Microsensor Development
for the Study of Droplet Spreading
by
Ho-Young Kim
S.B., Mechanical Engineering, Seoul National University (1994)
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 1996
© 1996 Massachusetts Institute of Technology
All Rights Reserved
Signature of Author:
- epartmet of Mechanical Engineering
August 15, 1996
Certified by:
7"
U
Dr. Jung-Hoon Chun
Edgerton Associate Professor of Mechanical Engineering
,•,---:- o..-rvisor
Accepted by:
)nin
Professor of Mechanical Engineering
Chairman, Department Graduate Committee
frY:f
DEC 2 71996
L 8,P's "
Microsensor Development
for the Study of Droplet Spreading
by
Ho-Young Kim
Submitted to the Department of Mechanical Engineering
on August 15, 1996 in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
ABSTRACT
Droplet-Based Manufacturing (DBM) process can produce a functional part directly from
raw material. The DBM process consists of generating and depositing molten metal microdroplets. Fundamental to the deposition process is droplet spreading on the substrate
surface, for it determines geometric definition and properties of the product.
The Uniform Droplet Spray (UDS) process is a novel method of DBM which generates
droplets of a uniform size. The UDS process can accurately control the dynamic and
thermal states of droplets, thereby creating an excellent opportunity to study the droplet
impact behavior.
The measurement techniques available today, however, are inadequate to monitor the highspeed impact behavior of micro-droplets due to limits on the temporal and spatial
resolutions. A novel technique to capture the transient spreading of molten metal droplets
has been developed using the Very Large Scale Integration (VLSI) technology. The
microsensor consists of thin conducting lines (Au) finely spaced and mounted on a
nonconducting base (Si).
In order to verify the UDS process capability to control the impact conditions of droplets,
molten tin droplets were sprayed with varied conditions such as orifice diameter, ejection
pressure, and charging voltage. Velocity of the droplets was measured using a high speed
camera at 6,000 frames per second. The simulation results were compared with the
experimental results and the comparison showed fairly good agreement between them.
Spreading behavior of a molten tin droplet was measured by depositing a 356 pm diameter
droplet at the velocity of 4.84 m/s onto the microsensor. The initial speed of contact area
expansion was found to be about 2.4 times the impact velocity. The spreading speed
decreased dramatically afterwards and the spreading process lasted over 450 jis. The
experimental results verified that the microsensor had satisfactorily monitored the transient
spreading behavior of molten metal droplets.
Thesis Supervisor:
Dr. Jung-Hoon Chun
Esther and Harold E. Edgerton Associate Professor of Mechanical Engineering
Acknowledgments
First of all, I would like to thank Professor Jung-Hoon Chun, my advisor, for
guiding and shaping my research through constant encouragement over the past two years.
My sincere appreciation goes to Professor Taiqing Qiu, who shared the novel concept of
the microsensor with me. My gratitude to Dr. Nannaji Saka for helping me to organize this
thesis.
It has been a great pleasure to work with the many friends at the Droplet-Based
Manufacturing Laboratory. Thank you, Dr. Chen-An Chen, who has been my guiding
light at MIT. Also, Jeanie Cherng, who kept me awake during the long days. My mentor,
Sukyoung Chey, for his words of wisdom. Jiun-Yu Lai and Juan-Carlos Rocha for all
their assistance. And Dr. Pyongwon Yim, whose laughter I will never forget.
Special thanks to my lab partners: Jim Derksen, Sangjun Han, Mark Hytros,
DongSik Kim, and Dr. Tom Nowak. Sincere appreciation to Paul Acquaviva, who has
been an exceptional friend.
Also, special thanks to Marcelino Essien of the Sandia National Laboratory,
Albuquerque, NM, who helped me with the high-speed photography experiments. My
deepest gratitude to Bernard Alamariu at MIT Microsystems Technology Laboratory for
fabricating the microsensors.
With the warmest regard and appreciation to my dearest friends, Youngjin Chang,
Jungin Kim and Minsung Jin, for their encouragement and support. Taewoong Koo,
thank you for assisting me in the preparation of this manuscript.
My biggest thank you to my parents who gave me the greatest love. I thank my
sister and brothers for their unconditional love and support. Without their love and
support, this thesis would not have been possible.
Table of Contents
Title Page
1
Abstract
2
Acknowledgments
3
Table of Contents
4
List of Tables
6
List of Figures
7
1
INTRODUCTION
8
1.1
8
1.2
1.3
2
Background and Motivation
1.1.1 The Uniform Droplet Spray process
1.1.2 Droplet spreading
1.1.3 Dynamic spreading behavior
Objective of the Investigation
Overview of the Thesis
8
9
10
11
11
DESIGN AND FABRICATION OF THE MICROSENSOR
12
2.1
12
2.2
2.3
2.4
2.6
Introduction
2.1.1 Contact area expansion
12
12
2.1.2 Resolution
Design Concept
2.2.1 Resistance network
2.2.2 Transient resistance change
Design Analysis
2.3.1 Electrical network
2.3.2 Circuit analysis
Design Criteria
2.4.1 Grid dimension
2.4.2 Sensor material
Design and Fabrication
2.6.1 Materials and dimensions
17
20
20
20
22
22
2.5.2 Fabrication process
23
13
13
14
14
14
2.5.3
3
26
3.1
3.2
26
26
26
3.3
3.4
Introduction
Flight Dynamics of the Droplet Spray
3.2.1 Drag force on a droplet
3.2.2 Force balance
Simulation of Droplet Flight
3.3.1 Scheme of the simulation
3.3.2 Determination of initial velocities
29
30
30
30
Experiments on Droplet Trajectory
3.3.1 Experimental setup
3.3.2 Analysis of experimental results
Results of Simulation and Experiments
3.4.1 Scattering distance
3.4.2 Effects of droplet size on velocity
31
31
31
33
34
34
3.4.3 Effects of ejection pressure on velocity
3.4.4 Effects of charging voltage on velocity
3.4.5 Discharge coefficient
37
38
38
DROPLET SPREADING EXPERIMENT
40
4.1
40
4.2
4.3
4.4
5
25
VELOCITY OF SPRAYED DROPLETS
3.3
4
Validation of design
Experiment Apparatus
4.1.1 Droplet generator
4.1.2 Spreading sensing setup
Experimental Procedure
Experimental Results
4.3.1 Impact conditions of droplet
4.3.2 Initial conditions of measurement setup
4.3.3 Voltage output
4.3.4 Spreading area
4.3.5 Spreading speed
Discussion
4.4.1 Spreading speed
4.4.2 Time scale of spreading
40
40
41
41
41
43
43
45
46
47
47
48
SUMMARY
50
BIBLIOGRAPHY
51
List of Tables
Table 1.1
History of Droplet-Spreading Imaging Techniques
10
Table 2.1
Electrical Contact of Tin Droplet and Polycrystalline Si Substrate
23
Table 2.2
Electrical Characteristics of the Sensor Materials
23
Table 3.1
Droplet Flight Experiment Conditions
34
Table 3.2
Droplet Charges
38
Table 3.3
Discharge Coefficients
39
Table 4.1
Spray Conditions
43
Table 4.2
Impact Conditions
45
List of Figures
Figure 1.1
Uniform Droplet Spray Apparatus
Figure 2.1
Sensor Surface
Figure 2.2
Transient Diameter and Resistance
Figure 2.3
Electrical Contact and Resistance
Figure 2.4
Network Construction by Spreading
Figure 2.5
Circuit Analysis
Figure 2.6
Discrete Resistance
Figure 2.7
Sensor Dimension
Figure 2.8
SEM Micrograph of the Sensor Surface
Figure 3.1
Flight of Droplets
Figure 3.2
Force Balance on a Droplet
Figure 3.3
Experiment of Droplet Flight
Figure 3.4
Analysis of Droplet Velocity
Figure 3.5
Droplet Flight Simulation and Experiments
Figure 3.6
Scattering of Droplet Spray
Figure 4.1
Spreading Sensing Setup
Figure 4.2
Droplet Collection
Figure 4.3
Velocity and Temperature Profiles
Figure 4.4
Transient Voltage Output
Figure 4.5
Transient Diameter
Figure 4.6
Spreading Speed
Chapter 1
1.1
INTRODUCTION
Background and Motivation
1.1.1 The Uniform Droplet Spray process
The Droplet-Based Manufacturing (DBM) process is based on metal droplet
deposition. Its application includes spray forming, thermal spraying, rapid prototyping,
and electronics packaging. In order to improve the quality of products made by the DBM
process, it is essential to understand how the process parameters such as size of droplets,
velocity, flux, and thermal state affect the geometry and the microstructure of the deposit.
