
I
C,
C2
0
10.0
12.5
25.0
5.0
5.0
10.0
2.5
66.4
44.8
-0.075
-0.2
+0.075
+0.2
+20
+40
-20
-40
Equation (6-10) was compared with the corresponding experimental data for the electrode shapes
shown in Table 6-1. In the theoretical calculations, a water evaporation rate of 8.5 x 10-6 kg/m 2s
%
was employed (experimentally obtained in a typical laboratory atmosphere at 25 'C and 32
humidity) in equation (6-19). However, in the chromatography papers, water evaporation is
negligible because the papers are relatively thick to the BDA surfaces; therefore, at a given height
the evaporation rate is small relative to the flow rate. As shown in Figure 6-7, the theoretical
calculations show good agreement with the experimental data for the BDA surfaces and the
chromatography papers. As a result, the suggested equations can predict the capillary flow speeds
on the highly wettable surfaces with varying surface width, thus they can be used to design capillary
flows. The results also validate conceptual models shown in Figure 6-1 and Figure 6-2.
143
e9
Reference
Type A-a
-- 0-0
Type B-a
Type A-b
-- 0--
Type B-b
Type C-a
S
60
50
POO
- 9--Type D-a
-
40
4'
S
Type C-b
- 6--Type D-b
00
1
304r4
BDA surfaces
$ 9-
20
Papers
10.0
0
50
100
150
2(0
Time (sec)
Figure 6-7. Capillary flows on the BDA surfaces and the chromatography papers with the surface
shapes shown in Figure 6-6 and Table 6-1. The symbols and the lines indicate the experimental data
and the theoretical expectations calculated by equation (6-10). The gray small dots and solid-line
show the reference capillary rise on a constant width surface.
6.4.2.
Case 2: Capillary flows with constant surface width and
varying capillary properties
As shown in Figure 6-5, the capillary pressure and the capillary diffusivity are dependent upon
the anodization potential, particularly when the electrolyte temperature does not exceed 25 *C. It
means that capillary pressure and capillary diffusivity can be modified locally using the electric
field, which can vary spatially depending upon the electrode spacing. Therefore, tailoring capillary
flows is possible if we know how capillary pressure and capillary diffusivity vary with electrode
spacing. First, we fixed the electrolyte temperature at 25
144
0
C to find simple linear relationships
between the electric field and the resulting surface properties because the capillary properties
linearly increase with anodization potential at 25 'C, as shown in Figure 6-8.
2
*1
1.8
1.6
1.4
Ca.
U,
M Pcap: 30 V, 25 0C
* Pcap: 60 V, 25 *C
A Pcap: 90 V, 25 *C
* Pcap: 120 V, 25 *C
200
180
160
140
1.2
120
1
100
0.8
-
SDcap:
* Dcap:
* Dcap:
* Dcap:
-
0.6
80
0.4
0.2
0 1
0
0
I
10
a
20
M 2-- 0
E
60
30 V, 25 *C
60 V, 25 *C
90 V, 25 *C
120 V, 25 *C
a
E
40
20
0
0
30
Figure 6-8. Capillary pressure (Pcap) and capillary diffusivity (Dap) with respect to surface
roughness (Ra) and electric potential (V) of breakdown anodization (BDA) at the electrolyte
temperature of 25 'C. The box, circle, triangle, and diamond symbols indicate the electric potentials
of 30 V, 60 V, 90 V, and 120 V, respectively. The red and the white colors inside the symbols
correspond to the capillary pressure and the capillary diffusivity, respectively. When the electrolyte
temperature is 25 'C, the capillary pressure and the capillary diffusivity are linearly proportional to
the surface roughness, which is linearly enhanced by the electric potential of BDA. The error bars
indicate + one standard deviation.
Varying electrode gap distance was employed during BDA, as shown in Figure 6-9a, to find the
relationship between the gap distance and the capillary pressure. The gap distance between the two
parallel electrodes was varied from 10 mm to 85 mm while BDA was conducted at 120 V for 30
145
min at 25 *C. At the specified BDA conditions, the capillary pressure linearly decreases with
increasing electrode spacing, as shown in Figure 6-9b. Therefore, we can find an empirical
relationship between electrode spacing and capillary pressure. As a result, when the electrode
spacing varies linearly with the height, the capillary pressure and capillary diffusivity also vary
linearly with respect to height. This linear variation can be expressed by Pcap(x) = PI-x + P2 [kPa]
and Dcap(x) = DIx + D2 [m2/s], where PI, P2, D, and D2 are constants obtained from the
experimental data. For the case of BDA at 120 V and 25 0C, PI, P2 , D, and D2 are -8.2x103, 1.76,
1.04x1 06 and 2.6x1 0 -4, respectively, when x is in millimeters. In addition, the semi-empirical
relationship between the surface roughness and electrode spacing can be obtained from Figure 6-9b.
At the specified conditions, the surface roughness is a linear function of electrode spacing, Ra(x)=
Rjx + R2 [pm], where R, and R 2 are constants: R1 = -0.21 and R 2 = 27.57 when x is in millimeters.
146
(b)
(a)
10
2
40
1.8
35
1.6
30 z
1.4
0.
1.2
2520
20
1
0
0.8
't
0.6
o Capillary
0.4
o Surface
0.2
h
15
0
0
0
pressure
roughness
5
.
0
x
C
0
10 20 30 40 50 60 70 80 90
Electrode gap distance (mm)
Figure 6-9. Capillary pressure and surface roughness produced by breakdown anodization (BDA)
with varying electrode gap distance, x. (a) Two parallel electrodes were used with varying the
electrode gap distance (x) in BDA processes. (b) The capillary pressure and the surface roughness
are inversely proportional to the electrode gap distance. The electric potential of 120 V and an
electrolyte temperature of 25 C were used to produce the BDA surfaces. The error bars indicate
one standard deviation.
To produce functionally varied capillary properties, we employed height dependent electrode
spacing for (a)-(b) (linear) and (c)-(d) (quadratic), as shown in Figure 6-10. Expressions for the
height dependent electrode spacing are shown in Table 6-2. Because the electrode spacing is a
function of height: x = J(h), as shown in Table 6-2, the capillary pressure can be expressed as a
function of the height, i.e. Pcap(x) = P1 -j(h)+ P2 . The BDA conditions were 120 V for 30 min at pH
3.0 and 25 'C, in each case.
147
Reference
Type A
Type B
Type C
Type D
T
E
E
E
E
0
E
E
65 mm
E
E
thi
10 mm
E
E
0
0
80mm
-80 mm
E
x
6 mm
x
120 mm
(a)
10 MM
(b)
+
H
10 mm
90 mm
(c)
(d)
Figure 6-10. Electrode distance profiles used in breakdown anodization (BDA) processes. The
constant gap distance profile was used to produce a reference surface. Four different gap profiles,
which linearly change (a)-(b) and quadratically change (c)-(d), were used in BDA processes. All
BDA processes had the same condition of electrolyte (pH 3.0 and 25 C), electrode width (10 mm),
and electric potential (120 V and 30 min). The left side electrodes (the red lines) in each image
indicate the anode electrodes converted to highly wetting porous surfaces. The anode electrodes
have different surface heights (H).
148
Table 6-2. Profile functions of electrode gap distance shown in Figure 6-10. In Type A and B,
linearly changed gap distance was employed. Circular shape electrodes were used in Tape C and D.
The reference BDA surface was produced with a constant electrode gap distance of 10 mm.
Function
Reference
Type A
Parameter
[mm]
C,
C2
xCihC 2
0
0.5
0.9
-0.9
Type C
x=Ch+C 2, 0 h < 60
x=Ch+C 2,60 h
(x-C,)2+(h-C2)2=C 22
10
120
10
65
10
80
Type D
(x-(C,+C 2)) 2+(h-C 2)2=C 22
10
80
Type B
Capillary rise measurements were conducted on the surfaces produced using the electrode
configurations shown in Figure 6-10. The capillary flow speed can be found from equation (6-10)
because the capillary pressure and capillary diffusivity are known from the results of Figure 6-9 and
the electrode gap profiles from Table 6-2. Equation (6-10) is compared with experimental data, and
the theoretical calculations show good agreement with the experiments, as shown in Figure 6-11.
149
250
200
150
Ee
00
-:
100
SReference
0 Type A
M Type B
50
50
0 Type C
0
0
200
400
600
Type D
800
1000
Time (sec)
Figure 6-11. Capillary flows on surfaces produced by breakdown anodization (BDA) with the
electrode gap profiles shown in Figure 6-10 and Table 6-2. The solid lines and the symbols indicate
the theoretical data and the experimental data, respectively. The solid-circle, solid-box, circle, and
box symbols are obtained with the electrode configurations shown in Figure 6-1 Oa, (b), (c) and (d),
respectively. BDA surfaces were produced with different electrode gap profiles but the same BDA
conditions: 120 V for 30 min in pH 3.0 electrolyte at 25 'C.
The surface roughness (Ra) was measured on the surfaces used in Figure 6-11. In our previous
work, we showed that the surface roughness is linearly proportional to the effective pore radius of
BDA surfaces [198]. Surface roughness is predictable using the relationship between surface
roughness and electrode spacing found from Figure 6-9. With the profile functions shown in Table
6-2, the surface roughness can be expressed as a function of the capillary height, i.e. Ra(h) = Rrf(h)
+ R 2. From
150
20
Figure 6-12, we can see that the surface roughness varies with capillary height and there is good
agreement between the experimental data (symbols) and the predictions (dashed-lines). This result
indicates that BDA can effectively produce functionally graded porous structures with designed
electric fields. From Figure 6-9b, we found that capillary pressure is a linear function of electrode
spacing. This relationship is also evident in Figure 6-12.
Type A
Type B
Type C
Type D
1
0.8
-
0.9
0.7
-a
-
0.6
CD
75
0.5
cc 0.4
Of
a
4-
0.3
0
0.2
2
I
0.1
0
0
10
20
30 0
10
20
30
0
10
20 30
Surface roughness (pmn)
Figure 6-12. Surface roughness changes with respect to the non-dimensional height of surfaces
produced by the electrode profiles shown in Figure 6-10 and Table 6-2. The surface height (H)
shown in Figure 6-10 was used to obtain the non-dimensional capillary height in the x-axis. The
surface roughness (Ra) is functionally varied according to the profiles of electrode gap distance.
The symbols and the dashed-lines indicate the measured data and the predictive data, respectively.
The predictive data were obtained from the relationship between the surface roughness and the
electrode gap distance.
151
6.5.
Conclusions
We've shown that breakdown anodization (BDA) can produce highly wettable porous films with
high capillary pressure and capillary diffusivity. These properties are attributed to the micro/nano
scale amorphous titanium dioxide structures. High anodization potentials and low temperatures are
necessary to yield hierarchical surface features.
In BDA, we used various electrode configurations to control capillary flows on the surfaces. We
successfully varied capillary pressure and capillary diffusivity on BDA surfaces by varying
electrode spacing. The alteration of wetting properties is attributed to changes in surface
morphology. Surface roughness of the BDA surfaces showed good correlation with electrode
spacing.
To predict the capillary flows, we suggested a conceptual model of highly wettable porous films.
From this model, we obtained simple equations of capillary flows dependent upon surface width
and capillary properties. Capillary flows on BDA surfaces and chromatography papers showed good
agreement with the theoretical predictions.
This work shows that capillary flows on BDA surfaces can be effectively manipulated with the
applied electric field and electrode configurations. The suggested formulas and the corresponding
BDA processes can be used to tailor capillary flows for applications including paper based
microfluidic devices and chromatographic analysis. This promotes new opportunities to develop
novel devices employing the control of capillary flows.
