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Numerical and Experimental Investigation on Evaporation of Water Droplet
on Surfaces With Mixed Wettability
Conference Paper · July 2020
DOI: 10.1115/ICNMM2020-1055
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Proceedings of the ASME 2020 18th International Conference on
Nanochannels, Microchannels, and Minichannels
ICNMM2020
July 13-15, 2020, Virtual, Online
NUMERICAL AND EXPERIMENTAL INVESTIGATION ON EVAPORATION OF WATER
DROPLET ON SURFACES WITH MIXED WETTABILITY
Akam Aboubakri
Mechatronics Engineering, Sabanci
University, Tuzla, Istanbul, Turkey
34956
Cenk Yanik
Sabanci University Nanotechnology
and Application Center (SUNUM),
Sabanci University, Tuzla, Istanbul,
34956, Turkey
Ali Koşar
-Faculty of Engineering and Natural Science, Sabanci
University, Tuzla, Istanbul, Turkey 34956
- Sabanci University Nanotechnology and Application Center
(SUNUM), Sabanci University, Tuzla, Istanbul, 34956, Turkey
-ESFUN Center of Excellence for Functional Surfaces and
Interfaces for nano-diagnostics,
Sabanci University, Tuzla, Istanbul, 34956, Turkey
Yiğit Akkuş
ASELSAN Inc., Communication
and Information Technologies
Business Sector, Yenimahalle,
Ankara, 06200, Turkey
Ali K Sadaghiani
-Faculty of Engineering and Natural Science,
Sabanci University, Tuzla, Istanbul, Turkey
34956
- Sabanci University Nanotechnology and
Application Center (SUNUM), Sabanci
University, Tuzla, Istanbul, 34956, Turkey
E-mail: a.sadaghiani@sabanciuniv.edu
ABSTRACT
Droplet evaporation is one of the most commonly observed
phenomena and plays an important role in many applications
such as in spray cooling, coating, and inkjet printing.
Mechanisms such as dynamics of the contact line, evaporationinduced phase transitions, and formation of patterns on the
substrate interact with each other in the evaporation of droplets.
In this study, we investigated the effect of surface mixed
wettability on water sessile droplet evaporation. The transient
contact angle, center-height, contact radius, surface area, and
droplet volume were experimentally measured and numerically
estimated. Surfaces with mixed wettability consisting of
hydrophilic islands surrounded by less hydrophilic area were
fabricated. Visualization was conducted to capture droplet
dynamics during evaporation using two high-speed cameras.
According to the obtained results, there were three distinct stages
in the water evaporation process: a constant contact radius
mode, a constant contact angle mode, and a mixed-mode. The
COMSOL 5.4 software was used for numerical analysis.
According to the results, the receding contact angle and
Marangoni instability in the droplet are two main factors that
alter droplet dynamics and droplet evaporation.
Keywords: sessile droplet evaporation, mixed wettability,
two phase heat transfer
NOMENCLATURE
a
Bo
C
Cout
Cv
D
d
g
h
p
RD
Rs
Rout
T
Tout
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length of the square/rhombic islands
Bond number
relative humidity
ambient relative humidity
Concentration of vapor
vapor diffusivity
distance of hydrophilic islands
standard gravity
height of the droplet
pressure
wetted radius
substrate radius
far-field radius
temperature field
ambient temperature
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ICNMM2020-1055
investigated the dynamics of droplet evaporation on mixed
wettability surfaces, which consist of hydrophilic islands
surrounded by the less hydrophilic area. The islands are circular,
square, and rhombic shaped. The sizes of the islands are one,
one-fourth, and one-sixteenth times of the droplet radius on the
pure hydrophilic surface, for each shape. Motezakker et al [18]
studied the optimum ratio of hydrophobic to the total area of the
surface for pool boiling. As a reference, we used this ratio for our
designs.
velocity vector
thermal diffusivity
thermal expansion
contact angle of the droplet
viscosity
density
surface tension
viscous dissipation term
diameter of circular hydrophilic islands
INTRODUCTION
SAMPLE PREPARATION AND CHARACTERIZATION
Droplet evaporation is one of the most fundamental
phenomena and has many applications such as in spray cooling
[1-3], inject printing [4, 5], DNA extraction [6, 7], and painting
[8]. Understanding the underlying physical mechanism of
droplet evaporation is of great importance in these applications.