Because conventional droplet spraying processes, such as gas atomization and plasma
spraying, produce droplets in randomly distributed dynamic and thermal states,
understanding the effects of process parameters is difficult.
The Uniform Droplet Spray (UDS) process, however, can overcome these
shortcomings by creating a spray of droplets with the same size, velocity, and temperature
(Passow 1992). By producing uniform droplets, excellent opportunities can be provided to
study the effects of various process parameters on the deposit quality. In addition, critical
process parameters can be independently and precisely controlled to produce desired
products with greater accuracy.
Figure 1.1 is a schematic diagram of the UDS process. The metal contained in a
crucible is melted by a heater and is ejected through an orifice with pressure applied from
an inert gas supply. The ejected molten metal forms a laminar jet, which is vibrated by a
piezoelectric transducer at the specified frequency. The disturbance due to the vibration
grows until the jet breaks up into a stream of uniform droplets. During the break-up
process, each droplet is electrically charged by a direct-current (DC) voltage charging plate.
The charged droplets repel each other, preventing them from merging. The magnitude of
electrical charge on each droplet can be controlled to affect the trajectory and mass flux of
the spray. The droplets are then deposited on a substrate whose motion and temperature is
controlled to produce the desired geometry and microstructure.
Thermc
Cruc
ge Source
Charging Plate
*
•·
•
Uniform Droplets
*:
.
*o.
Substrate
X-Y Linear Table~
Figure 1.1
Uniform Droplet Spray Apparatus
1.1.2 Droplet spreading
Droplet deposition is fundamental to the DBM process, for it determines geometric
definition, such as surface porosity and conformity to the substrate shapes, and mechanical
properties of the deposit. Deposition phenomena comprise the impact of individual
droplets on substrates, coalescence of adjacent splats after impact, bonding between
droplets and the deposit, and microstructural evolution of a sprayed deposit. The impact
and spreading behavior of each droplet are crucial to the overall deposition process, for
they govern the subsequent processes.
In spite of its importance in the DBM process, the study of impact or spreading
behavior of molten metal droplets has failed, so far, to yield satisfactory information for the
manufacturing process. It is not only due to the inherent complexity of the phenomena, but
also to the inadequate sensing capability. Since the conventional molten metal spray
processes create non-uniform droplets, accurate evaluation and control of droplet impact
conditions are in essence difficult. Furthermore, the lack of proper experimental data has
hindered a successful analytical approach to the impact phenomena.
Therefore, novel experimental approaches to the molten metal droplet impact are
strongly demanded. Viewed in this light, the UDS process can provide new opportunities
to experiment on micro-droplet impact. Precise control of the droplet conditions, such as
size, velocity and thermal state, attains consistent reliable data. The data obtained through
accurately controlled experiments can verify and improve the analytical approach to the
phenomena.
1.1.3 Dynamic spreading behavior
Central to a fundamental understanding of the dynamics of impact is the ability to
monitor the transient behavior of spreading droplets. For experimental observations on
liquid droplet spreading, a variety of high-speed imaging techniques have been used to
record the dynamic shapes (Worthington 1908a, b, Engel 1955, Wachters and Westerling
1966, Akao et al. 1980, Stow and Hadfield 1981, and Zhao et al. 1996b). The cited
researchers and the information regarding their experiments are listed in Table 1.1.
Although the developments in electronics and laser techniques have enhanced the
temporal and spatial resolution of the measurement immensely, the high-speed impact
behavior of micro-droplets is still beyond the scope of the current state-of-the-art. Due to
the profound difficulties in the experiments, the development of an innovative method to
capture the transient behavior is required. Exploiting the capability of the UDS system, an
innovative in situ measurement method is expected to provide a concrete understanding of
the spreading behavior of molten metal droplets.
Table 1.1
History of Droplet-Spreading Imaging Techniques
Researcher
Experimental
Droplet
Impact Velocity Camera Speed
Diameter (mm)
Technique
(m/s)
(frames/s)
Worthington
Electric spark
6
Unknown
N. A.
Engel
Schlieren
10
Unknown
10,000
photography
Wachters and
Stroboscopy
1.7
1.5
100
Westerling
1
5,000
High speed
2.5
Akao et al.
photography
4
N. A.
3
Camera
Stow and
Hadfield
triggering
2
N. A.
Holography
3
Zhao et al.
1.2
Objective of the Investigation
The objective of this thesis is to develop a novel experimental technique for the
measurement of the micro-droplet spreading. Exploiting the high electrical conductivity of
liquid metals, a microsensing technique to monitor the spreading behavior is developed.
The microsensor is designed and fabricated utilizing the microelectromechanical techniques.
Results of an experiment conducted with molten tin droplets generated by the UDS
apparatus are shown and discussed.
The key attribute of the UDS process in the droplet impact study is its precise
control mechanism of the impact conditions. A simulation model of the flight velocity of
droplets in the UDS process was developed. Experiments were conducted to measure the
velocity and the results were compared.
1.3
Overview of the Thesis
Chapter 1 describes the background, motivation, and objectives for the thesis.