152
Chapter 7. Scaling Laws for Drop Impingement
on Thin Porous Media
Reproduced in part with permission from
Young Soo Joung, Cullen R. Buie, "Scaling Laws for Drop Impingement on Porous Films and
Papers,"PhysicalReview E, 89, 013015 (2014).
Copyright 2014 American Physical Society.
153
7.1.
Introduction
Interesting phenomena can be observed when a droplet impacts liquid or solid surfaces. The
crown formation of milk droplets upon impact with water represents a well-known example of this
phenomena [200]. Recently, however, drop impingement on solid surfaces has gained significant
attention. This is largely due to state of the art micro and nano fabrication methods which have
enabled novel functional surfaces. Among the functionalized surfaces, superhydrophobic surfaces
have been a major thrust [201, 202] in part due to their unique impingement properties. Conversely,
drop impingement on highly wetting porous films has been largely neglected. Though there have
been investigations on the dynamic behaviors of droplets on porous media [203-207], most studies
have explored thick surfaces where the droplet radius is negligible compared to the substrate
thickness.
In this study we investigate droplet dynamics on highly wetting thin porous surfaces. First, we
present a modified energy equation accounting for capillary effects that successfully captures
droplet spreading upon impact on highly wetting porous surfaces. The modified energy equation
reveals a dimensionless parameter denoted the capillary-Weber number, which expresses the
relative influence of the matrix potential and the kinetic energy of the impinging drop. Additionally,
dimensional analysis leads to a new non-dimensional parameter, which we will call the WashburnReynolds number (Rew), which strongly correlates with impingement modes on highly wetting
porous surfaces. The Washburn-Reynolds number balances inertial effects of the impinging droplet
and capillary transport in the porous film.
154
7.2.
7.2.1.
Experimental
Preparation of micro and nanoporous films
Electrophoretic deposition (EPD) and breakdown anodization (BDA) were used to produce highly
wetting micro/nano porous surfaces [73, 196]. For EPD, TiO 2 nanoparticles (20 nm, anatase,
Sigma-Aldrich) and acetic acid were used to make 1 g/L TiO 2 suspensions. Electric potentials up to
120 V were supplied for 10-30 min during the anodization process to make thin films on the
substrate. DI water pH was adjusted to pH = 3 using nitric acid (70 % ACS reagent, Sigma-Aldrich)
for the electrolyte during BDA. The electrolyte was maintained at a specified temperature using a
water reservoir surrounding the BDA cell. Titanium plates (Ultra-Corrosion-Resistant Titanium
Grade 2, 0.020 inches thick, McMaster) were used as anode and cathode for both EPD and BDA.
BDA was conducted first to make micro-porous layers followed by EPD of TiO 2 nanoparticles on
the micro porous layers to realize hierarchical structures. In BDA, the electric potential and the
anodization time were varied to obtain different surface properties. In EPD, however, the same
conditions were used on each surface to provide consistent nanoscale features. BDA results in
micro-scale porous titania surfaces on titanium substrates (Figure 7-la). Nanoscale porous layers
were produced by EPD on the micro porous surfaces with titanium dioxide nanoparticles (Figure
7-1b).
155
Figure 7-1. SEM images of as-prepared surfaces show micro-scale and nano-scale porous structures
produced by breakdown anodization (BDA) (a) and electrophoretic deposition (EPD) (b),
respectively [198]. The combined BDA/EPD process yields highly wetting micro/nano scale
hierarchical porous structures.
The resulting surfaces display effective contact angles near zero degrees with high capillary
pressures and spreading speeds. The porous surfaces showed near perfect wetting for several liquids
including water, ethanol, ethylene glycol, and glycerol. The surfaces can be characterized with
respect to capillary pressure, Pcap, and spreading speed constant, Dcap, through capillary rise
measurements [180]. The capillary rise height, h, can be expressed as h2 = 'Dcapt (Washburn's
equation) [172], with Dcap = rcycos0/p, and rc is the capillary radius, y is the liquid surface tension,
0 is the native contact angle of capillary surface, and p is dynamic viscosity of the liquid. The value
of Dcap can be determined by the gradient of the time dependent experimental capillary rise height.
Capillary pressure can be obtained from the maximum rise height, hmax, and is expressed by Pcap =
pghmax= 2ycos0 Irc.
156
7.2.2.
Four impingement modes on wettable porous films
When liquid droplets impact the surfaces, we observed four impingement modes (Figure 7-2). We
find that impingement modes are determined by the value of Rew = Uoprecos9/p. Mode-Al
consists of oscillating and spreading of the droplet. In Mode-A2 the droplets show necking followed
by fast spreading. Mode-B consists of smooth spreading without oscillations or necking. Finally,
Mode-C is characterized by radial jetting and spreading.
Mode-Al
Rew=0.01
Mode-A2
Ref=fO.I
Mode-B
Rew=0.5
wm
12m
60m
Mode-C
Rew=2.0
Figure 7-2. Droplets show four different impingement modes depending on the WashburnReynolds number after impacting highly wetting porous surfaces. The Washburn-Reynolds number
can be expressed as Rew = Uoprecos9 /t, where U is the impact velocity, p is the liquid density, r,
is the effective capillary radius, 0 is the surface contact angle, and pt is the liquid viscosity. ModeAl: compressing-oscillating, Mode-A2: necking and spreading, Mode-B: spreading, and Mode-C:
radial jetting and spreading. A high-speed camera (Photron) was used to record the behavior of
liquid droplets on the surfaces. The scale bar in each image is 1 mm.
157
Table 7-1. Liquid and surface properties used in the drop impingement experiments and numerical
simulations. The properties of the glycerol and water mixture were obtained from the literature
[208]. Highly wetting porous titania (TiO 2 ) surfaces were produced by an electrochemical
fabrication method [198]. The porous titania surfaces showed wide variations in capillary pressure
and spreading speed. The thin layer chromatography (TLC) plates were obtained from SigmaAldrich. The Gel-Blotting paper is a chromatography paper (grade 230) obtained from Genesee
Scientific. The coffee filter is a commercial product made by Melitta USA, Inc. The symbols
correspond to the symbols in the plot of drop impingement modes (Figure 7-8).
Effective
Surface
Symbol
A
B
C
D
E
F
G
H
I
J
K
L
M
N
0
P
Liquid
Water
Porous Titania surface I
Water
Porous Titania surface I
Water
Porous Titania surface I
Water
Porous Titania surfae 2
Water
Porous Titania surface 3
Water
Porous Titania surface4
Ethanol
Porous Ttia surface 5
Ethyleneglycol
Porous Titania surface 8
Porous Tilanlasurface 8 Glycerol60 %+ water 40 %
Porous Titania surface 8 Glycerol90 %+ water10 %
Glycerol
Porous Titania surface 7
SJoaTLC
Water
Water
Ceuose TLC
Water
Ahuminum TLC
Water
Ge-loftng piper
Water
Coffoeflter
7.3.
7.3.1.
pore radius
re
(
10.6
10.6
10.6
13.4
13.1
13
8.85
28
25
21
13.6
4.2
5.8
5.1
5.6
7.9
Layer
Droplet
Surface
thicitess diameter tension
H
Win)
(urn)
8.6
8.6
8.6
9.2
9.2
9.2
9.5
10.5
10.5
10.5
9.4
250
100
250
340
120
Do
(mm)
2.8
2.2
5
2.8
2.8
2.8
2.2
2.8
3
2.9
2.8
2.8
2.8
2.8
2.8
2.8
y
(mN/m)
72.8
72.8
72.8
72.8
72.8
72.8
22.3
47.3
67
63.6
63
72.8
72.8
72.8
72.8
72.8
Viacoelty
i
(cP)
0.9
0.9
0.9
0.9
0.9
0.9
1.1
16
9
164
1258
0.9
0.9
0.9
0.9
0.9
y
p
(kgWrm)
998
998
998
998
998
998
789
1113
1154
1232
1261
996
998
998
998
998
Capilary
pressure
PW
(Pa)
783
783
783
1048
930
773
1084
863
733
665
495
959
1076
1546
1395
1420
Hydraulic
diffusivity
Dow
(mfs)
49
49
49
104.4
88.6
72.2
38.6
21.0
19.8
0.85
0.37
9.5
20.4
22.4
24.0
60.4
Theory
Energy conservation of a cylindrical model of droplets
Energy conservation is employed to predict droplet spreading upon impact. The energy
conservation approach has shown good agreement with experiments, and it has helped to find useful
scaling parameters for droplet dynamics [209-211 ]. In this study we modify the energy equation
with two additional terms accounting for viscous dissipation inside porous media and the matrix
158
potential, which we denote as (D, and Em,,p, respectively. The modified energy equation can be
expressed as
=0
.,+ t,+P,+k+D,+9,+9
(7.)
where Ek is the droplet kinetic energy, Eg is the gravitational potential energy, E, is the surface
energy of the droplet, D1 is line dissipation, and (D, is viscous dissipation inside the droplet.
For simplicity, we model water droplets impacting solid surfaces as cylinders with a time
dependent radius, R(t), and height, H(t) (Figure 7-3) [209, 210]. The model droplet has the same
volume as the actual droplet. Assuming mass conservation (neglecting evaporation) and fluid
incompressibility, the height and radius have the following relationship:
H(t)=
where
K, is the volume
,V
JrR (t)2
of the actual droplet with an initial diameter, D. The modeled droplet has
the same impact velocity as the actual droplet and thus the same kinetic energy.
159
UO: droplet velocity
Figure 7-3. Schematic diagram of the cylindrical droplet impact model with time dependent radius,
R(t), and height, H(t). The model cylindrical droplet has the same volume and impact velocity as the
real droplet.
7.3.2.
Kinetic energy
The kinetic energy of a droplet after impact can be calculated from the internal velocity field in
the droplet. In the cylindrical model, we assume flow in the droplet is irrotational [212]. The
vertical flow velocity, v, and the radial flow velocity, vr, can be defined as,
v =-2--
z dR
Rdt
r dR
R dt
and vr=-.
These velocities are internal flow velocities at a specific instant such that R and dR/dt are spatially
independent. The kinetic energy of the droplet can be obtained by integrating the internal velocities
over the droplet volume, -V 0, as follows:
160
E,=-y(+g#=--02
p
C
4iR6
2 (2
3 7?2R)
1
-+-
==
2
1
r
.
2
,6
i827R*
(7-2)
with the initial droplet kinetic energy, Ek,, = %pV 0 U0 2 , the dimensionless drop radius, R*
=
R(t)I(Dd/2), and the dimensionless time, t* = t-Uo/DO.
7.3.3.
Gravitational energy
Utilizing the location of the time dependent center of mass, H(t)12, gravitational energy can be
determined:
2 1
H~t) _pgV2
Eg=pg4-o
=
=Eg
32
2
2
2,rR
3R
(7-3)
where the initial droplet gravitational energy is defined as, Eg,o = %/2pgV0 D.
7.3.4.
Droplet surface energy
The surface energy of a droplet on a solid surface can be calculated by integrating the surface
tension of the entire surface, A. In the cylindrical impact model, the surface tension of the liquidsolid interface can be obtained with Young's equation, and the surface energy is found to be
E, = Ld
=r(A,, - -4,At, cos , ),
161
where Aair is the droplet surface area in contact with air, A,,,t is the wetted area (the projected area of
the solid-liquid interface), and 0, is the equilibrium contact angle on the surface. Since the surfaces
used in this work exhibit complete wetting (i.e. contact angle near zero), the equation for a
cylindrical droplet can be reduced as follows:
2ry o =-2 ayg,, =_,2 E,
E= 27iRH=
R
3 k
3
(74)
.
with the initial droplet surface energy, Eso = nyDO 2
7.3.5.
