A Reproducible and Low-cost Piezoelectric
Generator
Droplet Dropet
enertorOF
AR;ZNES
MASSACHUSETTS INSTITUTE
TECH-NOLOGY
by
JUL 3 0 2014
Tanya Liu
LIBRARIES
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Bachelor of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2014
(
Massachusetts Institute of Technology 2014. All rights reserved.
Author.
Signature redacted
..........
Department of Mechanical Engineering
May 9, 2014
redacted
Signature
Certified by..
...............
John W. M. Bush
Professor of Applied Mathematics
Thesis Supervisor
Signature redacted
........................
Annette Hosoi
Associate Professor of Mechanical Engineering, Undergraduate Officer
A ccepted by ...............................
A Reproducible and Low-cost Piezoelectric Droplet
Generator
by
Tanya Liu
Submitted to the Department of Mechanical Engineering
on May 9, 2014, in partial fulfillment of the
requirements for the degree of
Bachelor of Science in Mechanical Engineering
Abstract
This thesis presents the design for a piezoelectric droplet generator capable of producing highly repeatable droplets ranging from 0.60 mm to 1.60 mm in diameter.
The generator is low cost, simple to fabricate, and easily reproducible for use in other
fluids experiments. A series of experiments were conducted to investigate the effects
of various operating parameters on the droplet generation process, and high speed
imaging techniques were used to capture and analyze droplet diameter data.
Thesis Supervisor: John W. M. Bush
Title: Professor of Applied Mathematics
2
Acknowledgments
I would like to thank Professor John Bush for his guidance and support throughout
the duration of my time in the Applied Math laboratory. I would also like to thank
Dan Harris for all of the help, advice, and mentorship he has provided for the past year
regarding this research project and beyond. Finally, I would like to thank everyone
else in the Applied Math laboratory for creating such a great research environment
for me to work in.
3
Contents
7
1 Introduction
Background and motivation . . . . . . . . . . . . . . . . . . . . . .
7
1.2
DOD generator requirements. . . . . . . . . . . . . . . . . . . . . .
8
1.3
Review of relevant systems . . . . . . . . .. . . . . . . . . . . . . . .
9
.
.
.
1.1
12
2 System design
2.2
12
2.1.1
Pressure regulation at the nozzle plane . . . . . . . . . . . .
13
2.1.2
Bleeding procedure . . . . . . . . . . . . . . . . . . . . . . .
15
2.1.3
Electrical system . . . . . . . . . . . . . . . . . . . . . . . .
16
. . . . . . . . . . . . . . . . . . . . . . . . . .
17
Experimental set-up
.
.
.
.
Droplet generator components . . . . . . . .. . . . . . . . . . . . . .
.
2.1
21
Droplet generation regime dependence on pulse width and voltage
21
3.2
Droplet size dependence on nozzle diameter
. . . .
24
3.3
Droplet size dependence on pulse width . . . . . . .
25
3.4
Effect of reservoir height adjustment
26
3.5
Day-to-day repeatability of the droplet generator
.
27
3.6
Fluid pump requirement . . . . . . . . . . . . . . .
29
3.7
Bimodality of generated droplets
30
.
.
3.1
.
3 Experimental results
.
.
. . . . . . . .
.
. . . . . . . . . .
31
4 Conclusion and recommendations
4
List of Figures
2-1
Overall system schematic for the droplet generator. . . . . . . . . . .
2-2
Close up view of fluid chamber and nozzle geometry. Flexing of piezo-
12
electric causes liquid to be ejected from nozzle outlet. Piezoelectric
motion is exaggerated for the purpose of demonstration.
2-3
. . . . . . .
13
Reservoir fluid height relative to nozzle plane is denoted as Ah. The
reservoir fluid is perfectly in line with the nozzle outlet when Ah = 0.
14
2-4
Example of typical waveform used to drive the piezoelectric piece. . .
16
2-5
Result of edge detection on droplet photo with MATLAB algorithm.
Droplet diameter is calculated in pixels by taking the diameter of a
circle fitted through a least-squares method. . . . . . . . . . . . . . .
3-1
19
(a) Droplet generation sequence for a 0.90 mm nozzle and 30 V with
a 0.41 ms pulse width. No droplet is generated. (b) Successful droplet
generation occurs for the same operating parameters but with a 0.55 ms
pulse width. (c) Satellite droplet formation begins when pulse width
is increased to 0.67 ms. . . . . . . . . . . . . . . . . . . . . . . . . . .
3-2
Upper and lower pulse width limits for each operating voltage. Successful droplet generation occurs in the regime in between the limits.