Chapter 2 details the design of the microsensor, which consists of finely spaced electrically
conductive sensing lines on a nonconducting base. The electrical network comprising the
molten metal droplet and sensing lines is analyzed. Design criteria for the sensor are
discussed and the fabricated sensors are described. In Chapter 3, the droplet flight model
in the UDS process is discussed to verify the capability of the UDS process to control the
impact conditions of droplets. Experimental results are compared with the simulation
results based on the model. In Chapter 4, in situ measurement of the micro-droplet
spreading is performed using the microsensor and a high-speed data acquisition system.
The experimental setup and the results are discussed. A summary of this thesis is
presented in Chapter 5.
Chapter 2
2.1
DESIGN AND FABRICATION OF
THE MICROSENSOR
Introduction
2.1.1 Contact area expansion
The most characteristic feature of droplet impact is the radially expanding film at the
bottom of the liquid droplet. As the liquid film advances from the periphery of the contact
area, the top portion of the droplet collapses and disappears into the horizontal film.
The planar jet expansion plays a major role in identifying the spreading
characteristics of liquid droplets. The transient change of contact area determines the
spreading factor, 1r, defined as:
D(t)
SD()
d
(2.1)
where D is diameter of the circular contact area, changing with time, t, and d diameter of
the droplet before impact. The expansion speed of the contact governs the instability
phenomena at the periphery, and high expansion speed causes splashing (Allen 1975).
Therefore, dynamic sensing of contact area expansion is very important in the
observation of droplet spreading. Furthermore, a spreading area sensor can be used to
characterize the liquid fraction in a molten metal droplet. A partially solidified droplet does
not spread as much as a fully liquid droplet (Chen 1996), and thus a correlation between
the liquid fraction and droplet spreading can be established.
2.1.2 Resolution
To measure the transient spreading of droplets, the resolution of measurement
should be high, both temporally and spatially. Since the spreading of a liquid droplet takes
place in a very short time, a high speed measurement technique should be employed to
achieve high temporal resolution. In addition, the small dimension of the droplet requires a
high spatial resolution.
The required temporal resolution can be deduced from the time scale at which the
droplet impact takes place, i.e. spreading time scale, ts , defined as:
12
ts = -
,
(2.2)
Vimp
where Vimp is impact velocity. The measurement should be performed within ts to capture
the time sequence of impact motion. Hence, the temporal resolution, tr should satisfy the
criterion given by:
d
tr << -,
(2.3)
Vimp
i.e., the temporal resolution should be much finer than the spreading time scale.
The spatial resolution of the measurement system can be deduced from the size of
the droplet. To monitor the shape evolution of droplet during spreading, the spatial
resolution, sr, should satisfy the following:
sr << d,
(2.4)
i.e., the spatial resolution should be much finer than the droplet diameter.
In the UDS system, the typical diameter of a droplet is in the order of 100 .m and
the typical velocity is about 5 m/s. Consequently, the temporal resolution of the
measurement system should be tr << 10,s, and the spatial resolution sr << 100m.
These requirements imply that existing sensing techniques are inadequate to capture the
spreading process.
2.2
Design Concept
2.2.1 Resistance network
A finely spaced resistance network laid out on the nonconducting substrate is used
as the spreading sensor, utilizing the high electrical conductivity of the molten metal. The
schematic of the sensor surface is shown in Figure 2.1. In the figure, the width of the
sensing grid line and the spacing between the grid lines are denoted A, and A,s
respectively. The total width and length are denoted w and 1,respectively.
lA
-ýa
-
w
Figure 2.1
Sensor Surface
2.2.2 Transient resistance change
As a droplet spreads on the sensor surface, the closely spaced electrical resistors are
covered with molten metal and consequently connected. This leads to a drop in the total
electrical resistance of the network. The transient change in electrical resistance, R(t) is
correlated to the contact area expansion of the spreading droplet. The expected resistance
and diameter changes with droplet spreading are illustrated in Figure 2.2.
2.3
Design Analysis
2.3.1 Electrical network
The adjacent resistors on the sensor are electrically connected when a molten droplet
is brought into contact with them. The total resistance resulting from the contact can be
calculated from the schematic in Figure 2.3. It is the sum of the resistances of the
individual sensing lines, Rl, 1 and R1,2 , film resistance, Rf,l and Rf, 2 , constriction
resistance, Rc, 1 and Rc,2 , and splat resistance Rs . Therefore, the resultant resistance
across adjacent lines is given by:
Rr =(R 1 + R1 2 ) + (Rf + Rf,2) +(Rcl +Rc 2 ) + R.
14
(2.5)
(a) Droplet Spreading
D(t)
(b) Diameter
R(t) ý
(c) Resistance
Figure 2.2
Transient Diameter and Resistance
Rf, 1 + Rc, I
"A"L
Rf, 2 + ,2
j
view "A-A"
(a) Contact of Droplet and Sensor
i
R,,l
R,
Pc,1
Rs
R, 2
Rf,
(b) Resistance Schematic
Figure 2.3
Electrical Contact and Resistance
The resistance of an individual line, R1 , is given by:
R, = Pele
A
(2.6)
where Pe is resistivity of the sensing line, le and A are length and cross sectional area of
the current path, respectively. Constriction resistance, Rc , is approximately:
Rc =Pe+ ed
(2.7)
where Pe,d is resistivity of the droplet.
In order to eliminate the uncertainties in resistance measurement, it is desirable that
resistances other than those of the sensing lines should be negligible. Film resistance can
be minimized by removing the oxidized surface and impurities. To ignore the constriction
resistance compared with sensing line resistance, the following should be satisfied:
Pe + Pe,d
t
Pele
A
(2.8)
i.e., the constriction resistance should be much smaller than the resistance of the sensing
lines. The splat resistance can be ignored if the area of current flow in the splat is much
larger than those in lines even when the resistivity of the splat and sensing line is
comparable.
Then the resultant resistance, Rr, becomes:
Rr =
(le, 1 + le,2),
(2.9)
where le,1 and le,2 are the lengths of current path in each line. If a droplet size is negligibly
small compared with the sensing line length, the sum of the current paths is essentially the
same as the whole length of one line. Therefore, electrical connection between the grid
lines is ideal and Rr is nothing but R1 , with le in Equation (2.6) equal to grid line length:
R,. = R.
(2.10)
2.3.2 Circuit analysis
To correlate the transient resistance and spreading area, it is necessary to analyze the
total circuit made by spreading as in Figure 2.4. Figure 2.5 (a) demonstrates a circuit
which consists of resistors stemming from each connection line with electrical potential
difference. Node voltages marked V2 and V3 are identical due to ideal connection.
Therefore, the electrical network is simplified as shown in Figure 2.5 (b) and (c).
V
Figure 2.4
Network Construction by Spreading
Consequently, if N sensing lines from each connection line, therefore, total 2N sensing
lines are connected by a droplet, then the equivalent resistance, Req, is given by:
1
Req
=-
I
RO
N
+-,
RI
where Ro denotes the initial resistance of the sensor.