Line dissipation
Dissipation occurs in the process of moving the contact line and the amount is proportional to the
contact line speed, VR, and an effective viscosity, PL. According to the de Gennes approach [213],
the line dissipation can be expressed by
12
(DI =-pL
2
1
8
S
VRdS=PL
s
YR d-
R
2
L
where, S is the moving contact line,
dt
2( R2
dR*2=D
dt*
VR
is the line velocity,
obtained from
162
(7-5)
R* (dR
4 dt*
1,o
= Y2pLTDO
U02 , and pL can be
31*
where 1* = ln(lmax/min) with maximum length scale, 1m. (the droplet diameter), minimum length
scale, min (the microscopic length scale, 2r, in this work), and 0, the sliding contact angle, which is
the contact angle at the interface of the droplet, the top surface of the porous layer, and air when the
droplet is spreading, as shown in Figure 7-4. In other words, the sliding contact angle is the
advancing contact angle of the spreading droplet. Sliding contact angles were experimentally
obtained from high speed images at 2R/D0 =2.5 when the actual droplets were spreading after impact,
e.g. to obtain Figure 7-6, sliding contact angles were determined to be 2.60, 2.90, 7.4', 5.7*, and
19.60 for water, ethanol, ethylene glycol, a 60/40 (v/v) glycerol and water mixture, and a 90/10 (v/v)
glycerol and water mixture, respectively.
Viscous dissipation inside a droplet
The total viscous dissipation in the boundary layer can be found by integrating the shear stress,
,
7.3.6.
multiplied by slip velocity, vs, for the non-slip area, As. To calculate the shear stress generated in the
boundary layer inside the droplet, the boundary layer thickness must be estimated. It is clear that the
boundary layer thickness is time-dependent from lubrication theory, and the time-dependent
boundary layer thickness has shown close agreement with experimental results [214, 215]. However,
to simplify the analysis, we employ a time-independent boundary layer thickness assuming
irrotational flow inside the droplet. In the literatures [210-212, 216], others have successfully
formulated the kinetic energy and the viscous dissipation assuming irrotational flow and timeindependent boundary layer thickness to predict the droplet behaviors. To calculate the shear stress,
163
we assumed that the effective boundary layer thickness is D/(2fb), where fb is a correction factor,
which was proposed by Bechtel et al. [211]. The slip velocity, v,, was assumed to be the radial
velocity, vr, and the non-slip area is equal to the projected area of the cylinder. Thus, we obtain the
following expression for viscous dissipation,
J4
'
-rsd4-A ~,
S
4
Ir APR 2(
dR
2 D
dt
fbU
D0
2
vrdA
R
I
'"64 A
d
d2R*
2
(7-6)
)
D, =
dt*
with
Dvr=
2
andf4=j,
where the Ohnesorge number is Oh = p/(pyD 0 )".
7.3.7.
Matrix potential
Matrix potential is the surface energy inside the capillary network that drives fluid transport [217].
The matrix potential is proportional to the wetted volume of the porous region and the capillary
pressure [218]. Taking the droplet as the system of interest, work is done on the droplet so the
matrix potential can be expressed as
E =,HR
2
164
=-f
(7-7)
where
4
,,t is the wetted volume of the porous region, H, is the height of the porous region, f, is the
ratio of the height of the porous region to the pore diameter, 2re,
(
=
He/2r,) (Figure 7-4), and E,,,,,
is the reference matrix potential,
Emp,
.>
= 2cr,PpKr
Here, the thickness, He, is the average height of the porous layer considering its void volume
measured by a profilometer (Measurement system: Tencor P-16 Surface Profilometer (TM)). The
negative sign indicates that energy is put into the droplet.
7.3.8.
Viscous dissipation within the porous media
The shear stress, xc, in the porous region can be approximated in the same manner used to
estimate the viscous dissipation in the droplet (equation (7-6)) as follows:
c
.
CP Vr
where v,. is the flow velocity in the porous region at a distance R from the center of the droplet
(Figure 7-4). If we assume that the contact line of the droplet coincides with the wetted boundary of
the porous region, the total viscous dissipation inside the porous region can be expressed as
165
,4
~-7R
cv=
=o16,V 4 r2
-
(Dc =f zd
2r
(7-8)
,)
where A, is the non-slip area of the porous region and the characteristic viscous dissipation can be
expressed as,
= pV-wet,o
,
<De
r
7
and the reference volume of the wetted porous region is -J ,o=rHDo2/4.
2r4
R
I
I2rc
Hc=fc-2rc
Vr
I
Droplet
Porous layer
HcI
Solid substrate
I R
Figure 7-4. Schematic diagram of capillary flow for the assumed cylindrical droplet geometry. The
porous region can be considered as several cylindrical capillaries in parallel, each having a height,
2rc. The porous region has height, He, and the flow velocity, Vr, at a distance, R(t), from the center,
assuming the ratio of the height of the porous region to the initial droplet diameter, H/D0 , is small.
6, is the sliding contact angle, the contact angle of the droplet on the top surface of the porous layer
during spreading.
166
7.3.9.
Dimensionless energy equation with the capillary-Weber
number
When equations (7-2) to (7-8) are substituted into equation (7-1), the final energy conservation
equation can be obtained as a function of the time dependent droplet radius,
UO d
1
8
E
16 1 ) (dR*
dt*
27 R*6
2
2 1
2E
+E'"o3 - 2 +3 R
3 R. )2 1 R(dR. 2
R2 t
'64 .t0' 64
"'"16
*2
-EP,oR
=0
We can divide this equation by Eko-(Uo/Do) to obtain a dimensionless energy equation:
1
TdI 8
+
f3
1
dt 8Re2dt* 8 ReC dt = 2 Re
16 1
27R*
dR*
2 1
d R**2
1
S2(7-9)
*2 IdR*
3 1
. dR*
.
8
1
12 R*2
e R*Wee
+3
+
R*2 ( dR*
(
d
0
Here, the initial drop diameter, Do, and impact velocity, UO, are used to formulate a dimensionless
time, t* = t/(D/Uo), andfL
=
pL/p is the dimensionless contact line viscosity. The first term is the
kinetic energy of droplet. The gravitational energy and the surface energy are a function of the
Froude number, Fr = U0 IgDo, and the Weber number, We = pDOU 0 2/y, respectively. The matrix
potential is a function of the capillary-Weber number, Wec, where
167
We
pD0 U
fyrcos0
Eko
E,
p U0
F,,oP,
(7-10)
The capillary-Weber number is the ratio of the initial kinetic energy (Eko) of the droplet to the
= Hx7r(Do/2)2
)
reference matrix potential (Emp,o) corresponding to the initial wetted volume (,,et,o
of the surface. In the case of either Hc=O (no porous region) or 9=90' (non-wetting), the capillary
energy term is negligible. In the dissipation terms, we can see the dimensionless contact line
viscosity,fL = pLp, the Reynolds number, Re = pDOUO/p, and the capillary-Reynolds number, Rec=
.
prcUO/P
To solve equation (7-9) numerically, the initial conditions were specified in order to yield the
same surface energy and kinetic energy as the real droplet [210]. Therefore, the radius and the
impact velocity of the cylindrical model droplet are slightly different from those of the real droplet
used in the drop impingement experiment. First, we set the initial radius of the cylindrical model
droplet as R(0) = D,/2. The initial height of the cylindrical model droplet, H(0), can be calculated
using mass conservation as H(O) = Vd/(nR(0) 2), where V = 1/6nD"3 . The cylindrical model droplet
has the same initial surface area as the real droplet, Amocie = Areai, where Amodel and Areal are the
surface areas of the cylindrical model droplet with radius R(0) and the real droplet with radius Rreal,
respectively. This information is used to calculate the initial radius of the cylindrical model droplet.
2
The cylindrical model droplet has the same initial kinetic energy as the real droplet; %p V U
00
2p
Vrea Ureai 2, where Vrai and Ureai are the volume and the impact velocity of the real droplet used in
the experiment. The initial spreading speed of the droplet radius, dR/dt,=o, can be calculated using
equation (7-2). As a result, the initial conditions for equation (7-9) are R*(0) = 1 and dR*/dt*t=o
=
1.18.
We find that each dissipation term in equation (7-9) has different significance depending on Wee,
168
as shown schematically in Figure 7-5. Contact line dissipation and viscous dissipation inside the
droplet are important at high Wec (Figure 7-5a). However, for low We, (Wee < 10), viscous
dissipation inside the porous region is the main dissipation term in equation (7-1). As depicted in
Figure 7-5b, line dissipation and viscous dissipation are negligible at low Wec because droplet
expansion can be considered as a free surface flow driven by the capillary pressure in the porous
region.
(b)
Viscous dissipation
Contact line inside the droplet
Solid substrate
dissipation
(a)
Viscous dissipation
inside the porous layer
Porous layer
Capillary energy driven flow
Kinetic energy driven flow
Figure 7-5. Schematic illustrations of droplet spreading on highly wetting porous surfaces. At high
capillary-Weber numbers (Wee > 103), the kinetic energy determines droplet expansion, while the
contact line and viscous effects dissipate mechanical energy (a). At low capillary-Weber numbers
(Wec < 10), the capillary energy governs droplet spreading, and viscous dissipation is most
prominent inside the porous region (b).
7.4.
7.4.1.
Results and discussion
Simplified energy equation at high capillary-Weber
number
In Figure 7-6, we compare the predicted droplet spreading obtained from equation (7-9) with the
169
experimental results when Wee > 103. The liquid and surface properties utilized are given in Table
7-1. As suggested in Figure 7-5, viscous dissipation inside the porous layer was not considered in
the energy equation for high Wee. The surfaces showed varying Pcap and Dcap values depending on
the liquid utilized. The predicted droplet spreading is in good agreement with the experimental data
(Figure 7-6). This suggests that the matrix potential is essential to appropriately predict droplet
spreading. In spite of the geometrical simplifications, the energy equation captures the major energy
transfer mechanisms during impingement.
We derived simplified energy conservation equations for four cases with different We, Fr, and
We, regimes to investigate the dependence of R*(t) on each dimensionless parameter. To simplify
the expressions, we ignored the constant values of each term and consider the line dissipation
dominant because Rexff' is smaller than the other dissipation terms, as shown in Figure 7-6. In
addition, the initial conditions of R*(O) = 0 and/or dR*/dt*,=o = 1 are used to derive the simplified
expressions as functions of well-known dimensionless parameters. These initial conditions are
different from those of the numerical solutions shown in Figure 7-6. Table 7-2 provides a summary
of the simplified energy equations and the dimensionless droplet radius change with different ranges
of We, Fr, Wec. From Table 7-2, we see that the gravitational energy and the surface energy do not
significantly affect droplet spreading. The kinetic energy influences expansion largely in the initial
stage of impact, and the radius is asymptotes to a specific value dependent upon the Re. With
respect to the matrix potential, the dimensionless droplet radius increases linearly with time, and the
expansion rate is proportional to the ratio of Re to Wec. As the matrix potential is dominant in Table
7-2, equation (7-9) can be simplified to dR*/dt*~Re/Wec for large t* when the kinetic energy is
dissipated (We0 << 1). This simplified equation means that the droplet expansion rate is determined
by the ratio of Re to We0 . Therefore, theoretically, R(t)* does not achieve a constant value if the
capillary pressure (Pcap) is non-zero. In Figure 7-6, the curves for highly viscous liquids appear to
170
converge to constant values but in actuality they slightly increase at a rate of Re/We. In Figure 7-6,
the initial drastic increase of R* is mainly attributed by the kinetic energy, and the linear increase of
R* after the initial stage of impact is due to the matrix potential. As a result, the assumption that the
line dissipation is dominant can be justified by comparing the simplified energy equations and the
experimental data in Figure 7-6. The kinetic energy and the matrix potential are the main driving
forces for droplet spreading when We >> 1 and We0 << 1, respectively.