One of the first studies on droplet evaporation is done by Picknett
and Bexon [9]. They reported that a sessile droplet shows three
extremely different types of behavior during evaporation: (1)
constant contact radius (CCR) mode, characterized by the
reducing of contact angle and pinning of the contact line; (2)
constant contact angle (CCA) mode, characterized by receding
in the contact line and negligible variations in the contact angle;
(3) and the mixed-mode of two previous modes.
Besides, droplet evaporation on heterogeneous surfaces has
attracted much interest due to its potential in the aforementioned
applications. Droplet evaporation on mixed wettability surfaces
causes the change in the shape of the triple contact line (TCL)
and the pinning of the droplet. From the heat transfer application
point of view, the TCL plays an important role in heat transfer.
Many studies have reported that at a specific wetted area, the
larger was the length of the triple contact line, the larger was the
heat transfer coefficient [10-14]. Generally, there are two
methods to increase the ratio of the TCL-to-wetted surface area.
The first one is splitting the droplet into smaller droplets during
the evaporation and the second one is making the triple line of
the droplet asymmetric [15]. For instance, Shan et al [15]
numerically investigated the effect of the ratio of TCL-to-wetted
surface area. They compared the evaporation rate of circular
droplets with droplets of square and triangular contact lines,
where their TCL-to-wetted surface area was 1.29 and 1.13 times
bigger than circular contact line, respectively. They showed that
the evaporation rates on triangular and square contact areas, was
21% and 15% higher than the circular contact area, respectively.
The reason arises from the difference in the ratio of the TCL
length-to-wetted surface area. Besides, Yu et al [16] established
a three-dimensional thermal multiphase LB model for liquid–
vapor phase change on biphilic surfaces. They reported that the
sudden decrease in contact line perimeter results in notable
changes of the evaporation rate. Jansen et al [17] investigated
the dynamics of asymmetric droplet evaporation on biphilic
surfaces. They reported that as the ratio of TCL-to-wetted
surface area decreased, the evaporation rate decreased as well.
The use of biphilic surfaces is a promising method for the
enhancement of the evaporation rate. In this study, we
First, the silicon wafers were cleaned in three consecutive
steps: i) removal of the organic contaminants, ii) removal of thin
oxide layer and iii) removal of ionic contamination. These three
steps are known as RCA cleaning (standard of Radio
Corporation of America). After the RCA cleaning, 50 nm oxide
layer (for hydrophobicity) was deposited via PECVD (plasmaenhanced chemical vapor deposition) system on 1cm × 1.5cm
silicon substrates. Electron beam lithography was performed to
define the hydrophilic region. In order to improve the lift-off
quality, a short time (10 seconds) O2 plasma was processed to
remove any remaining resist residues after development. 100 nm
thick Al2O3 deposition by e-beam evaporation was evaporated,
and the substrates were left for an over-night acetone lift-off.
After the lift-off process, substrates were immersed in acetone
and isopropanol respectively and dried with nitrogen gas. Figure
1 shows a schematic of the surfaces. The black islands represent
the silicon oxide spots, and the blue parts on the surface represent
the aluminum coated parts of the surfaces.
FIGURE 1. a) Schematic figure of the surface with square islands
Figure 1. a) shows the schematic sizes and shapes of the
surfaces of square islands. The experiments are done on three
different surfaces with square-shaped islands. The length of the
largest square spots is 2400 μm and the distance between them
is 600 μm. For the middle-sized squared-shaped islands, the
length of the squares is 1200 μm which are 300 μm far from the
neighbor spots. In the third surface, which is composed of small
size hydrophilic spots, the length and distance between the
square spots are 600 μm and 150 μm, respectively. These three
spot sizes represent the one times, one-fourth times, and onesixteenth times of the water droplet on SiO2 surface, respectively.
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u
α
β
θ
µ
ρ
σ
Φ
φ
Figure 1. b shows the shape of the rhombic islands on the
surfaces. The sizes of the rhombic islands are summarized as
follows: the length of the rhombic sides are 2600, 1300, and 650
μm, and the distances between islands are 600, 300, and 150 μm
respectively.