(2.11)
JJ II IVV•lVI I •ll IV
Connection
Line
+ Rc, 1 + Rs + Rc, 2 + Rf, 2 )
0
0
0
(a) Equivalent Circuit I
(b) Equivalent Circuit 2
(c) Equivalent Circuit 3
Figure 2.5
Circuit Analysis
2.4
Design Criteria
2.4.1 Grid dimension
Grid dimensions determine the resolution and accuracy of a measurement. The
dimensions consist of the width of grid lines, Al, and the spacing between them, As.
Since grid lines have finite width and spacing, the resistance is measured as a discrete
signal. Figure 2.6 shows the discontinuous resistance change with the increase of area
covered.
For illustration, assume that spreading starts from the center of the spacing. When
the spreading diameter reaches one spacing, As, two grid lines are connected and the
resistance decreases from the initial resistance, Ro. This resistance stays the same until the
spreading droplet touches the next grid lines. Therefore, the second drop of resistance
takes place when the diameter reaches As + 2(Al• + As). The resistance falls the same
amount each time the diameter increases by 2(A, + A,).
Hence, the maximum amount of uncertainty in the diameter corresponding to one
resistance value is 2(, l + As), which is in turn the measurement resolution. The grid
dimension should be much smaller than the droplet diameter, d, to capture the transient
diameter change accurately. Consequently, the design requirement for grid dimension is:
Xtl+As << d.
(2.12)
2.4.2 Sensor material
Selection of sensing line material is important to ensure the accuracy and reliability
of the measurement. The most important factor in the selection is good physical and
electrical contact between the droplet and the sensor surface. Good physical contact can be
achieved through enhancing wetting of liquid metal to the sensor.
As discussed in Section 2.3.1, sensor material should minimize the film and
constriction resistance. Film resistance is minimized by eliminating the oxidized surface or
by adopting a material less likely to oxidize. Equation (2.8) states the condition necessary
to neglect the constriction resistance, which can be rewritten as below:
Pe
+
Pe,d << Pe
(2.13)
t
A1
As
(a) Increase of Spreading Diameter
Req
B
C
Spreading Diameter
AS 2(Al + A) 2(Resist + A) 2(vs.
(b) Resistance vs. Spreading Diameter
Figure 2.6
Discrete Resistance
since the cross section of the current path, A, is A = A2ullt, At being thickness of the
sensing line. If the resistivities of the sensing line and of the droplet are of the same order,
this condition is satisfied when the thickness, At, of the grid line is much smaller than the
total length, le.
Candidates of the sensor material included aluminum (Al), polycrystalline
silicon (Si), copper (Cu), and gold (Au). To investigate the wetting and electrical contact
between molten metal and the materials listed above, pure tin droplets were deposited onto
the sensors made of each material. The dimension of the sensors are shown in Figure
2.7 (a) except the copper sensor whose dimension is 500 times larger than the dimension
presented.
The initial resistance and the final resistance due to spreading of the droplets were
measured. The aluminum and polycrystalline silicon sensors turned out to have very poor
electical contact with tin droplets. The resistance change of the aluminum sensor was
negligible, and the results for the polycrystalline sensors are presented in Table 2.1. The
resistance of individual polycrystalline silicon sensing line was 9 kQ.
In Table 2.1, the ratio of ideal to actual resistance is exteremely low, which shows
the poor electrical contact between the polycrystalline silicon sensor and tin droplets. Since
the poor contact of aluminum and polycrystalline silicon sensors was hypothesized to be
due to their poor wetting with liquid tin, such a material with good wetting behavior as
copper was tried. Droplets were deposited on two copper surfaces, one of which was
cleaned with hydrochloric acid (HC1) and the other was not. The final resistance of the
cleaned surface agreed with the ideal value, while the other showed a great discrepancy, as
the polycrystalline silicon, although both surfaces were well wet by the droplets.
Since the difference in electrical contact results from the oxidized layer, which was
cleaned off the surfaces by HC1, it is concluded that the sensor material should be free of
oxidized layer as well as be well wet by the droplet. Therefore, gold was selected as an
ideal material, which does not form an oxide on its surface and has a good wetting
behavior.
2.6
Design and Fabrication
2.6.1 Materials and dimensions
The microsensor consisted of a base, and sensing and connection lines. A silicon
wafer was used as the base, and pure gold (Au) and copper (Cu) were deposited onto the
Electrical Contact of Tin Droplet and Polycrystalline Si Substrate
Table 2.1
Ideal Final Actual Final Ratio of Ideal to
Diameter of
Initial
Experiment
Actual
Resistance
Resistance Covered Area Resistance
Number
Resistance
(Q)
(2)
(mm)
(4)
0.038
40
1059
2.81
1
1915
0.032
780
25
2.84
1915
2
522
0.034
18
1465
4.06
3
0.037
1390
1.35
52
1715
4
wafer as sensing and connection lines, respectively. To facilitate thee deposition process,
titanium (Ti) was placed under the gold lines.
The electrical charateristics of Au and Ti lines are listed in Table 2.2. The
dimensions of the sensor and the Scanning Electron Microscopy (SEM) micrograph of the
sensor surface are shown in Figure 2.7 and Figure 2.8, respectively. The length of the
sensing line is 5 mm, while the width and spacing of the lines are both 2 gm.
2.5.2 Fabrication process
The microsensors were fabricated by Microsystems Technology Laboratory at MIT
using a VLSI (Very Large Scale Integration) technology. The process flow is summarized
below:
(1) Silicon wafer was cleaned.
(2)Silicon surface was oxidized and 0.1
gm thick silicon dioxide (SiO 2 ) grown.
(3) 0.1 gm thick Ti film was deposited onto the wafer surface.
(4) 0.1 gm thick Au film was deposited onto Ti layer.
(5) Photolithography mask was placed on Au layer to etch sensing lines.
(6) Sensing lines were etched through the mask.
Table 2.2
Electrical Characteristics of the Sensor Materials
Single Line
Thickness
Film Resistivity
Bulk Resistivity
Material
Resistance (kQ)
(x 10-82m)
(m)
(x10~Omm)
1
4
0.1
2.2
Au
22.5
90
43.1
0.1
Ti
7 mm
5 mm
Connection Line
Sensing Line
Base
E
E
(a) Top View
Au
Ti
xx
-----
K
"-
2
~m
_ _ 21m _
I
Silicon Wafer
(b) Perspective View
Figure 2.7
Sensor Dimension
gm
-0.1
v. ImIII
2
2gm
Figure 2.8
SEM Micrograph of the Sensor Surface
2.5.3 Validation of design
The width, Ai, and spacing, As, of the sensing lines were both 2 gm and the
resolution of diameter measurement was 8 gLm. This yields fairly fine spatial resolution for
droplets whose diameter is on the order of 100 gm, which is the case in the UDS process.