Table 7-2. Simplified energy conservation equation and dimensionless droplet radius at different
physical regimes. The line dissipation in equation (7-9) is considered dominant and the other
dissipation terms are ignored to obtain simplified energy conservation equations as functions of
common dimensionless parameters. The dimensionless droplet radius can be expressed as a function
of the Reynolds number and another dimensionless parameter; therefore, we can characterize the
droplet radius change with respect to the relative influence of the Reynolds number.
Dominant
Dimensionless
effect
Simplified energy equation
parameters
d rrdR'f
-) R (
R* =Kinetic
e tanh4 energy
t* asymptoticto We>>
Re%
1, Fr >>1, Wee>> 1
Gravitational
potential energy
Surface energy
We << 1, Fr >> 1, Wee>> 1
C
Matrx potential
energy
e
droplet radius
Characteristic
smpoi oR
.)
~
d
We >> 1, Fr << 1, We >> 1
1
Dimensionless
d*
2
1 (1(2Re
dt FrR
eFr)
-
dt* kWe R*
d
I
dt
We,
R* =(R-t*rt
R*
-
Re
R*
Re
171
2
RR
(R*2
R* =
dt *
dt*
(~we
*d=
We.
t)
weak
due
to the
powerofl1/5
rdfIto the
power of 1/4
linearly proportional
to Re/Wee.
7.4.2.
Simplified energy equation at low capillary-Weber
number
In the case of We. < 10, viscous dissipation in the porous region is the dominant dissipation
mechanism and the other dissipation terms are ignored, as shown in Figure 7-5. To justify this
assumption, note that Re, is small relative to Re in the energy equation. When Re, and Re are
compared in the dissipation terms, however, we must carefully consider the no-slip area (A,). In the
viscous dissipation inside the droplet and the line dissipation, the contact surface between the
droplet and the surface is assumed as the no-slip surface. This assumption is valid when We0 is
sufficiently high (We0 > 103). When We. is small, however, the no-slip surface becomes a slip
boundary because the flows inside the porous layer induce spreading via capillary pressure.
Therefore, the viscous dissipation inside the droplet and the line dissipation are negligible when
We0 is small (We, < 10). Furthermore, gravitational energy and droplet surface energy are much
weaker than the matrix potential when We0 < 10 and R* > 1. Therefore, the energy equation
becomes a function of the viscous dissipation and matrix potential. In this case equation (7-9) for the
dimensionless droplet radius becomes
d
dt
12
1
R
3
R*2 +---fR
We'
Rec 8
.
dR*
2-,
dt*)
=0.
From equation (7-11), the dimensionless droplet expansion rate is found to be
dR*
dt
64 Re
--,- --64
c.=
-
1
f We. R
D*
(7-12)
R*
By integrating equation (7-12), the droplet radius can be expressed as
172
(7-11)
R
12=
t*=128D t*
2 8 IR
fc Wec
(7-13)
As a result, R(t)* is only dependent to t* and Dcap* and the initial condition of equation (7-13) is not
needed.
Equation (7-13) effectively predicts the droplet radius change on wetting surfaces at low We,, as
shown in Figure 7-7. Here the independent axis is Dcap*xt* and the dependent axis is R*2 in Figure
7-7 to display the linearity of equation (7-13) and the corresponding experimental data. We used
We, less than 100 for the drop impingement experiments in Figure 7-7, but the theoretical data
obtained from equation (7-13) assumes that We, is less than 10. Our intent was to show that the
experimental data becomes closer to the theoretical data when their We, is close to 10. As shown in
Figure 7-7, the experimental data obtained with We0 higher than 10 show larger deviations from the
theoretical data. However, the nearly linear experimental data obtained when We, is higher than 10
is recovered after initial impact because the kinetic energy is dissipated through the initial moments
of droplet expansion. We0 only reflects the initial impact speed of the droplet. Therefore, after the
droplet loses it's kinetic energy the expansion more closely follows the theoretical prediction. This
is why droplets with We, higher than 10 show nonlinearity in the initial impact region. It reveals
that the droplet expansion rate at low We is governed by hydraulic diffusivity, Dcap. In highly
viscous liquids, the initial kinetic energy is dissipated through droplet deformation resulting from
viscous effects inside the droplet after impact. The impingement modes of highly viscous liquids are
confined to Mode-A and mainly governed by the matrix potential.
173
6
0
Experimental date
5
00
4O
R* 3
2
100
Kinetic
energy
Matric potential
dominant
dominant
0
Data Surface
15
10
5
0
Wec RexfC1 Rexfb 1 R
Fr
We
355
212
69
374
224
73
14700 27.9
7100 21.6
4100 12.3
258.0
199.5
114.1
Rew
Mode
83.4
64.5
38.8
2.1
1.6
0.9
B
B
B
'xf
1
2
3
A
A
A
4
G
89
149
1400
7.0
91.8
16.6
1.9
B
5
6
7
1
H
J
265
427
205
402 15200
772 17800
327 17800
8.0
6.8
1.5
82.9
76.7
146.0
47.4
38.8
1.7
1.9
1.7
0.1
B
B
Al
Figure 7-6. Theoretical and experimental droplet spreading for multiple liquids after impact on
highly wetting porous surfaces. Solid lines represent spreading radii obtained from equation (7-9)
while circles are experimental data. The impact velocities are selected such that Wec exceeds 103.
The table provides the surface and liquid properties and the dimensionless parameters of the energy
equation for each data set. Viscous dissipation inside the porous layer, which is the column
highlighted in gray in the table, is not considered when Wec > 103. Here we only considered
impingement Mode-Al and Mode-B because the droplet mass is not conserved in Mode-A2 and
Mode-C due to necking and jetting behavior, respectively.
174
10
9
8
7
6
R
2
5
4
0 1. Water
3
0 2. Ethanol
2
A 3. Ethylene glycol
* 4. Glycerol 60%
5. Glycerol 90%
6. Glycerol 100%
0
11
0.02
Data Surface Fr We
1
A
0.9 0.9
2
G
0.7 1.2
3
H
0.9 1.6
4
1
1.3 2.0
5
J
15.3 24.4
6
K
0.1 0.2
0.04
C*Cap
We
15
7
37
81
86
43
0.06
.
---
0.08
*
0
Recxfc' Rew Mode
4.14
0.1
A2
1.47
0.2
A2
1.82
0.2
Al
3.32
0.1
Al
0.45 0.003 Al
0.01
0.002
Al
Figure 7-7. Experimental results for droplet spreading at low capillary Weber number for the
liquids shown in Table 7-1. The symbols and the black solid line indicate the experimental data
when We, < 100 and the theoretical data obtained from equation (7-13), respectively. Viscous
dissipation inside the droplet and line dissipation, which are the columns highlighted in gray in the
table, are not considered in the energy equation because Wec is low. The square of the
dimensionless radius change is linearly proportional to the dimensionless time. The table provides
the surface and liquid properties and the dimensionless parameters of the energy equation for each
data set. The impingement modes are confined to Mode-Al and Mode-A2 because Rew < 0.2 when
We, < 100.
175
7.4.3.
The Washburn-Reynolds number
We can see Mode-Al and Mode-B in Figure 7-6 (high We0 ), and Mode-Al and Mode-A2 in
Figure 7-7 (low We,). In Figure 7-6 and Figure 7-7, we used the experimental data obtained from
Mode-Al and Mode-B because the mass conservation isn't valid in Mode-A2 and Mode-C due to
necking and jetting behavior, respectively. From the investigation of We0 and Rew, we can say that
very low and high We, numbers correspond to Mode-A and Mode-C, respectively, because these
We0 regimes correspond to low and high Rew. However, to predict the transition between the
impingement modes, viscous dissipation inside the porous region must be considered. From
equation (7-13), we see that Dcap includes the viscosity effects in the porous region; therefore, Rew
incorporates the effects of kinetic energy, matrix potential, and viscous dissipation. This is why we
can predict impingement mode transitions with Rew. Dimensional analysis is a useful tool to extract
pertinent dimensionless groups using parameters obtained from the modified energy equations.
Dimensionless groups are formed from the parameters, Dcap, Pcap, and He, which relate to the highly
wetting surfaces in addition to the parameters, Do, Uo, p, p, and y. We find that a dimensionless
parameter obtained from a combination of the dimensionless hydraulic diffusivity, D*cap =
Dcap1(U 0D0), and the Weber number governs the drop impingement modes. We denote this nondimensional number the Washburn-Reynolds due to its similarity to the traditional Reynolds
number and its relationship with Washburn's equation [219]. The Washburn-Reynolds number,
Rew, is expressed by,
Re,=D* -We -U,prp(7-14)
cos6
07
CWU
176
4
Hydraulic diffusivity, Dcap, is obtained from capillary rise measurements and combined with the
Weber number to obtain Rew. Using the liquids and surfaces in Table 7-1, drop impingement
experiments were conducted with varying impact velocities. It is worth noting that the WashburnReynolds number Rew is close to the capillary-Reynolds number Rec when the contact angle is
small (cos9 ~ 1). For the case of contact angles near zero, Rew approaches Rec, the Reynolds
number inside a single capillary tube with radius r, and flow speed U.
7.4.4.
Impingement mode transitions correlate with the
Washburn-Reynolds number
When the impingement modes were plotted with respect to We or Re, there were several orders of
magnitude differences between mode transitions for different liquids. However, Re w correlates with
mode transitions for a wide range of liquid and surface properties, impact velocities, and for various
highly wetting porous surfaces (Figure 7-8). As shown in Figure 7-8, increasing Rew governs
transitions between impingement modes. Interestingly, in Mode-A (Rew < 0.5), observation of
Mode-Al or Mode-A2 appeared to vary with cos9/Oh 2, where Oh is the Ohnesorge number
expressed as Oh = p/(rep) and 9 is the Young's contact angle of the surface. This parameter has
the same form of another dimensionless group of Dcap/u, where v is the kinematic viscosity of
liquids used. We found that these two dimensionless groups can effectively characterize the wetting
ability of surfaces for various liquids. In Mode-Al we believe that kinetic energy is transferred to
viscous dissipation through the observed oscillations in the low cos9/Oh 2 region (cos9/Oh 2 < 30).
Conversely, for the high cos9/Oh2 region (cos9O/h2 > 30) the matrix potential is compensated by
177
the necking behavior observed in Mode-A2. Mode-Al and Mode-A2 are combined as Mode-A
since both are observed in the same Re w range. Further investigation is needed to illuminate the role
of D,,p for the transition between Mode-Al and Mode-A2. The biggest advantage of the WashburnReynolds number is that we can predict the impingement modes based upon three factors: surface
properties (r, and 6), liquid properties (p and p), and impact velocity (U). Therefore, once the
surface and liquid are determined, we can change the impingement modes using the impact
velocity. Alternatively, if the impact velocity is limited to a specific range, the impingement modes
can be altered by the surface and liquid properties. However, in this case, the modes available are
limited because Dap and p have narrower ranges than U,.