3-3
22
23
(a) Upper and lower curves represent the upper and lower pulse width
limits for nozzle diameters 0.60 mm - 1.60 mm. (b) Measured droplet
diameters for each nozzle evaluated at upper and lower pulse width
limits.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
24
3-4 Effect of pulse width on droplet diameter with a 0.90 mm nozzle and
amplitude 30 V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
3-5 Effect of reservoir height adjustment on droplet diameter. Ah = 0
arises when the fluid in the reservoir is at the same height as the nozzle
outlet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
3-6 Day-to-day repeatability of droplet diameters generated from a 0.90
mm nozzle with a pulse width of 0.50 ms and voltage of 30 V. Between each measurement, air was introduced into the chamber and the
bleeding procedure was repeated. . . . . . . . . . . . . . . . . . . . .
28
3-7 Comparison of droplet generation (a), with pump, and (b), without a
pum p. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
29
Chapter 1
Introduction
1.1
Background and motivation
Under certain conditions, bouncing droplets on a vibrating fluid bath can achieve
lateral propulsion across the fluid surface through interaction with their own wave
field[1, 21. These walking droplets represent a macroscopic realization of Louis de
Broglie's pilot-wave theory for microscopic quantum particles[1, 3, 4, 5]. The behavior
of these droplets is strongly dependent on their size[1, 2, 6}, meaning these experiments
require a reliable and repeatable droplet generation method. Previous experiments
have created droplets by rapidly extracting a submerged pin from a fluid bath by
hand[1J, but this method makes it difficult to repeatedly generate droplets of the
same diameter.
Repeatable droplet generation is required for a spread of diverse applications ranging from inkjet printing to liquid crystal display manufacturing[7]. Droplet generators
used in these applications are typically split into two categories: droplet on demand
(DOD) generators that eject a single droplet on command, or continuous jet generators that produce a stream of droplets.
The controllability of DOD generators makes them well suited for use in walking
droplet experiments. The rest of chapter 1 delineates the requirements of a typical
DOD generation system and reviews existing system designs. Chapter 2 presents an
original droplet generator design intended for use in walking droplet experiments with
7
the goal of producing highly repeatable droplets at a relatively low cost. Experimental
results regarding the repeatability and operating range of the droplet generator are
presented in chapter 3, and chapter 4 discusses the potential of the overall system
design for use in walking droplet experiments and beyond.
1.2
DOD generator requirements
A variety of droplet on demand (DOD) generators are described in the literature,
many of which rely on piezoelectric or pneumatic actuators for droplet generation[8,
9, 10]. Existing DOD generator designs, however, are often complex, costly, and
difficult to adopt for use in other studies.
Piezoelectric generators have emerged as popular configurations for DOD applications due to their relatively straightforward operating principles. For such reasons,
the droplet generator design presented in this thesis uses a circular piezoelectric element. The remainder of this chapter will focus on describing existing DOD generator
designs with piezoelectric actuators.
A typical piezoelectric generator consists of a piezoelectric actuator, fluid chamber,
nozzle, and some sort of pressure regulatory device. A voltage pulse sent to the
piezoelectric element causes the element to contract and retract in turn, leading to
the formation of a pressure fluctuation in the chamber. Depending on the amplitude
and duration of the pressure fluctuation, either no droplet, a single droplet, or a
primary droplet plus satellite droplets may be ejected from the nozzle opening.
The piezoelectric component can be a ceramic disc, or in the case of "squeeze
mode" DOD designs, a piezoelectric sleeve bonded concentrically to a glass capillary
tube[11, 12]. Nozzle designs reported in the literature range from simple openings
in flat plates[13] to precisely fabricated glass nozzles of very specific geometries[7,
9]. The pressure regulatory device is one of the most important components of any
piezoelectric DOD system, as a constant pressure must be maintained at the nozzle
plane when no external pressure fluctuation is applied. Existing designs have relied
on pressure pumps[10], fluid reservoirs[9, 14, 13], or failed to mention the type of
8
pressure regulation system used.
1.3
Review of relevant systems
Yang et al. made an early effort to present a simple, reproducible droplet generator
design that served as the inspiration for the generator presented in this thesis[9]. Their
system uses a piezoelectric disc for actuation and a fixed fluid reservoir for pressure
regulation. The piezoelectric is driven by a square waveform from a pulse generator
with a pulse width and amplitude less than 10 ms and 30 V, respectively. Yang et
al. run into a "first drop problem," however, in which the first few ejected droplets
are inconsistent and require a higher pulse width or amplitude[15, 9}. The generator
also fails to always operate properly in a true DOD mode, and successful droplet
generation sometimes requires the piezoelectric transducer to be driven at very low
frequencies in a quasi-DOD mode. Yang et al. tested a range of glass nozzles from
125 pm to 250 pm in diameter, and their droplet diameter uncertainties were less
than
10% of the measured droplet diameters.