The extremely small thickness, At , of the Au line, i.e. 0.1 gim, increases the resistance of
an individual sensing line and ensures that constriction resistance is negligibly small. In
addition, gold is not oxidized and shows good wetting behavior with usual molten metal.
Therefore, good electrical contact can be achieved and film resistance is ignored.
Chapter 3
3.1
VELOCITY OF SPRAYED DROPLETS
Introduction
As a starting point of the study of molten metal droplet impact, an accurate
knowledge of impact conditions is crucial. Droplet impact conditions include diameter,
velocity, temperature, and liquid fraction of a droplet. Therefore, it is essential to identify
dynamic and thermal states of the droplets generated by the UDS process.
Passow (1992) modeled the trajectory and heat transfer of droplets in the UDS
process. Chen (1996) verified the heat transfer model using a splat quenching method. In
an effort to verify the models, experiments were conducted to measure the droplet flight
velocity. This chapter experimentally verifies the analytical modeling on the flight velocity
of the droplets.
3.2
Flight Dynamics of the Droplet Spray
As described in Chapter 1, electrically charged droplets generated from the liquid jet
interact with each other within the stream. As they travel down, droplets veer off the center
of the stream due to intial transverse disturbance and electrical repulsion imposed on each
other. Figure 3.1 shows the droplet flight.
Droplet velocity and trajectory can be predicted by balancing the force acting on a
droplet, i.e. gravitational force, drag force, and electrostatic repulsion force. Figure 3.2
shows the forces acting on a droplet. In the Figure, g denotes the direction of gravity, v
the direction of flight, r12 the distance between droplets Dl and D2, Fd the drag force, Fg
the graviational force, F,, 2 , F,,3 , and Fe4 are the Coulomb forces between droplets D1
and D2, Dl and D3, and Dl and D4, respectively.
3.2.1 Drag force on a droplet
When a droplet falls in a gaseous atmosphere, the drag force decelerates the droplet.
The drag force, Fd, can be expressed as:
d c= d
d2
pg |1,
(3.1)
t-r
9
Liquid Jet
0
Droplets
Aligned
Aligned Droplets
0
0
O
0
0
Scattered Droplets
Figure 3.1
Flight of Droplets
9
e13
Fe
\.__..
Figure 3.2
Force Balance on a Droplet
where Cd is drag coefficient, d diameter of a droplet, pg density of the gas, and v velocity
of a droplet. The drag coefficient of sphere moving in fluid is a function of Reynolds
number, Re:
Re = pgvd
(3.2)
jUg
where ug is viscosity of surrounding gas.
In the UDS process, the droplets are initially in an aligned stream; the velocity field
of the surrounding gas is obviously different from the case of individual droplet (Liu,
1988). Consequently, a different model of the drag coefficient should be employed for the
UDS process.
Due to wake effects, the drag force acting on a droplet in an aligned stream is less
than that on an individual droplet (Mulholland et al, 1988). The drag coefficient of a
droplet in a train of droplets is a function of Reynolds number, defined by Equation (3.2)
and a spacing between droplets. Mulholland et al. (1988) assumed that the drag coefficient
of droplets in an aligned stream, Cl, could be correlated as follows:
[Ce,(Re, L/d)]11 = CD(Re,L/d)]-n +[CE(Re)]-n ,
(3.3)
where L is spacing between two droplets, d droplet diameter, C° asymptotic form for Ca
as L/d - 1, CE drag coefficient for isolated sphere, and n is empirical parameter
(n=0.678). C° is defined in this case as:
CD(Re, L/d) = C'(Re) + aRe-1(L/d- 1),
(3.4)
where Cj is drag coefficient when L/d = 1, and a is empirical parameter (a = 43.0).
This is based upon the assumptions that the extent to which droplet spacing influences the
local drag coefficient depends on the length of wake behind each droplet and that the wake
length increases approximately linearly with Re. CO is given as follows:
[CD'(Re)]-n = [Crod(Re)]- n - [CE(Re)]-,
(3.5)
where Crod is drag coefficient of a long rod. This is because as droplet spacing approaches
the droplet diameter, the drag coefficient may be assumed to approach the drag coefficient
of a long rod, which is given by:
0.755
Crod(Re) = Re
(3.6)
The drag coefficient, CY , of an individual droplet is proposed that (Mathur et al., 1989):
CY (Re)= 0.28 +
6
1I~
21
+ -R
· e
Re
(3.7)
The drag coefficient described above is for droplets which move along a centerline
of a stream. Droplets in the UDS process, however, do not stay on the centerline along
their path: This requires the following modification in the case when the droplets remain
less than one drop radius from the centerline:
CD(Re, Lid, rc/rd) = (1- rccrd)CE+ (rCrd)Cý,,
(3.8)
where rc is distance from the centerline and rd radius of the droplets. Once the droplets
have scattered by more than one drop radius from the centerline, the drag coefficient for a
single sphere should be used.
3.2.2 Force balance
The Coulomb force, Fe, due to electrostatic repulsion between two droplets with
equal charge, qd, at distance r is defined as:
2
Fe = 1E qd, '
(3.9)
where E0 is the permittivity of free space, eo = 8.8542 x 1 0-12 2 /N
of charge induced in each droplet, q,, is (Passow, 1992):
qd
e
-f
Inde/di) f
V,
m 2 ). The amount
(3.10)
where dc and dj are the diameters of the charging ring and the jet, respectively, vj jet
velocity, f perturbation frequency, and V charging voltage. The total Coulomb force
acting on droplet i due to its n nearest neighboring droplets is given by:
=
1
4e 0 i
(3.11)
, rir
where ri is distance between droplet i and j. On the other hand, gravitational force, Fg,
acting on a droplet is:
4 3
Fg = 3 crpg
(3.12)
Using the force balance between the drag, gravitational and electrical forces,
equation of motion for a droplet becomes:
mi = Fcd + Fg + Fe,
(3.13)
where ii is acceleration of a droplet.
3.3
Simulation of Droplet Flight
3.3.1 Scheme of the simulation
Numerical simulation was performed to describe the trajectory of droplet sprays
(Passow, 1992). Using the input conditions of a spray, namely orifice size, ejection
pressure, charging voltage, and vibration frequency, a fourth-order Runge-Kutta numerical
integration scheme was employed to calculate the velocity and trajectory. Additional
information on the simulation program was discussed by Passow (1992) and Abel (1993).
3.3.2 Determination of initial velocities
The ideal velocity of a laminar jet through an orifice can be calculated using the
Bernoulli's equation, and is given by:
2AP
Vj,ideal =-
PP ,
(3.14)
where Vj,ideal is ideal velocity of the emerging jet and AP pressure loss. The initial
velocity of a droplet, therefore, can be obtained by assuming that it is equal to the jet
velocity, vj:
i =Vj =kf
2A.PP,
(3.15)
where vi is the intial velocity of a droplet and AP the ejection pressure, which is the
pressure difference between crucible and spray chamber. The discharge coefficient, kf, is
due to the friction of the flow through the nozzle as well as to the surface tension of the
liquid (Yim, 1996).