The Washburn-Reynolds number (Rew) can be interpreted as the ratio between the inertia of the
impinging droplet and capillary driven transport in the porous thin film. At high Rew, the droplet
inertia is dominant, resulting in Mode-C (jetting). In Mode-B, the inertial and capillary effects are
balanced and smooth spreading is observed. Conversely, Mode-A (low Rew) results in capillary
driven flows. When the capillary radius is large and the contact angle is small, the surfaces
generally show high spreading speed. This can result in oscillating motions (Mode-Al) at low Dap
and necking (Mode-A2) at high
Dcap. In
Mode-A, droplets spread largely due to the matrix potential
since the initial droplet kinetic energy is negligible.
178
10
'Mode C
I0
0.1
*A
Mode Al
C Mode A2
H
MN
m
0.01
L
10
-
1
0.001
0.1
G
M N C;
K
0.01
-
0.0001
a -""IM
a am''""E I -
0.001
0.01
100
10
1
0 .0 0 0 1
IN
' men
- - '"I
0.1
1
2
cosO/Oh
-' ""0 onoe
M
I -- I So@
10
100
1000
Figure 7-8. Impingement mode transitions correlate with the Washburn-Reynolds number, as
shown in the log-log plot of Rew vs. cos0/Oh2 , where Oh is the Ohnesorge number and 0 is the
Young's contact angle of the surface. Dcp/u has the same form of cos9/Oh 2, where u is the
kinematic viscosity of liquids used. Both dimensionless parameters can be used to distinguish
wetting properties of the surfaces. Droplets fall from heights ranging from 0.003 m to 1 m prior to
impact. Symbols: 0, El, A,
and 0 indicate Mode-Al, Mode-A2, Mode-B, and Mode-C,
respectively. The capital letter under each vertical line indicates the surface name shown in Table
7-1. The inset shows the mode transitions in a narrow Dcap/u region of 1 to 100.
179
7.5.
Conclusions
In this work, we propose a modified energy equation to predict droplet spreading on highly
wetting porous thin films. Notably, we include the matrix potential to accurately simulate droplet
spreading. This effect can be evaluated with the capillary-Weber number, Wec, which is the ratio of
the initial kinetic energy to the initial matrix potential. Furthermore, we discovered a dimensionless
parameter, the Washburn-Reynolds number (Rew), which correlates with impingement modes on
highly wetting porous surfaces. Rew can be derived from dimensional analysis or the simplified
energy equations at low and high Wec. At high Wec, the Weber number governs the droplet
expansion rate but at low We0 numbers, the dimensionless hydraulic diffusivity, D*CaP, governs
droplet spreading. Rew can be obtained from We and
D*cap.
Rew has the same form as the Reynolds
number but possesses an effective length scale, recos9, which reflects the wetting properties of the
surface. Rew effectively correlates with impingement modes across a wide range of fluid and
surface properties. Rew provides useful insight into droplet dynamics and can be used to guide the
design of highly wetting surfaces for applications ranging from spray cooling to paper microfluidics
and inkjet printing.
180
Chapter 8. Sparkling Droplets: Evidence of
Aerosol Generation from Drop
Impingement on Porous Media
181
8.1.
Introduction
Aerosols, which disperse chemicals and microorganisms into the atmosphere [220, 221], have
been intensively investigated because of their significant impact on the environment and human
health [222-226]. To date, bubbles breaking on the sea and fossil fuel combustion have been
considered the main origins of atmospheric aerosol dispersion [224, 227-230]. However, aerosol
generated from rainfall on soil has not been considered to date. Furthermore, the origins of
atmospheric bioaerosols consisting soil elements and environmental microorganisms still remain
illusive [220, 226]. Here we report that rainfall on soil can also generate aerosols. High-speed
imaging provides visual evidence of aerosol generation when liquid water droplets hit soil at
velocities consistent with rainfall. During drop impingement, tiny gas bubbles form inside the
droplet and are fed by air escaping from the porous soil. When the tiny bubbles break, they release
jets that quickly break into droplets tens of microns in diameter. Within a specified range of impact
velocities, we observed frenetic bubble generation and ejection of tiny droplets, producing aerosol
above the surface. We can predict when the frenetic aerosol generation will occur from the surface
properties and impact conditions. This work demonstrates that aerosols can be generated on porous
surfaces like soil when impinged by a liquid droplet. Hence, our work has widespread implications
for future remediation of air pollution, global warming, and the migration of disease causing
microbes from aerosol.
We have found evidence of aerosol generation from raindrops hitting soil (Figure 8-la-c). Using
different impact velocities, we observed the drop impingements on the soils with a high-speed
camera. When small water-droplets imitating raindrops were dropped on three representative types
of soils: sandy, clay and loam-clay [231], aerosol generation was successfully reproduced with both
of the clay and loam-clay soils but not with the sandy soil. When a droplet, which was the similar
182
size to a rain drop (~ 2.6 mm), hit the clay soil surface at an light rainfall velocity of 2 m/s (Figure
8-la), trapped bubbles were observed inside the droplet (Figure 8-1b). Then, multiple tiny jets,
which diameters were approximately few tens of micro meters, were ejected from the droplet at a
top speed of around 10 m/s during the droplet was flattened and spreading (Figure 8-ic). It can be
speculated that the bubbles pinned on the soil surface break when the upper surface of the droplet
compresses the bubble tops, resulting in simultaneous water jets, as it is known that water jets occur
when gas bubbles break at the interface of air and water [232-235].
This phenomenon was first observed during drop impingement on thin layer chromatography
(TLC) plates. TLC plates can be considered ideal soil-like surfaces, because they have a similar
range of water absorption speeds to soils while they are topologically and chemically homogenous
and mono-colored (Table 8-1). When a water droplet hit a TLC plate, which has the similar waterabsorption speed to clay soil, at an impact speed of 0.4 m/s, a large bubble was trapped inside the
droplet (Figure 8-1d). When the bubble met the water-air interface and broke (Figure 8-le), a thin
water pillar spurted (Figure 8-1f). Then, the water pillar was separated into small droplets, which
can float in the air (Figure 8-1g). Depending on impact speeds and surfaces, we observed different
bubble generations and breaking. Interestingly, frenzied water-jets (aerosol dispersion) were
investigated in a specific range of impact velocity depending on surface property, as shown in
Figure 8-ih. In this mode, hundreds water-jets, which diameters were in the range of 10 - 50 micro
meters, were ejected from the droplet on an area of 30 mm 2 for 20 micro-seconds. At the moment,
hundreds of bubbles inside the droplet were breaking in a short time. This frenzied aerosol
dispersion is very attractive because quite a number of aerosols can be produced within a few
microseconds to trigger aerosol generation, transportation, and reaction [236].
Aerosol generation after drop impingement on porous media is a three step process consisting of
bubble formation, bubble expansion, and bubble bursting, as shown in Figure 8-2. To account for
183
the mechanism of aerosol generation, we observed bubble's life inside droplets with different
impact velocities and surfaces. From the high speed images of Figure 8-2a-c, we can simply express
the process of aerosol generation with the schematic illustrations of Figure 8-2d-g. When a droplet
hits the surface, the droplet compresses the solid surface due to the kinetic energy of the droplet,
and tiny bubbles are trapped at the interface of the droplet and the surface because the expansion
speed of the droplet is higher than the water absorption speed of the surface (Figure 8-2d). After the
droplet reaches the maximum radius, the droplet oscillates or trembles, relieving its compressive
pressure. At this time, bubbles are growing by receiving air escaping from the pores of the surface
due to water soaking into the pores (Figure 8-2e) while the height of droplets is thinning because
water is being absorbed into the surface (Figure 8-2f). Finally, the bubble tops meet the air-water
interface, resulting in breaking of the bubbles (Figure 8-2g) and consequently ejecting small
droplets [223, 228, 237]. From the observation, we know that bubble's behavior inside droplets is
strongly affected by impact condition and surface property, resulting in different characteristics of
aerosol generation.
184
Figure 8-1. Aerosol generation from droplets hitting soils and porous surfaces. a, The clay soil has
irregularly rough surfaces and a droplet falls with an impact speed of 2.0 m/s. b, Tiny bubbles are
formed under the droplet. The bubbles are inside the white circles in the image. c, Tiny water-jets
are ejected from the droplet during impact. The white circles and arrows in the image highlight
aerosols and jets ejected from the droplet. d-g, High-speed images of the process of generating
aerosol when a single bubble breaks inside the droplet. d, A bubble is trapped inside the droplet. e,
The bubble breaks at the interface of water and air. f, A water pillar is jetted from the droplet. g,
The water pillar breaks up into tiny droplets. h, Many simultaneous water-jets and aerosols are
generated on a thin layer chromatography plate within a specific range of drop impact speeds.
185
Figure 8-2. Bubble generation, growth, and breaking inside droplets hitting porous surfaces. a-c,
High-speed images of bubble formation inside water-droplets on a thin layer chromatography plate
with respect to impact velocity. Bubble size and distribution become uniform with impact velocity,
resulting in simultaneous water-jets on the droplet surface. d-g, The schematic illustration of the
process of water-jet generation. d, A droplet impacts a porous layer and the droplet radius is
expanded. e, After it reaches the maximum radius, tiny bubbles are inflated at the interface of the
droplet and the porous surface. f, The droplet height thins due to the absorption of water into the
porous layer and the bubble size grows due to the inflation with air squeezed from the porous layer.
g, Finally, the tops of the bubbles meet the interface of air and water, and they are ruptured,
generating tiny water jets. The maximum number of bubbles inside the droplet increases with
impact velocity. The scale bars in a-c indicate 1 mm.
8.2.
8.2.1.
Theory
Measurements of hydraulic diffusivity
186
The capillary rise measurement (CRM) has been widely used to characterize liquid transports in
porous media [180, 238, 239]. CRMs were performed to evaluate hydraulic diffusivity on the
prepared surfaces and soils (Table 8-1). For the capillary rise measurements of the soils, we used a
common experimental setup according to other literatures [180, 239, 240]. A glass tube, which
inner-diameter is 10 mm, is filled with soil up to 100 mm in height and capped with a glass
membrane, which pore size is in the range of 70-100 micron, at the bottom (the glassware and
membranes purchased from ACE glass). The glass tube is fixed vertically and the height of the
liquid bath is slowly increased to initiate contact between the sample and the liquid surface. The
capillary rise is recorded using a digital camera. For the capillary rise measurements of the other
surfaces, the samples, which measured 2 cm and 10 cm in width and length, respectively, were used
instead of the glass tubes.
Hydraulic diffusivity was originally derived from Darcy's law; therefore, we need to understand
how the hydraulic diffusivity can be measured with the capillary rise measurement. As a result, we
can say that the hydraulic diffusivity obtained from the capillary rise measurement has the same
meaning as one obtained from Darcy's law, under the assumptions of uniform porous structures and
unit changes of the moisture content inside the porous media. Following two sections describe the
derivations of hydraulic diffusivity from both approaches.
8.2.2.
Hydraulic diffusivity from the capillary rise
measurement
Capillary flows can be considered a subset of Poiseuille flow in a narrow tube with radius, r.
The velocity within a capillary can be written as
187
vC =
where
,
(8-1)
aP/Oz is the pressure gradient in the direction of z. In the tube, the capillary pressure, Pcap,
can be calculated from the Young-Laplace equation,
Pa, =
2,vcos 0
r2
(8-2)
,
where y is the surface tension, 0 is the native contact angle on the capillary surface.
If the capillary pressure is higher than the hydrostatic pressure in the capillary tube, the liquid rises.