FIGURE 2: Schematic figure of contact angle (θ), droplet height (h),
and contact area radius (RD)
FIGURE 1. c) Schematic figure of the surface with circular islands
Each of the experiments was repeated for at least three
times. Before each experiment, the surfaces were cleaned in
three consecutive steps: ultrasonic baths of acetone and
isopropanol, and after these two steps, they were further cleaned
by distilled water. Subsequently, nitrogen gas was used to dry the
surfaces more rapidly. A schematic of the set-up is shown in
Figure 3.
Figure 1. c represents the shapes of circular islands, made of
silicon dioxide, surrounded by aluminum oxide area. The
experiments are conducted on two distinct surfaces. For the first
case, the diameter of the circular islands is 1400 μm and the
minimum distance between islands is 100 μm. The islands on the
second circular-shaped surface have the diameter and the
minimum distance of 700 μm and 50 μm, respectively. The 1400
μm spots represent the size of one-fourth times of the water
droplet diameter and the 700 μm islands represent the onesixteenth times of the water droplet on SiO2 surface.
Also, it is worthwhile to state that the droplet on the bare
silicon oxide surface is considered to be on a large size island,
with a circular contact line.
EXPERIMENTAL SETUP AND PREPARATION
Using a standard micro-syringe, a 5 µl water droplet was
placed on the test specimens. The change in the contact angle
and contact area of the evaporating water droplet was measured
with time. In order to reduce the influence of airflow from
FIGURE 3: Schematic diagram of experimental set-up
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FIGURE 1. b) Schematic figure of the surface with rhombic islands
outside, the whole set-up was secured by a housing. The
temperature and relative humidity of the environment were
maintained at 23 ± 1 °C and 60 ± 5%, respectively. During the
evaporation, the videos of the evaporating droplets were
recorded by two high-speed cameras. From the recorded videos
of the evaporating water droplet on all surfaces, the contact angle
(θ), droplet height (h), and contact area radius (RD) were
obtained. Figure 2 shows a schematic of water droplet. Constant
heat flux (500 ± 2% W/m2) was supplied by a power supplier.
First, it was ensured to have steady-state condition after
sufficient time. The experiments were performed under steadystate conditions at a surface temperature of (38 ± 1°C). Since the
thermal conductivities of the substrates are sufficiently high, the
substrate temperature was almost constant during the
experiments. Moreover, the equilibrium contact angles of the
water droplet are 30° and 65° for silicon oxide and aluminum
oxide surfaces, respectively.
NUMERICAL DOMAIN
(1)
𝛁. (𝜌𝒖) = 0
𝜌(𝒖. 𝜵)𝒖 = 𝜌𝒈 − 𝜵𝑝 + 𝜇𝜵2 𝒖
(2)
𝒖. 𝛁𝑇 = 𝛼(∇2 𝑇) + Φ
(3)
−𝒖. 𝛁𝐶𝑣 + 𝛁. (𝐷𝛁𝐶𝑣 ) = 0
(4)
FIGURE 4: The simulation domain
𝛽𝜌𝑔ℎ 2
Since the Bond number (𝐵𝑜 = 𝜎 ) is smaller than unity
for all droplets, the shape of droplets is assumed as spherical
caps. The following boundary conditions for the liquid (droplet)
domain are imposed:
1.
2.
3.
At the left boundary, which is the axis of the
axisymmetric domain, symmetry boundary condition is
applied.
On the solid substrate (i.e. at z=0) no-slip boundary
condition is applied. Although a constant heat flux was
supplied during the experiments, surface temperature
𝜕𝜎
𝜕𝑢𝑡
= −𝜇
𝜕𝑡
𝜕𝑛
(5)
where n and t are normal and tangential directions,
respectively, and 𝜇 is the viscosity of the liquid. Also,
using the experimental data, an average evaporative
mass flow rate was calculated. This rate is converted to
the evaporative heat flux and distributed to the interface
assuming linear variation, which was also reported in
previous studies [19].
Size of the gas domain is selected much larger than the liquid
domain to enable the formation of buoyancy driven flow pattern
without any boundary effect. Boussinesq approximation is
utilized to include the effect of buoyancy in the gas domain.
Details of the boundary conditions in gas domain are provided
below:
1. The outer boundary of the gas domain has far field
conditions: temperature is equal to ambient temperature
and pressure is equal to atmospheric pressure.
2. At the left boundary, which is the axis of the
axisymmetric domain, symmetry boundary condition is
applied.