An empirical discharge coefficient is different for each orifice, and depends on
nozzle geometry, properties of the liquid, and the jet velocity. Hence, evaluation of kf is
possible only when vi is known. In the simulation, the experimental data were used to
determine the value of kf .
3.3
Experiments on Droplet Trajectory
3.3.1 Experimental setup
Experiments to measure the velocity of droplets were conducted using Kodak
EktaPro EM Motion Analyzer. The experimental appratus is schematically shown in
Figure 3.3. The droplet spray was recorded at 6000 frames/s and the data were
downloaded to a personal computer utilizing the software MAW (Motion Analysis
Workstation). MAW could also control the motor to move the camera to the desired flight
distance.
3.3.2 Analysis of experimental results
Droplet video images were analyzed making use of MAW. A schematic of the
analysis is presented in Figure 3.4. A droplet was selected at a certain frame and the
distance the droplet moves until the next frame was automatically measured by MAW.
High pressure
Droplet generator
Gas chamber
Figure 3.3 Experiment of Droplet Flight
MAW counted the number of pixels on the screen which corresponds to the travel distance
of a selected droplet, and calibrated it to the actual distance. The distance was divided by a
frame duration to obtain a velocity of the droplet. The analysis was carried out for four
droplets at each flight distance.
In Figure 3.4, the flight distance of a selected droplet is represented as Al and the
elapsed time between the frame is At. The recording speed employed in the experiment
was 6000 frames/s, hence At = 1/6000s. Consequently, the velocity of the selected
droplet can be calculated as:
SAl
v = A.
At
I
(3.16)
*1
t
Amm
I..
t + At
Figure 3.4
3.4
Analysis of Droplet Velocity
Results of Simulation and Experiments
Experments were conducted to verify the simulation of the droplet velocity and
trajectory for four different spray conditions. Melt material used in the experiment was
pure tin and melt temperature was kept at 3000C. The experimental conditions are listed in
Table 3.1. These conditions were chosen to verify the effects of important input
conditions of sprays, such as orifice diameter, ejection pressure, and charging voltage.
With experiment I as the control experiment, the effect of orifice diameter was
investigated in experiment 2, the effect of ejection pressure in experiment 3, and the effect
of charging voltage in number 4. In all cases, as shown in Figure 3.5, measured velocities
and simulation results are in good agreement. The investigation results are discussed
below.
Experiment
Number
1
2
3
4
Table 3.1
Orifice
Diameter
(pRm)
100
150
100
Droplet Flight Experiment Conditions
Ejection
Charging
Pressure
Voltage
(V)
(kPa)
137.9
500
137.9
500
206.9
500
100
137.9
1000
Vibration
Frequency
(kHz)
10.91
8.48
12.63
11.36
3.4.1 Scattering distance
Scattering distance is defined as the flight distance where droplets scatter more than
one drop radius from the centerline. After the scattering distance, droplets experience drag
force of single sphere. Generally, the velocity of a droplet in the UDS process increases
from the break-up point to the scattering distance since the gravitational force exceeds the
drag force in an aligned stream. Once the spray reaches the scattering distance, the drag
force relevent to a single sphere surpasses or becomes comparable to the gravitational
force. Therefore, the velocity decreases or slightly increases depending on the droplet
momentum.
It has been found that the input conditions of droplet sprays - orifice size, ejection
pressure, and charging voltage - have strong influences on the scattering distance. The
differences in the scattering distances play a major role in determining the velocity profiles.
The experiments confirmed that the flight model can accurately predict the scattering
distance as well as the velocity profile. Figure 3.6 shows photographs of droplet sprays
before and after the scattering distance, respectively.
3.4.2 Effects of droplet size on velocity
Comparison of experiments 1 and 2 shows the effects of orifice size, thus droplet
size on the velocity. The diameter of a droplet, d, generated from the liquid jet can be
calculated using the mass conservation (Passow, 1992):
(6A.)
d=
1/3
,
(3.17)
where Aj is cross-sectional area of the jet and 2 wavelength of the oscillations, i.e. the
6
4 ....
......
......
-Sctttt--------------
*3
2
Experiment
O,+,X, *
1
:Simulation
0
0.1
0
0.2
0.3
0.4
0.5
0.6
Flight Distance (m)
(a) Experiment 1 - Control Experiment
6
5
~~~";~~----"~---r~-
-- ------------~'-----
-4
......... ............ Scattered...............
o3
2
.O,+,X
1
*
:Experiment
:Simulation
0
0
0.1
0.2
0.3
0.4
Flight Distance (m)
(b) Experiment 2 - Larger Droplets
0.5
I
0.6
5
4~..............
....... . ...... .........
• . ei°........................... ............ .
• Scattered.
S
.
0
o3
2
:Experiment
O,+,X,
1
-------------------------Simulation-------------
:Simulation
II
0
0.1
0.2
0.3
0.4
0.5
O.E
Flight Distance (m)
(c) Experiment 3 - Higher Ejection Pressure
I
7
...
....
. .............................................
------------... Scattered.: .........
............... ...............
S: Experiment
:Simulation
---
0.2
0.3
0.4
Flight Distance (m)
0.5
(d) Experiment 4 - Higher Charging Voltage
Figure 3.5
Droplet Flight Simulation and Experiments
0.6
(a)
(b)
Before Scattering
After Scattering
Imm
Figure 3.6
Scattering of Droplet Spray
distance between two neighboring droplets. Rayleigh (1878) and Weber (1931) calculated
the ratio of the wavelength, A, to the jet diameter, dj, and found it to be:
Am = 4.508
Rayleigh
(3.18)
Am = 4.443
Weber,
(3.19)
dj
dj
where Am is wavelength of the oscillation when the growth factor is the maximum. The
growth factor determines how fast a neck on the surface of liquid jet contracts (Yim, 1996).
Considering these relationships, the droplet diameter becomes about twice the jet diameter.
The initial velocity of experiment 1 (100 gm orifice) is almost identical to that of
experiment 2 (150 gtm orifice). However, the velocity of experiment 2 becomes higher
than that of number 1 in the further downstream. This can be attributed to the difference in
the scattering distance described above. Larger droplets have greater inertia than smaller
ones and it takes longer for larger droplets to be scattered off the center of the stream by
electrostatic repulsion. Although larger droplets have more electrical charging, it cannot
overcome the inertia. This is because inertia is proportional to the volume of a droplet
while the amount of electrical charging is proportional to the diameter.
3.4.3 Effects of ejection pressure on velocity
Comparison of experiments 1 and 3 reveals the effects of ejection pressure. Higher
ejection pressure (experiment 3) results in higher initial velocity and longer scattering
distance than in experiment 1. The greater scattering distance is caused by increased inertia
due to higher initial velocity.