When a vertical capillary tube comes into contact with the free surface of water, the flow velocity
can be expressed by modifying equation (8-1). For a vertical tube with the rise height, h, from the
liquid free surface to the propagating liquid front, and the average velocity, vc, can be expressed as
the change in capillary height with respect to time. Finally, Washburn's equation is obtained as [172]
v
dh
=
dt
r2
2 cos0
8ph
r
(8-3)
pgh
If h is small, the gravitational effects can be neglected and Washburn's equation can be simplified
to
dh =rycos0
dt
(8-4)
4ph
188
Equation (8-4) can be integrated with respect to h and t to obtain a function relating rise height with
time, resulting in the expression:
h2
=
2pu
t =--D2
2
t,
(8-5)
where Dcap is hydraulic diffusivity with the units of m 2/s. Therefore, hydraulic diffusivity can be
obtained from the capillary rise speed.
8.2.3.
Hydraulic diffusivity from Darcy's law
From Darcy's law, the water discharge, q, through porous media can be expressed as
q=-K-,
(8-6)
az
where K is the hydraulic conductivity and ah/az is the hydraulic gradient. When we assume the
capillary head, hcap, only the driving force for the water discharge, from equation (8-1) and
equation (8-6), we can express the hydraulic conductivity as
PcaP
h
.
K=C8/rc-
(8-7)
Considering of the continuity of water content, the Richards' equation [241, 242] can be derived
from equation (8-6) as
189
= a (K
at
az
(8-8)
az
where 0 is the moisture content of porous media. Here, capillary pressure is also considered only
the driving force, and finally we can express equation (8-8) with hydraulic diffusivity, D, as
follows:
at
(8-9)
where
D=K ah".
(8-10)
ao
If we assume that the porous medium is initially dry (0 = 0) and becomes fully wet (0 = 1) after
capillary suction, and the capillary pressure become zero when 0 = 1, the hydraulic diffusivity
when the porous medium is dry can be expressed as
= D
(r =rycol=
,
(8-11)
from equations (8-7) and (8-9). Therefore, the hydraulic diffusivities obtained from Washburn's and
Richard's equations have the same form.
8.3.
8.3.1.
Experimental
Preparations and characterizations of porous media
190
We used twenty eight different porous media (see Table 8-1) to examine aerosol generation
from droplets hitting the porous media. Eight kinds of soils (from clay loam soil to peat) were
purchased from World's Science (Nasco soil samples, Fort Atkinson, Wisconsin). We used the
classification of the soils based on the product information from the company. The following eight
kinds of soils collected at Boston area in USA. The detailed locations of sampling the soils are as
-
follows; Soil-A: Killian court of MIT, Soil-B: Amherst Alley, Soil-C and -D: Briggs field, Soil-E,
F, and -G: Charles River, and Soil-H: Nahant beach. The soils were approximately classified with
the consideration of the particle sizes and the locations of sampling. The five kinds of commercial
thin chromatography (TLC) plates purchased from Sigma-Aldrich, and the seven different titania
porous films produced by electrochemical processes [243]. The porous titania plates were produced
by an electrochemical fabrication method with different electric-potentials [243].
To prepare dry soil substrates, first we gently broke the soils into fine grains with hands. We did
not filter and grind the soils. Then, each soil was placed on a dish with the soil height of 1 cm and
then wet with water-spray. The wet soils were dried on a hot plate at the temperature of 50 *C for
three days. After cooling the soils down to the ambient temperature, the soils were used for the drop
impingement experiments. The thin layer chromatography plates were used without any purification
and rinse. The porous titania plates were rinsed with deionized water for 1 minute after the
electrochemical processes and dried in a common laboratory environment. From the capillary rise
experiments, the hydraulic diffusivities of the media were evaluated with six different liquids: water,
ethanol, ethylene glycol, and glycerol. For the soils, the hydraulic diffusivity and the aerosol
generation were evaluated with water, and for the TLC and porous titania plates with the every
liquids. The particle sizes of the media were approximately evaluated by an image processing and
analysis software (ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA). Table
191
8-1 shows the summary of the surface properties and the liquids used in this works for the
measurements of hydraulic diffusivity and aerosol generation.
192
Table 8-1. Characteristics and wetting properties of the media used to examine aerosol generation.
Medium
thickness
Particle size
(ptm)
(pm)
104
104
104
104
104
104
104
104
< 500
< 300
300-600
Clay loam soil
Loam soil
Sandy soil
Clay soil
Muck
Sandy loam soil
Silt loam soil
Peat
Soil A (Clay loam)
Soil B (Peat)
Soil C (Loam)
Soil D (Sandy loam)
Soil E (Sandy Clay)
Soil F (Sand gravel)
Soil G (Silt loam)
Soil H (Beach sand)
TLC A (Silica)
TLC B (Cellulose)
TLC C (Aluminum)
TLC D (Silica)
TLC E (Cellulose)
TLC A (Silica)
TLC B (Cellulose)
TLC C (Aluminum)
TLC D (Silica)
TLC E (Cellulose)
TLC A (Silica)
TLC B (Cellulose)
TLC C (Aluminum)
TLC D (Silica)
TLC E (Cellulose)
Titania A (120 V, 10 *C)
Titania B (150 V, 10 *C)
Titania C (120 V, 75 *C)
Titania D (120 V, 25 *C)
Titania E (90 V, 25 *C)
Titania F (150 V, 25 *C)
104
104
250
100
250
200
250
250
100
250
200
250
250
100
250
200
250
190
330
80
150
140
240
Titania G (60 V, 50CC)
80
20-50
Titania G (60 V, 50 *C)
Titania G (60 V. 50 *C)
80
80
20-50
20-50
< 100
< 500
200-500
< 400
< 500
< 600
104
104
104
104
< 1000
< 1500
< 1000
< 300
100 - 5000
< 500
100 -400
10
2-20
11-14
25
50
10
2-20
11-14
25
50
10
2-20
11-14
25
50
50-100
20 -200
20- 100
< 400
10-200
< 600
193
Liquid
Hydraulic diffusivity
(mm2/s)
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Water
Ethanol
Ethanol
Ethanol
Ethanol
Ethanol
Ethylene glycol
Ethylene glycol
Ethylene glycol
Ethylene glycol
Ethylene glycol
Water
Water
Water
Water
Water
Water
Ethanol
Ethylene glycol
Glycerol
2.9
3.1
91.9
3.4
0.1
28.4
3.7
0.1
3.8
0.02
14.8
33.5
16.8
26.4
7.2
80.0
9.5
20.4
22.4
24.0
37.0
2.3
14.7
4.7
4.7
26.4
0.5
2.2
1.1
1.2
2.9
85.6
50.1
52.4
144.6
117.8
88.3
38.6
21.0
0.4
8.3.2.
Characteristics of typical soil and rainfall
To display the regimes of rainfalls hitting soils on the characterization map of aerosol
generation shown in Figure 8-4, we used the contact angles and effective pore radius of soils and
the radius and terminal velocities of rainfalls, which have been reported in other literatures [164,
240, 244-252]. In the literatures, the contact angles and effective pore radius were obtained from the
capillary rise merriments same as the method we used in this work. If we assume that glass surfaces
have nearly zero contact angles, the effective pore radius of soils ranges from 1 micron to 1 mm
corresponding to clay and sand, respectively [244, 245]. The contact angles of various soils have
been reported in many literatures [164, 240, 246-251]. Based on the literatures, we know that the
contact angles are approximately varied from 300 to 80* depending on the chemical compositions of
soils. Therefore, the range of the hydraulic diffusivity of each soil can be estimated by equation (8-5)
with the contact angles and the effective pore radius obtained from the literatures. Rain types can be
classified with light, moderate, and heavy rains depending on their precipitation rates [252]. The
drop size of rainfalls is varied from 0.5 mm to 2.5 mm with the terminal velocities of 2.1 m/sec and
9.1 m/s, respectively [252]. From the relationship between the drop size and the terminal velocity,
the Weber numbers can be estimated with respect to the kinds of rainfalls.
8.3.3.
Characteristics of droplets and bubbles with respect to
drop heights
We investigated the behaviors of droplets hitting porous surfaces using high-speed imaging. We
used the three different TLC plates (TLC-A, TLC-B, and TLC-C), with wetting properties shown in
Table 8-1, and varied the drop height to change the impact velocity. First, we compared the droplet
194
film thickness after spreading and the bubble diameters, as shown in Figure 8-3a. The droplet film
thickness is measured when the droplets reach their maximum radius after impact. The bubble
diameter is the average diameter of the bubbles inside the droplet when the first bubble breaks. At
low velocities, the droplet film thickness is greater than the bubble diameter. However, the film
thickness and the bubble diameter become similar at 1 m/s impact velocity. Therefore, impact
velocity governs the maximum bubble diameter because bubble diameter cannot exceed the droplet
film thickness. The maximum number of bubbles is linearly proportional to the impact velocity, as
shown in Figure 8-3b, because the number of bubbles is linearly proportional to the droplet contact
area to the surface. As a result, the number of bubbles increases with impact velocity.
Jetting initiation time is the time it takes to observe the first aerosol dispersion after the droplet
reached the maximum diameter after impact. The jetting initiation time shows the effects of surface
wettability and impact velocity on aerosol generation. The jetting initiation time is mainly governed
by the wetting properties of the surface at low impact velocity (Figure 8-3c). However, the droplet
film thickness significantly affects the jetting initiation time at high impact velocities. TLC-A and
TLC-C have the lowest and the highest hydraulic diffusivities, respectively. Therefore, the initial
jetting occurs on TLC-C first and on TLC-A last at low impact velocities (less than 1.4 m/s). At
higher impact velocities (higher than 2.0 m/s), however, the droplet height is the highest on TLC-B,
as shown in Figure 8-3d; therefore, the initial jetting time is the greatest on TLC-B.
195
(a)
(b)
1.4
45
0
1.2
Bubble diameter
1
40
0 Liquid film thickness
S35
1
30
E
E 0.8
Frenetic aerosol
4 dispersion
~0.6
25
20
I0.4
15
BWb
Z 10
0.2
03
5
0
0.5
1
1.5
U 2 (m/s)
0
2
I0
(d)
dominant I 0 TLC-A: Dc,, = 9.5 mm 2/s
2
0 TLC-B: D, = 20.4 mm /s
0)
.
d
6
2
TLC-C: D, = 22.4 mm /s
E
Droplet film
"b
7
I
thickness dominant
0.01
- - - - -- - - ---- - - 0.5
1
1.5
2
U 2 (m/s) 2
4
3
%b
2
GOI TLC-A:D = 9.5 mm /s2
-0- TLC-B: D. = 20.4 mm /s
2
SI
0m. TLC-C: D,
0.001
-a--!-
0
--
2
-------
4
- -
6
0
U02 (m/s) 2
2
4
U 2 (m/s) 2
= 22.4 mm 2/s
-
-
(c)
2
-
0
0
6
Figure 8-3. Characteristics of droplets and bubbles generated after the droplets hit the three TLC
plates. The hydraulic diffusivities of TLC-A, TLC-B and TLC-C are 9.5, 20.4, and 22.4 mm 2 /s,
respectively. (a) The average bubble diameter does not change significantly by impact velocity U
2
but the average droplet film thickness is inversely proportional to U 2 . (b) The maximum number of
bubbles inside the droplet linearly increases with respect to U 2 . (c) The time it takes to observe the
first jet is affected by the surface wettability at low impact velocity but by the droplet film thickness
at high impact velocity since the droplet film thickness governs the maximum bubble size at high
impact velocity. (d) The droplet film thickness h,ni, after hitting the surfaces is the highest on TLCB.
196
8.4.