Terwagne designed a droplet generator for use in bouncing droplet experiments
that uses an air pump for pressure regulation[10]. Like Yang et al., Terwagne's actuator is a piezoelectric disc driven by a square signal from a pulse generator. The pulse
width of Terwagne's signal is similar to Yang et al.'s at 5 ms, but the amplitude of
the waveform is much higher at 80 V. Terwagne's design does not use a nozzle, but
instead has an excimer laser cut hole at the bottom of a fluid chamber. The geometry
of the hole is designed to have a groove that pins the contact line of the liquid. With
a 600 pm hole, Terwagne was able to produce droplets of 700 pm in diameter with an
uncertainty of
3%. Terwagne also found that droplet size increases with waveform
amplitude and was able to produce droplets from 650 pm to 750 pm in diameter with
the same hole size by varying the amplitude from 50 V to 80 V.
Hawke's generator design similarly bypasses the use of a nozzle and ejects droplets
through an opening in the bottom of a fluid chamber[13}. Instead of an excimer laser
cut hole, however, Hawke's opening is a simple through-hole in the center of a stainless
9
steel plate. Hawke manufactured three steel plates with openings of 0.40 mm, 1.00
mm, and 1.25 mm in diameter, but data is only provided for the 1.00 mm diameter
hole. Droplets averaging 1.07 mm in diameter were produced from this hole with an
uncertainty of 4.6%.
Castrejon-Pita et al. designed a generator with interchangeable nozzles ranging
from 0.15 mm to 3.00 mm in diameter[14]. Instead of a fixed fluid reservoir for
pressure control, a height adjustable fluid reservoir allows the reservoir height to be
changed for fluids of varying viscosities and surface tensions. The design actually
uses a loudspeaker cone for an actuator instead of a piezoelectric element, but the
two operating principles are very much the same. The electrical set up for the loudspeaker actuator uses a DC power supply, electrical relay, pulse generator, and delay
generator. Droplet diameter data was not provided for the whole range of nozzle diameters, but droplets 1.75 mm in diameter were produced from a 1.25 mm diameter
nozzle with driving waveform parameters of 15 ms and 6 V. Uncertainty data was
not provided.
Many other DOD systems are described in the literature, but the majority are
designed for the generation of droplets less than 500 um in diameter[16, 17, 18].
These diameters are smaller than droplet diameter range desired for walking droplet
experiments, which generally ranges from 0.50 mm to 1.30 mm [1, 21. Many of these
systems also do not quantify the repeatability of the droplet generation process, a
parameter that is very important for walking droplet experiments. The provided
uncertainty values are usually measurement uncertainties from image analysis and
do not specifically quantify the variation between droplets generated during a single
run[13, 9]. There is a need, therefore, for a simple, repeatable DOD system designed
for larger scale droplet generation in the walking droplet size range.
This paper presents an original droplet generator design that aims to surpass existing systems in the areas of affordability, reproducibility, and overall system simplicity.
The generator is capable of producing highly repeatable droplets with diameters in
the range of 0.60 mm to 1.60 mm, and each component can be fabricated using only
manual mill and lathe equipment. A fluid reservoir is used for pressure regulation,
10
and the only electrical components necessary are a DC power supply, Arduino board,
and H-bridge circuit. The generator is tested with pure silicone oil of viscosity 20 cSt
over a range of operating parameters, and the effects of various operating parameters
on droplet diameter are examined through high speed imaging analysis.
11
Chapter 2
System design
2.1
Droplet generator components
Translation
stage
Piezoelectric bu
Fluid reservoir
er
a
o
DC supply
ir
Fluid
chamber
I
Hbig
Nozzle
PUMP
Arduino
Uno
Figure 2-1: Overall system schematic for the droplet generator.
The droplet generator was designed with the goal of being as low cost, simple to
fabricate, and repeatable as possible. As seen in Figure 2-1, the droplet generator
consists of five main components: a piezoelectric disc, fluid chamber, nozzle, height
adjustable fluid reservoir, and fluid pump. The piezoelectric actuator is a commercially available piezoelectric buzzer (CUI CEB-35D26, diameter 35 mm). To create
12
Figure 2-2: Close up view of fluid chamber and nozzle geometry. Flexing of piezoelectric causes liquid to be ejected from nozzle outlet. Piezoelectric motion is exaggerated
for the purpose of demonstration.
an airtight seal between the piezoelectric and fluid chamber orifice, the piezoelectric
is first bonded to the top of the fluid chamber with an RTU silicone sealant, then
secured in place by an acrylic ring that provides an extra compressive force on the
edges of the piezoelectric.