3.4.4 Effects of charging voltage on velocity
Charging voltage determines the amount of electrical charge imparted to each
droplet and thus the electrical repulsion force. In experiment 4, a charging voltage twice
that of experiment 1 was applied on the same size of droplets with almost the same initial
velocities. Higher charging voltage makes the scattering distance shorter by increasing
electrical repulsion force. Consequently, the velocity of experiment 4 is lower than that of
experiment 1 after the scattering distance while they have the same velocity profile before
the scattering distance.
The amounts of droplet charge in each experiment can be calculated by
Equation (3.10). The diameter of charging ring, dc, used in all experiments was 9 mm.
Table 3.2 shows the droplet charges calculated using measured jet velocity.
Table 3.2
Experiment Number
1
2
3
4
Droplet Charges
Droplet Charge (C x 1012)
2.96
3.97
2.97
5.64
3.4.5 Discharge coefficient
The discharge coefficient, kf , defined in Equation (3.15), determines the ratio of
actual initial velocity of the jet to the ideal velocity. As described previously, kf depends
upon orifice size, viscosity, surface tension and density of the liquid, and jet velocity. The
experimental values of kf are listed in Table 3.3.
Experiment
Number
1
2
3
4
Table 3.3
Average Initial Velocity
(m/s)
5.22
4.95
6.06
5.18
Discharge Coefficients
Ideal Jet Velocity
(m/s)
6.28
6.28
7.69
6.28
Discharge Coefficient,
kf
0.831
0.788
0.788
0.873
DROPLET SPREADING
EXPERIMENT
Chapter 4
4.1
Experiment Apparatus
4.1.1 Droplet generator
Molten metal droplets are generated by the Uniform Droplet Spray (UDS) apparatus
as described in Section 1.1.1. The velocity, trajectory, temperature, and liquid fraction of
the droplets can be predicted by numerical simulation (Passow, 1992). The models were
verified by Abel (1993) and Chen (1996), and in Chapter 3 of this thesis. Since the UDS
process is capable of precisely controlling the dynamic and thermal states of droplets, it is
possible to accurately control the impact conditions for the spreading sensor.
4.1.2 Spreading sensing setup
Constant current is supplied to the sensor by a current source (Hewlett Packard
E3610A) and the resistance change resulting from droplet spreading is measured in voltage
by a digital oscilloscope. To rapidly capture the transient voltage output due to spreading,
necessary is an oscilloscope of high data acquisition rate. Discussion in Section 2.1.2
suggests that the temporal resolution should be smaller than order of 10 gs.
A Tektronix TDS 520A Digitizing Oscilloscope, whose sampling interval is 4 ns,
was used in the experiment. Its recording or acquisition rate can be adjusted to the
characteristics of the system. Figure 4.1 shows the measurement system and the sensor.
Droplet
Spreading Sensor
Digital
Oscilloscope
Figure 4.1
Current Source
Spreading Sensing Setup
4.2
Experimental Procedure
The spreading sensor is located below the nozzle of the UDS apparatus to collect a
droplet. The distance between the nozzle and the sensor can be adjusted to control the
impact conditions which depend on flight distance as well as initial spray conditions. Since
a stream of droplets is ejected from the nozzle, the sensor has a shield on top which ensures
that only a single droplet arrives at the sensor surface. The shield, which has 1 mm
diameter hole, also protects the sensor surface and tiny electrical connection around the
sensor.
Figure 4.2 shows the droplet generation and collection units. Since droplets should
be sprayed in an inert gas environment (Yim 1996), the sensor is located inside the gas
chamber. The measurement setup was placed outside the chamber and connected with the
sensor by the wires through the vacuum conductor.
4.3
Experimental Results
4.3.1 Impact conditions of droplet
Pure tin was used as a droplet material with a melting temperature of 232 C. Initial
spray conditions are listed in Table 4.1. Mass flow rate was measured during spray to
deduce the initial velocity of the jet. Mass flow rate was 7.69 x 10- 4 kg / s, and thus initial
jet velocity was 4.57 m/s using the orifice diameter given in Table 4.1. With the initial jet
velocity and vibration frequency, the diameter of the droplet is calculated to be 356 Rim.
The spreading sensor was placed at 0.25 m below the nozzle and the velocity and
temperature of the droplets were obtained by a numerical simulation. The velocity and
temperature profiles versus flight distance are presented in Figure 4.3. Using the
simulation results, impact conditions are listed in Table 4.2 with Reynolds and Weber
numbers. Reynolds number, Re, is defined as:
Re = P
(4.1)
where p is density of the liquid droplet, vimp impact velocity, d diameter of the droplet,
and y viscosity of the liquid. Weber number, We, is defined as:
High Pressure
Droplet Generator
Gas Chamber
Microsens
Vacuum C
Current Source
&
Oscilloscope
Figure 4.2
Droplet Collection
2d
We =-pvind
(4.2)
where a is surface tension of the liquid.
4.3.2 Initial conditions of measurement setup
The initial resistance of the sensor before a droplet is delivered was measured to be
69.9 Q. A constant current of 13.5 mA was supplied to the sensor throughout the
experiment. Therefore, voltage before the droplet impact was maintained at 0.944 V.
Since the characteristic spreading time, ts , defined in Equation (2.2), was 74 ps,
time axis limits were set to cover up to 500 jis, and the acquisition interval was chosen to
be 1 gs. The oscilloscope converts analog input signal to digital data each sampling
interval, 4 ns, and averages all samples taken during an acquisition interval, 1 Rs, to create
a record point. Consequently, every record point corresponds to an average of 250
sampling data acquired for 1 gs.
4.3.3 Voltage output
Resistance change of the sensor due to spreading was monitored by the
oscilloscope in voltage and it is shown in Figure 4.4. A droplet arrives at the sensor
surface when the time is zero, before which constant voltage is maintained. A dramatic
drop of voltage is seen at the first moment of impact and subsequent voltage fluctuation
proceeds with the decreasing slope being less steep. Although the time axis was
intentionally set to cover the signal after the spreading had been completed, the voltage
turned out to continue decreasing even after the recording range.
The fluctuation of voltage from 0 to 100 gs is speculated to be induced from the
dynamic aspect of current supply performance. As the resistance falls very quickly, the
amount of current supplied to the system also decreases instantly. The current source tries
to recover the current which results in the overshoot and subsequent damped oscillation in
current and thus voltage.
-r.JO
0
0.05
0.1
0.2
0.15
0.25
0.3
0.35
Flight Distance (m)
(a) Velocity
"•111|
............
.....
....... --------..........
...............
290
....................
--------..........
.......
.............
...........
...........
*.........
280
270
260
------------I ............
-----------
...........
....................
...........
. . . .. . . . . . . . .. . . . .. . . . .
-----------
....
............ ................
............
. . . . . . . . .. . . . . . .
. .. . . . .
-------- -........... ............ -------------..............I............ I............ ............
250
---------
* .............