3. On the solid substrate (i.e. at z=0), no-slip boundary
condition is applied. For the part of the surface inside
the gas domain, a constant temperature (measured
during the experiment) is used. For the rest part of this
boundary, ambient temperature is applied.
4. At the droplet interface, no-slip boundary condition is
used. In other words, tangential velocity of the gas
phase at the interface is assumed to be equal to the one
in the liquid phase. Normal velocity is also assumed as
zero, which, in turn, leads to the omission of Stefan
flow at the gas side of the interface. One future research
direction for modeling will be the inclusion of normal
velocity at the interface. Besides, the heat, which enters
the air domain, is considered to be extracted from the
interface of the droplet volume.
After the mesh dependency analysis, the effects of natural
convection and Marangoni convection were used to analyze the
evaporation rate.
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In order to have a better understanding about the evaporation
mechanism, a quasi-steady numerical study based on the data
from the experiments was conducted. Finite Element Method
(FEM) based solver of COMSOL 5.4 software was used to solve
the governing equations, which are conservation equations for
mass, linear momentum and energy in both liquid and gas phases
together with the convection-diffusion equation for vapor
transport in the air (Figure 4):
did not vary noticeably because of the sufficiently high
thermal conductivity of the substrate. Therefore, the
temperature measured during the experiments is used as
the constant temperature boundary condition.
At the interface of the droplet, tangential velocity
dominates its normal counterpart because of the strong
thermocapillary flow and the flow pattern is primarily
dictated by tangential velocity [19]. Therefore, normal
velocity is assumed to be zero. Moreover, shear stress
of the gas on the interface is neglected. As a result,
tangential force balance at the interface reduces to:
RESULTS AND DISCUSSION
1.
Numerical Results
FIGURE 5: Marangoni flow inside the droplet
FIGURE 6: Temperature field inside the droplet
The objective of the preliminary simulations conducted in
this study is to explore the concurrent physics inside each domain
and to determine their importance in the modeling. The
preliminary simulations considered each phase separately. A
liner heat flux (based on the averaging of the experimental data)
was imposed on the interface. The next task will be to prepare a
more detailed simulation, which couples the liquid and gas
domains appropriately such that the evaporation rate measured
during the experiments will be tried to be confirmed by the
numerical model. We believe that then, the model will be able to
predict the evaporation rates for the various configurations
without the need of conducting further experiments.
FIGURE 7: Velocity field in air domain
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The simulation exhibits a small temperature gradient on the
surface of the droplet, but it was sufficient to trigger the
thermocapillary flow. Counter clock wise convection cell shown
in Figure 5 was associated with the thermocapillarity [19].
Temperature distribution inside the droplet (Figure 6) also
suggests the fact that heat is transferred from the substrate to the
droplet surface by thermocapillary convection in addition to the
conduction. Therefore, modeling of the evaporation should
account for the Marangoni flow.
The temperature gradient leads to a gradient in the density
field, which at the presence of gravity ends up with a fluid flow,
which is also known as buoyancy flow. This flow occurs in both
the droplet domain and the air domain. Although it is dominated
by the thermocapillary flow inside the droplet, natural
convection plays an important role in the gas domain. Chen et al.
[20] reported that the percentage of contribution of buoyancy
flow at the air domain in evaporation of a sessile droplet is 29%64%. Therefore, natural convection should be always included
in the simulation of air domain. Our preliminary simulations
show that natural convection in the gas phase creates an upward
flow (Figure 7), which carries the warm air from the substrate to
the apex of the droplet along the liquid-gas interface (Figure 8).
While the presence of warm air near the interface seems to limit
the heat transfer across the interface, the presence of a
continuous gas flow along the interface can promote the heat
transfer from the interface. Accordingly, the overall effect of the
buoyant gas flow on the evaporation rate is also a function of the
geometry of the substrate together with that of the liquid droplet.
FIGURE 8: Temperature field in air domain
2.
Experimental analysis
As a reference to mixed wettability surfaces, it is worthwhile
to first investigate the evaporation dynamics on simple silicon
oxide and aluminum oxide substrates. The initial water contact
angle on the silicon oxide surface was 30º. The lifetime of an
evaporating droplet on SiO2 can be categorized into three stages.