Results and discussion
From the relationship between the kinetic energy and the surface energy of the droplet, we can
estimate the size and distribution of bubbles after impact. It is known that jet-size and -velocity are
strongly correlated with bubble size [227, 234, 253]. Therefore, different aerosol generation
behaviors can be interpreted by the relationship between bubble size and impact velocity. By the
energy conservation of the kinetic and surface energy of a droplet, the maximum radius of the
flatten droplet after impact is linearly proportional to the impact velocity; therefore, the minimum
droplet height is inversely proportional to the square of impact velocity as following: U'
l/hmin, where U is the impact velocity, d,, is the maximum droplet diameter, and hmin is the
minimum height of the droplet (Figure 8-3). The size and the maximum number of bubbles can be
measured from snap shots of high speed movies. From the observation, we know that the number of
bubbles is proportional to the wet area of the surface. The wet area can be calculated with the
maximum radius of the flatten droplet. Therefore, we can find the relationship between the
maximum number of bubbles and the impact velocity as following: U0 2
-x
Nma, where A.,, is
the maximum wet area of the surface, and N,,a is the maximum number of bubbles formed inside
the droplet. (Figure 8-3) Therefore, we can employ the Weber number; We = p DU 2/a, where p is
the liquid density, D, is the initial droplet diameter, and a is the liquid surface tension, to evaluate
the effect of impact velocity on the number of bubbles and the bubble size. When We >> 1, we can
expect that aerosol generation cannot be observed because the height of the droplet is too low to
reach the sufficient bubble size to generate aerosols after breaking. In contrast, when We << 1, the
number of bubbles decreases and the bubble size is much smaller than the droplet height, resulting
in the delay of bubble bursting.
197
The droplet permeation and the initial aerosol dispersion are affected by surface properties,
mainly the wettability (see Figure 8-3c). The water absorption speed of porous media can be
characterized by the hydraulic diffusivity, Dcap [242]. If we assume that dry soil becomes fully wet
after capillary suction (e.g. there are no impenetrable pores), the hydraulic diffusivity can be found
using the equation for capillary rise in the absence of gravitational effects: h2 ~ Dcapt, where h is the
rise height and t is time [172, 198, 254]. The hydraulic diffusivity can be experimentally estimated
from capillary rise measurements [198]. We now define a modified Peclet number (Pe =
(U-D 0 )/Dea), where D, is the initial droplet diameter and U is the impact velocity of the droplet.
The modified PNclet number is the ratio of the advective transport rate (U -D,) to the hydraulic
diffusivity (Dap) and used to represent the effects of surface wettability.
198
14
103V
-
We 102--
Frenetic Jets
region
10
1
Commercial soils
Local soils
Nano-porous plates
Smooth absorption
Micro-porous plates
1 4
0
1
10
102
103
104
105
106
Pe
Figure 8-4. Characterization of aerosol generation when droplets hit soils and porous surfaces. The
x-axis indicates a modified Peclet number (Pe
(U&-Do)/Dap), where U and D, are the impact
velocity and the diameter of the droplet. The y-axis indicates the Weber number (We
pDU2
mainly varied by the impact velocity. We and Pe represent the impact condition and the surface
property, respectively. The Dcap values of the soils were measured by the capillary rise experiments.
The red symbols indicate the observation of aerosol dispersion from the droplets at the
corresponding We and Pe. The blue circle named "aerosol generation region" highlights the group
of the data points where aerosols are generated. The yellow symbols inside the aerosol generation
region show the data points of frenetic aerosol generation. Rainfalls on soils are placed on the upper
part of the characterization map, and clay and sandy-clay soils have concentrated regions in the
sparling zone. a-c, the reprehensive images of drop impingements in the regions classified with We.
199
Based on the drop impingement results, we found a domain which resulted in aerosol generation.
We employed the Weber number (We) and the modified PNclet number (Pe) parameters in a two
dimensional map of our experimental conditions. We observed drop impingements on various types
of porous media, including soils, with different liquids and impact velocities. In total we conducted
roughly 600 experiments. Experiments were performed on sixteen different soils (eight commercial
soils purchased from World's Science, and other soils collected from the local area), five different
TLC plates (Sigma-Aldrich, micro- and nanoporous surfaces: silica, cellulose, and aluminum oxide
with different pore sizes), and seven porous titania films fabricated in-house [198] (Micro-porous
surfaces fabricated with different conditions) with four different liquids (water, ethanol, ethylene
glycol, and glycerol) (see Table 8-1).
Figure 3 summarizes the observations with respect to Pe and We. We and Pe were varied from 1
to 104 and from 1 to 106, respectively. Aerosol generation is observed in a specific region of We
and Pe, as shown in Fig. 3. There was no aerosol generation in the low and high We regions (We <
10 or We > 103). When We > 103, we do not observe aerosol generation because splashing in radial
direction (Figure 8-4a) leads to air entrainment. By contrast, when We < 10, few bubbles are
entrained and they're much smaller than the droplet height, resulting in delayed bubble bursting and
reabsorbed bubbles into the surface. In addition, the surfaces did not show aerosol generation at
high or low hydraulic diffusivity (Pe < 10 or Pe > 104). When Pe > 104 , bubbles cannot become
sufficiently large to generate aerosols during droplet spreading because the droplet does not
permeate into the surface. Conversely, if Pe < 10, the droplet quickly absorbs into the porous
surface, faster than the droplet expands. Therefore, air is not trapped at the interface of the droplet
and the surface, and there is no aerosol generation.
Frenetic aerosol generation is observed at the core of the aerosol generation region on the
characterization map (c.f. yellow symbols in Figure 8-4). To achieve frenetic aerosol generation,
200
bubbles have to be pinned on the surface for the duration of reaching sufficient size to disperse
aerosol when they break. Therefore, moderate Pe (102 < Pe < 103) is necessary for frenzied aerosol
generation since this balances bubble size (favoring low Pe) while minimizing the time it takes for
the initial droplet to spread and the bubbles to burst (favoring high Pe). At low We (Figure 8-4c),
bubble-bursting is delayed because the average bubble height is smaller than the average droplet
height after impact. When We is high, bubbles forming inside the droplet are not large enough to
generate water-jets because the droplet becomes very thin after impact. According to the study by
Lee et al. [234], bubbles must have a minimum size (the minimum radius is about 26 pm in water)
to generate liquid jets when they burst. The average bubble height and the average droplet height
become similar within a specific range of We (Figure 8-3a). Frenetic aerosol generation occurs
when the bubble diameter is very close to the droplet height, leading multiple bubbles to burst at
roughly the same time after impact. This frenetic aerosol dispersion is very attractive because quite
a number of aerosols can be produced within a few microseconds, which could be useful for
applications requiring fast aerosol generation at ambient temperature.
From the characterization map we conclude that aerosol generation can occur during light and
moderate rainfall on soils with hydraulic diffusivity less than sand. To locate the impingement
domains for rainfall on soil (red, yellow, and green regions in Figure 8-4), the hydraulic diffusivity
of the soils were obtained from the literature [240, 244, 246] and the impact velocity of raindrops
was set from light rain (U < 4.0 m/s) to heavy rain (U 0 > 7.0 m/s) [252]. When the impingement
domains are added to the characterization map, the overlapping regions of aerosol generation and
rainfall are evident (Figure 8-4). We verified aerosol generation experimentally for conditions
consistent with light and moderate rain on soil with similar water-absorption properties as clay and
sandy-clay soil. Aerosol generation was not observed on sand or during conditions consistent with
heavy rainfall.
201
8.5.
Conclusions
This work is meaningful in two respects: first, we present visual evidence of aerosol generation
from rainfall hitting soil; and second, we provide an effective means to generate aerosol using
simple drop impingement on porous media. Until now, the effects of aerosol from soil have been
rarely investigated due to the lack of knowledge of its generation. However, from the result of this
work, we can understand the strong correlation of aerosol generation with wetting property of soils
and impact velocity of droplets. This is the key to open the study of the environmental and
geological effects of aerosol generation from soil. Using the correlation, the rate and the duration of
aerosol generation can be effectively controlled. In addition, the chemical composition of aerosols
can be altered with porous surfaces pre-permeated with the chemicals. Therefore, this aerosol
generation method using liquid droplets and porous surfaces will provide crucial opportunities to
develop novel chemical synthesis methods for next-generation materials beyond the aerosol
investigation itself. Furthermore, we will possibly illuminate the mechanism of the human infection
and the migration of viruses and bacteria originated in soils.
202
Chapter 9. Thesis Summary and Future Work
203
9.1.
Thesis Summary
The use of electric fields is both cost- and time-effective, as well as mass-producible, when
creating and customizing nano- and micro-scale structures and properties. In this dissertation,
electrophoretic deposition [73] and breakdown anodization [198] were used as electro-fabrication
methods to structure nano- and micro-morphologies and to vary their material properties (Figure
9-1). Electrophoretic deposition uses electrophoresis of nanoparticles dispersed in suspensions. In
this work, the use of suspension stability to control nanostructures is unique. Depending upon the
quality of dispersion, the nanostructures of the deposition layers can be effectively controlled. In
addition to electrophoretic deposition, breakdown anodization was used to create microporous
structures with nano-scale feather patterns, resulting in highly porous films [196, 255]. The porous
structures can be functionally varied with customized electric fields [256-258]. A hybrid method of
electrophoretic deposition and breakdown anodization was proposed to control surface roughness
and deposit various nanoparticles on surfaces.
In this work, diverse functional surfaces and films were produced by using electro-fabrication
methods. Superhydrophobic and superhydrophilic surfaces are good applications for demonstrating
the effective control of surface structures and properties using electric fields [73, 198]. Wettability,
as a function of surface roughness and energy, can be varied from superhydrophilic to
superhydrophobic regions using customized electric fields and different nanoparticles [198, 256].
This technology has been successfully applied to produce highly durable anti-wetting fabric that
maintains its original breathability and flexibility [259]. The anti-wetting fabric is a strong
candidate for cost-effective and large-area membranes for water desalination and oil-water
separation (Figure 9-2a). Critical heat flux in pool boiling was greatly enhanced with hierarchically
204
structured
superhydrophilic
surfaces
produced
by both
of breakdown
anodization and
electrophoretic deposition (Figure 9-2b) [196, 255].
Electrophoretic Deposition
Breakdown Anodization
DC PowerSup
DC Power SupPlY
Electrode
Acidic
electrolyte
00
St
Nano-structure
0
Mc
Nano
stimng
Micro-structure
Figure 9-1. Fabrication processes for micro/nano hierarchically structured surfaces and Scanning
Electron Microscopy (SEM) images (a)-(f). For micro-porous structures, breakdown anodization
(BDA) is used with different electric fields, (a)-(c). For nano porous structures, electrophoretic
deposition (EPD) is used with different nanoparticles, (d)-(f). The hierachical micro- and nanoporous structures are produced by a series of BDA and EPD, (g)-(i). The electrolyte temperature
and the nanoparticles affect the surface morphology and the surface energy, respectively.
205
Figure 9-2. Functional surfaces produced by electro-fabrication. (a) Anti-wetting fabric with biomimicked coating-layers for water harvesting. Each fiber of the fabric was uniformly coated with
hydrophobic silica nanoparticles, resulting in high static contact angle and low roll-off angle. The
fabric maintains its original flexibility and breathability after the modification. The water droplets
were growing with a regular pattern similar to those on a real leaf during condensation. (b)
Hierarchical surfaces for critical heat flux enhancement. The micropillars, created on a silicon wafer,
were coated with hydrophilic silica nanoparticles, enhancing hydrophilicity. The coatings prevent
vapor-blankets on the heater surface and dramatically enhance critical heat flux and heat transfer
efficiency in pool boiling [255].