240
230I
0
0.05
0.1
0.15
0.2
0.25
Flight Distance (m)
(b) Temperature
Figure 4.3
Velocity and Temperature Profiles
44
0.3
0.35
0.8
"5 0.6
0
0.2
n
0
100
200
300
400
Time (!ks)
Figure 4.4 Transient Voltage Output
4.3.4 Spreading area
A transient contact area can be deduced from the transient voltage output based on
Equation (2.11). The number of sensing lines connected is the function of the diameter of
the spreading area, given by:
N(t) =
D(t)
D()
2(Al + A,)'
(4.3)
where width (/I,) and spacing (A,s) of grid lines are identically 2 gm in the sensor. The
maximum error resulted from the estimation of Equation (4.3) is 2(2I + A,) = 8 tgm as
discussed in Section 2.4.1. Therefore, the transient diameter, D(t), is calculated from the
voltage ouput, V(t), as follows:
D(t) = 2(At
As)R(I
( V(t)
,
Ro
(4.4)
where I denotes the constant current.
Figure 4.5 shows the transient diameter of the spreading area. Rapid increase in
diameter at the initial period of impact lasts a few microseconds and the increase rate slows
down. The diameter reaches about 720 gm at 450 gs after impact, while later investigation
of the splat revealed that the final diameter was 800 gm.
800
700
600
500
400
300
200
100
0
0
100
200
300
400
Time (gs)
Figure 4.5
Transient Diameter
4.3.5 Spreading speed
The spreading speed of a contact area between the droplet and the sensor can be
deduced based on the transient diameter profile. Since the diameter dramatically increases
from 0 to 2 gs and the increasing rate diminishes significantly afterwards, the expansion
speed was calculated in two regimes. Figure 4.6 (a) shows the initial radius expansion
speed from 0 to 2 gs directly obtained from the experimental data points. Figure 4.6 (b)
shows the radius speed calculated from the polynomial best fit of the fourth order to the
diameter from 2 to 450 gs after impact. The best fit formula, Dp, to the diameter is:
D,(t)= 0.0456+ 0.588t+ 1.06t 2 + 1.69t 3 + 1.02t 4 ,
(4.5)
4C
10-1
0)
E
Cn
CM
ci
0._
0T)
Cz
CL
U)
W
-1
U
0
2
0
100
200
Time (gs)
300
400
Time (js)
(b) Subsequent Speed
(a) Initial Speed
Figure 4.6
Spreading Speed
and the corresponding spreading speed, vspr , is:
pr(t)
4.4
dD = 0.294 + 1.06t + 2.54t2 + 2.04t 3 .
2 dt
(4.6)
Discussion
4.4.1 Spreading speed
The initial spreading speed, which corresponds to Figure 4.6 (a), is about 2.4 times
higher than the impact velocity. This is because the curved bottom shape is rapidly
deformed into a planar one (Lesser 1981) with negligible deformation of the upper portion.
The rapid expansion of a liquid film was predicted by numerical simulations although the
impact conditions were different. For example, calculations by Harlow and Shannon
(1967) and Trapaga and Szekely (1991) predicted that the radial expansion velocity during
the early stage of impact is about 3 and 1.6 times, respectively, the initial impact velocity.
The spreading speed drops dramatically as shown in Figure 4.6 (b), which grows
again from about 0.3 to 1.5 m/s. This indicates that the initial spreading stage, where the
film expansion is dominant, is completed as the bottom portion loses its steep curvature and
that the deformation of the whole droplet body starts to govern the spreading process. The
fact that the spreading speed increases even at 450 gs shows that the spreading process
continues beyond the measurement time.
4.4.2 Time scale of spreading
The characteristic spreading time is based on the time taken for a droplet to travel as
far as its diameter and is calculted to be 74 gs. On the other hand, Trapaga and Szekely
(1991) derived the following correlation for the time, to. 9 , required to reach 90 %
completion of spreading, using regression analysis of the computed results:
to.9
2d Re 0 .2.
(4.7)
3vimp
For a droplet used in the experiment, to.9 is calculated to be 284 gs using Equation (4.7)
while the time for the actual droplet to reach 90 % of its final splat diameter, 800 gm, is
about 450 js.
Although the effects of viscosity and surface tension were considered in Trapaga
and Szekely's (1991) model, there is still significant discrepancy between the
computational and experimental values of to. 9 . The physical factors which retard the
spreading of the droplet are speculated to be (1) the complex interaction at the liquid
droplet/solid substrate interface and (2) the solidification during spreading. In spite of the
lack of the proper knowledge of their role on the spreading process, the wettability,
dynamic contact angle, and the motion of the contact line should be taken into account to
fully describe the droplet spreading behavior (Dussan V. 1979, Haley and Miksis 1991,
and Hatta et al. 1995).
Solidification time scale, tsol , is proposed as (Gao and Sonin 1994):
tsol =
r2 2
11
a3
S
I[ln(l+p)+-i,
(4.8)
where r is radius, a thermal diffusivity of droplet. Temperature ratio, P/, is defined as:
Td
- Tf
Tf - Ts
(4.9)
where Td is droplet temperature, Tf freezing temperature, and Ts substrate temperature.
Stefan number, S, is defined as:
s= CP
QL
S)
(4.10)
where CP is specific heat and QL laten heat of droplet. Using the experimental conditions
listed in Table 4.2, ts l = 2ms, which is much longer than spreading time.
However, the computation of Zhao et al. (1996a) revealed that the fluid temperature
at the spreading front is substantially lower than the temperature at the splat center.
Therefore, it is possible that solidification will initiate around the spreading front if its
temperature reaches the freezing temperature before spreading is completed. In
consequence, the thin solid layer formed around the periphery may tackle the liquid metal
flow and retard the spreading process.
Chapter 5
SUMMARY
A novel technique was developed to investigate the molten metal droplet impact and
spreading behavior. Using the capability of the UDS process to create molten metal
droplets, whose dynamic and thermal states are accurately controlled, the microsensor was
designed and fabricated to capture the transient spreading phenomenon.
The sensor consists of a finely spaced resistance network mounted on a
nonconducting silicon substrate. The sensing lines are made of gold (Au) and their width
and spacing are both 2 gm. The VLSI technology was employed to fabricate the
microsensor.
The droplet flight model was experimentally examined to verify the control of the
UDS process over the droplet impact conditions. Molten tin droplets were sprayed with the
varied conditions such as the orifice diameter, ejection pressure, and charging voltage. The
velocity of the droplets was measured using a high speed camera at 6,000 frames per
second. The simulation results agreed fairly well with the experiments.
An experiment was conducted to investigate the performance of the sensor by
depositing a molten tin droplet, whose diameter and impact velocity were 356 Rm and 4.84
m/s, respectively. The initial speed of the contact area expansion was about 2.4 times
higher than the impact velocity. The spreading speed decreased dramatically afterwards
and the spreading process lasted over 450 gis. The experiment showed that the
microsensor performed satisfactorily to monitor the transient spreading behavior of molten
metal droplets.
BIBLIOGRAPHY
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