First, the droplet starts to evaporate at Constant Contact Radius
(CCR) mode for the first 61% of its evaporation time. At the
second stage, (corresponds to 22% of its lifetime) the droplet
evaporates in a Constant Contact Angle (CCA) mode. For the
rest (of 17% time), a mixed-mode was observed. The total
evaporation time was 531 seconds. Figure 9 shows the droplet
evaporation on the SiO2 substrate.
Even though the initial contact angle of the droplet on the
SiO2 is smaller than that of Al2O3 surface, their evaporation time
is almost the same. The result arises from the fact that the droplet
on aluminum oxide has a tendency to evaporate at a CCR mode,
and the triple line of the droplet remains almost the same for
more than 80% of its evaporation time. Conduction resistance
decreases as evaporation proceeds in CCR mode, which is
expected to enhance the evaporation rate continuously.
However, on the silicon oxide surface, the radius of the droplet
starts to shrink much sooner, which ends up with lowering the
evaporation rate at the CCA state. Consequently, although the
droplet on the Al2O3 has a bigger initial contact angle, its average
evaporation rate is not very different from the droplet on SiO 2
surface.
However, mixed wettability surfaces show different
dynamics of evaporation. Our experiments show that the
evaporation rate of the droplet on mixed wettability surfaces is a
function of the shape and the size of the islands. Figure 11 shows
a comparison of the evaporation rate on different surfaces with
respect to evaporation rate on the SiO2 sample. As mentioned
before, the experiments are done on three different shapes of
islands: the rhombus (R), square (S), and circle (C). The sizes of
the islands are one time (L), one-fourth times (M), and onesixteenth times (S) of the droplet radius. As can be inferred from
Figure 11, the square-shaped islands are not promising for heat
transfer enhancement. However, the rhombic and circular shaped
islands enhance the evaporation rate. Besides, it can be
concluded that the circular shape islands enhance the
evaporation rate much better than the rhombic islands.
FIGURE 9: Evaporation of water droplet on SiO2 substrate
On the other hand, the initial water contact angle on the
aluminum oxide surface was 65º. Similarly, the Al2O3 surface
shows three different stages of evaporation lifetime. The droplet
starts to evaporate at a CCR mode for more than 80% of its
evaporation time. At the second stage, a transient CCA mode was
observed which almost lasted for 2% of the evaporation lifetime.
The rest of the evaporation took place in a mixed-mode. The total
evaporation time for the droplet on aluminum oxide surface was
544 seconds, which is shown in Figure 10.
0
R-L
S-L
C-L
R-M
S-M
C-M
R-S
S-S
C-S
0.5
1
1.5
ratio of evaporation rate of the surface to evaporation
rate of silicon oxide sample
FIGURE 11: Comparison of evaporation rate on different surfaces with
respect to SiO2 sample
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FIGURE 10: Evaporation of water droplet on Al2O3 substrate
Figure 14. Evaporation of split droplets
ACKNOWLEDGEMENTS
Figure 12. Evolution of TCL on mixed wettability surfaces
Moreover, it is worthwhile to claim that during the
evaporation split of the droplets could be seen on the circularshaped islands. Figure 13 shows the split droplets on mediumsize and small-size circular-shaped surfaces, respectively. After
the split of the droplet on circular islands, the evaporation rate
suddenly increased.
FIGURE 13: Split of water droplet on circular islands, the red lines
represent the inner boundaries
The considerable fact is that in all experiments evaporation of
group droplets is dominant at the outer boundary of the group
droplets. The reason for this phenomena can be explained by the
numerical analysis. Figure 7, shows the velocity flied at the air
domain. As can be expected from the velocity field of the air
domain, at the inner boundary the natural convection does not
provide air from the outside of the inner boundary. Therefore, the
TCL is in contact with more vapor concentration in respect to the
outer boundaries, and as a matter of fact, the evaporation due to
less concentration of vapor tends to happen easier at the outer
boundaries. Figure 14 shows a snapshot of an evaporating a
group of split droplets. A more detailed analysis will be provided
in a later study.
The equipment and the characterizations support provided
by Sabanci University Nanotechnology Research and
Application Center (SUNUM), and its staff are appreciated. This
work was supported by the TUBITAK 115Y344 project number,
Science Academy Outstanding Young Investigator Support
Program (BAGEP) Turkish Academy of Science (TUBA) and
outstanding Young Investigator Support Program (GEBIP).
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