In drop impingements on porous films, a new dimensionless parameter, named the WashburnReynolds number, is suggested to predict the impingement modes of droplets hitting the porous
films [260, 261]. Use of the Washburn-Reynolds number offers a convenient method for controlling
the impingement behaviors of liquid droplets for ink-jet printing, spray painting and spray cooling.
The energy equation suggested in this work can be generally utilized for understanding liquid
propagation mechanisms on wettable porous films. Furthermore, aerosols can be generated from
droplets hitting porous surfaces (Figure 9-3b) [262, 263]. The aerosol generation provides clues to
explain the migration of bacteria and viruses encapsulated in the aerosol.
206
Figure 9-3. Aerosol generation from droplets hitting porous surfaces. Frenzied aerosol dispersion
can be observed in a specific region of the Weber number of droplets and the hydraulic diffusivity
of surfaces.
9.2.
9.2.1.
Future Research
Porous Thin Film Microfluidic Devices Designed by
Breakdown Anodization
A new methodology is presented to develop microfluidic devices using highly wetting porous
titania films. Production of low cost diagnostic tools, allowing for small sample volumes, is in high
demand. Thus the use of capillary flows employed in paper-based microfluidic devices has been
considered highly attractive. Capillary driven flows through thin porous media have been widely
utilized for small-scale liquid transportation systems, including chromatographic
analyzers,
biosensors, micro-chemical reactors, and paper-based microfluidic devices (Figure 9-4).
207
(a)
Reagent
Sample
Microfluidic
I:Pump
P
device
(b)
Porous thin film microfluidic device
I
00 0
-0
-r
Reagents
-00 Sample
-_O
- 0
_
Porous thin
film channel
Figure 9-4. Schematic comparison between (a) a conventional microfluidic device and (b) the
porous thin film microfluidic device.
Capillary flows show different characteristics depending on the porous substrate. Examples include
glass capillary tubes, porous media composed of densely packed particles or fibers, and sponges.
However, for most media it is challenging to realize arbitrary shapes and spatially functionalized
micro-structures with variable flow properties. It is also difficult to control the liquid transport
properties and to scale-down dimensions under hundreds microns with media such as paper.
Recently, we developed a unique anodization technique, called breakdown anodization (BDA),
with titanium plates to produce highly wetting porous thin films. The porous layer thickness is a few
tens of microns, which is much thinner than nearly all types paper. Furthermore, when we
characterize liquid transport speed in terms of hydraulic diffusivity, the porous films showed much
higher hydraulic diffusivity than commercial chromatography paper. Hydraulic diffusivity of BDA
surfaces linearly increases with electric potential during anodization, and the liquid transport
distance can be predicted with a conceptual capillary tube model.
208
In this work, BDA is applied to the development of microfluidic devices using porous titania thin
films. Using a conventional soft lithography technique, micro-patterned electrodes are prepared on
titanium sheets for anodization (Figure 9-5). After BDA, highly wetting porous films is generated
on the micro-patterned surfaces (Figure 9-6). The porous thin film microfluidic (PTFM) channels
show fast liquid transport over long distances with minimal sample volume.
A
B
UV illumination
4 I
Photo
IIIIImask
C
Developing
D
Electrolyte Counter electrode
Breakdown anodization
E
BDA surfaces
Figure 9-5. Fabrication process. A photoresist
Figure 9-6. Porous thin film microfluidic
layer
channels produced by BDA. (a)-(c) Patterned Ti
is
patterned
using
photolithography.
Breakdown anodization is conducted with the sheets
patterned Ti electrode in an acidic electrolyte.
after
BDA
with
different
electric
potentials. (d)-(f) Thin channels generated by
BDA.
The PTFM chips will be used to identify various properties of a simulated urine sample including
the presence of glucose, phosphate, chloride, and pH. The corresponding reagent, placed on the
209
PTFM chip changes color depending on the concentration of each element. By comparison with
commercial porous media, the PTFM chips facilitate precise test results with one sixth smaller
sample volumes in m 2 /L and five times faster diagnosis in m 2 /sec than a commercial
chromatography paper (Figure 9-7). Thin titania porous films produced by BDA are an attractive
alternative substrate for microfluidic diagnostic devices requiring small sample volumes.
Advantages of this technique include design flexibility, fast and low sample volume diagnosis, and
low-cost fabrication. For our future work we will demonstrate multi-channel electrospray from
PTFM devices, which can be used in ambient ionization sources, for high sensitivity sample
analysis.
120$
E 1.5 *21
Hydraulic diffusivity
100 E
80
60
-
E
.
Wetted area
-
2-
40-a
S0.50
-20
1rN 1 AUmmmm
0
Wicking media
Figure 9-7. Wettable area and wicking speeds of different porous media with a one microliter
sample of 1 g/L Rhodamine B in deionized water. The wetted area of the BDA surface is
significantly larger due to its high permeability and low thickness.
210
9.2.2.
Conductive Hydrogel Produced by Electrophoretic
Deposition at the Interface of Two Immiscible Liquids
A novel method is presented to fabricate hydrogel composite nanomaterials using electrophoretic
deposition at the interface of two immiscible liquids. Hydrogels have been employed for biomaterials due to their outstanding bio-compatibility, high porosity, and notable swelling capabilities.
Thin hydrogel membranes are desired because diffusion and mass transfer effects across the films
can be improved. Further, conductive hydrogel films have been investigated because they can
provide a critical methodology to sense and diagnose biological systems or used for energy storage.
To date, vacuum filtering techniques and electrochemical deposition have been utilized to fabricate
conductive polymer films. However, the filter textures and pressure gradients distort the polymer
structures; especially when mechanically weak hydrogels are used.
Here, we propose a novel process employing electrophoretic deposition (EPD) at the interface of
immiscible liquids to create composite hydrogel films (Figure 9-8). During interfacial EPD,
nanoparticles such as carbon nanotubes (CNTs) migrate to the oil/water interface, where crosslinking of polymers is induced to form composite hydrogel membranes. The key aspect of this
method is that polymerization occurs away from a solid substrate while surrounded by both polar
and nonpolar media, allowing for the integration of CNTs or other nanoparticles and hydrogel.
Properties of the composite hydrogel films are controlled by the deposition and polymerization time,
allowing for mass production without the need for complex machinery. This fabrication method is
cost-effective and scalable for composite hydrogels with tunable electrical, mechanical, and
biological properties. Potential applications include fabrication of doped hydrogels for drug delivery
and conductive hydrogels for biological sensing.
211
Oil phase
Cross-linker
CNT & hydrogel compositeayr
Water phase
Electrophoretic deposition
CNT&
surfactant
Hydrogel _-
monomer
Materials
" Sodium alginate
" Carbon nanotube
" Sodium dodecyl sulfate (SDS)
" Calcium chloride
Figure 9-8. Fabrication procedure for the carbon nanotube and hydrogel composite layer and the
experiment setup for electrophoretic deposition with two immiscible liquids. Both water and oil are
added to a container and the electrode assembly is placed into the container. The oil-water interface
must be positioned at the middle of both electrodes. During an electric potential is applied to the
electrodes, the crosslink solution is added to the top of the oil phase. After the polymerization, the
oil phase is extracted and then the composite hydrogel film is gently lifted up. Experiment setup for
electrophoretic deposition at the oil-water interface.
9.2.3.
Dispersion of Carbon Nanotubes in Aqueous Solutions
of Ionic Surfactants
A mean-density model of surfactants is suggested to illuminate the mechanism of carbon
nanotube (CNT) dispersion in aqueous solutions of ionic surfactants. Ionic surfactants have been
used to make well-dispersed aqueous CNT suspensions. However, the mechanism of the dispersion
is not clear. To understand the mechanism, molecular dynamics (MD) simulations were recently
employed, but they require high computing power to obtain significant results. With the meandensity model, we can effectively estimate the mean force potential between CNTs stabilized with
212
surfactants. Notably, we find that the osmotic pressure between CNTs plays an important role in the
suspension stability. The mean-density model can help to determine appropriate surfactants and
concentrations necessary for stable CNT dispersions.
In the mean-density model, the surfactant heads suspended on a CNT are assumed to constitute a
single cylindrical group. When a CNT is dispersed in aqueous solutions with ionic surfactants, the
surfactant tails are attached to the CNT due to its hydrophobicity. However, the hydrophilic heads
of the surfactants orient towards the water (Figure 9-9a). If we assume that the surfactants are
attached on the CNT surface uniformly, the CNT and surfactant assembly can be simplified as
shown in Figure 9-9b. In the mean-density model, there are two cylindrical groups corresponding to
the surfactant head and the CNT. The CNT has uniform carbon atom density, resulting in the same
weight as the actual CNT. Similarly, the surfactant head group has uniform density and valence
charge.
(b)
Surfactant
CNT Cylindrical surfactan
head group
2Rs
s
Rc
Head: As
CNT
Tail: Ls
Figure 9-9. Schematic illustrations of carbon nanotube and surfactant assemblies. The surfactant is
composed of a hydrophilic head, which has the cross sectional area of A, (the head radius is R,) and
a hydrophobic tail, which has length L. (a) In reality, multiple surfactants are attached on the
surface of the CNT. (b) In the simplified model, the surfactant heads are considered a single
cylinder.
213
To verify the mean-density model, we compare the total interaction potentials obtained from our
model and the molecular dynamics (MD) simulation. In our model, the total interaction potential is
calculated by superposing the van der Waals force, the electrostatic force, and the osmotic pressure
between two the CNT-surfactant assemblies shown in Figure 9-10b. As a result, the total interaction
potential obtained from the mean-density model (Figure 9-1 Oa) agrees well with the MD simulation.
Furthermore, our model successfully shows the effect of surfactant concentration on dispersion
stability. When the bulk solution concentration is higher than the surfactant critical micelle
concentration (CMC), micelles of the surfactant form in solution, maintaining the bulk monomer
concentration at CMC. Therefore, the osmotic attraction force becomes significant when the bulk
concentration is higher than CMC, lowering the maximum potential barrier, as shown in Figure
9-10b. From this result, we show that the CNT dispersion is unstable when the surfactant
concentration is higher than the CMC.
Osmotcpress.re
.
0 van
-
o
*
(b)
der Was force between CNTs
Electrostatic force
osmoticpressure
van der Wasis between surfactants
Total interaction potential
-
20 -
01
0
37
30so
70
90
100
van der Waaft force between CNTs
Electrostatic force
O
M van der Waals between surfactants
Total interaction potential
*
110
b
dlnmJ
401.Wj
a
0 ,0
'
(a)
-Tf
j~~I
SX0 60
7
/
6d90
rn
uIoJI
Figure 9-10. Total interaction potentials between two CNT-surfactant assemblies. The total
interaction potential can be obtained by the summation of van der Waals force, electrostatic force,
and osmotic pressure. The total interaction potentials of (a) and (b) are obtained with the surfactant
coverage ratio of 30 % and the tail stretching ratio of 100 %.
Different bulk surfactant
concentrations of CMC (8.7x 10- mol/L) and 2xCMC are used in (a) and (b) to compare the effect
of micelle formation
214
The mean-density model can show reasonable predictions for the interaction potential between
CNT-surfactant assemblies with much less computational time than the molecular dynamic
simulations. Furthermore, this model will illuminate the effects of osmotic pressure between the
assemblies on dispersion stability. This result will show that more CNT agglomerates form when
the surfactant concentration is higher than the CMC, and the most stable CNT-surfactant suspension
is obtained around the CMC.
215
216
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