The fluid chamber is a small aluminum block bored out to create a cylindrical
chamber of 28.575 mm in diameter. The cylindrical chamber maintains a constant
diameter for a certain depth, then tapers down to a tapped hole in the bottom of
the chamber where the nozzle is attached and sealed to the generator with an 0ring. Ten stainless steel nozzles ranging from 0.60 mm to 1.60 mm in diameter were
machined and tested for this droplet generator design. Each nozzle is split into three
main features: a threaded portion that screws into the opening in the bottom of the
fluid chamber, a hexagonal segment that allows a nozzle to be easily attached and
detached from the fluid chamber, and a tip with a 450 outer taper and opening of a
particular size that determines the nozzle diameter. Figure 2-2 shows a close up view
of the fluid chamber and nozzle geometry.
2.1.1
Pressure regulation at the nozzle plane
In order for the droplet generator to operate consistently, the fluid pressure at the
nozzle plane must be carefully regulated. Ideally, the pressure at the nozzle opening
should be such that a fluid meniscus forms right at the nozzle outlet.
13
If the fluid
F
-- I N i
Ah = hro-
hn
1L:-J=W
.
1
Figure 2-3: Reservoir fluid height relative to nozzle plane is denoted as Ah. The
reservoir fluid is perfectly in line with the nozzle outlet when Ah = 0.
pressure is too high, the pressure difference at the nozzle outlet will cause fluid to
drip out of the nozzle continuously. If the pressure is too low, air will be drawn into
the chamber.
To maintain the proper pressure balance at the nozzle outlet, a fluid reservoir is
connected to the fluid chamber. The height of the reservoir relative to the nozzle outlet
determines the hydrostatic pressure at the outlet, and static equilibrium requires that
this hydrostatic pressure be balanced by the capillary pressure at the outlet. If the
fluid is approximated as having a pinned contact line and spherical geometry at the
nozzle outlet, this equilibrium can be written as
_2o-
pgAh = R,
R
(2.1)
where Ah is the height difference between the reservoir fluid and nozzle outlet as seen
in Figure 2-3, and R is the fluid radius of curvature at the outlet. Static equilibrium
14
is satisfied for radii greater than
ozie,
and fluid dripping and air intake occur
when IRI = R,.Ie. The range of reservoir fluid heights that satisfy this equilibrium
requirement is then given by
-
2apgRnzxe
< Ah <
2upgRnzze
.
(2.2)
To study the influence of reservoir fluid height on the generation process, the
reservoir is mounted onto a micrometer drive translation stage (Thor Labs PT1).
The reservoir design consists of two concentric cylinders 69.85 mm and 50.80 mm
in diameter. A small peristaltic pump (Williamson 100 series) continuously pumps
fluid into the inner cylinder and causes it to overflow into the outer cylinder. The
excess fluid in the outer cylinder is continuously recirculated by the pump back into
the inner cylinder, maintaining a constant fluid level relative to the nozzle outlet.
This way, both the height of the reservoir and the height of the fluid itself remain
constant, ensuring accurate regulation of the pressure at the nozzle outlet. If the fluid
reservoir is made to be sufficiently wide, the decrease in fluid height due to droplet
generation may be so small that the effect on the nozzle outlet pressure is negligible.
The performance of the system without the peristaltic pump is explored in chapter
3.
2.1.2
Bleeding procedure
For optimal operation of the droplet generator, all air bubbles must be eliminated
from the fluid chamber. To do this, an effective bleeding procedure has been developed
in which the chamber is removed from the generator body, inverted, and held at a
lower height until fluid begins to flow out of the top of the nozzle opening. This
ensures that the chamber is completely filled with fluid only and any air bubbles
are released through the nozzle tip. In its normal configuration, the chamber is held
against an upright portion of the generator body by two bolts. This upright portion
is an aluminum plate with a series of tapped holes patterned vertically along the
length of the plate, making it easy to unbolt and rebolt the inverted chamber at a
15
50
40
30
20
Amplitude
10-10
-- Pulse width
-2C
-30
-4
-51
0
10
20
30
40 50 60
Time (rs)
70
80
90
100
Figure 2-4: Example of typical waveform used to drive the piezoelectric piece.
lower height during rebleeding. During normal operation, this procedure need only
be performed once at the beginning of the experiments.
2.1.3
Electrical system
The electrical components responsible for driving the piezoelectric element consist of
an adjustable DC power supply (0-72 V), H-bridge circuit, and Arduino Uno microcontroller.
Driving waveform The piezoelectric piece is driven by a square voltage waveform
shown in Figure 2-4. When not in use, the piezoelectric piece is supplied with a
constant negative voltage. The sudden application of a positive voltage causes the
piezoelectric piece to contract and generates a positive pressure pulse in the chamber
that forces liquid through the nozzle. Returning to a negative voltage causes the
piezoelectric to expand and creates a negative pressure fluctuation that draws liquid back in to the chamber. Under the right operating conditions, this sequence of
expansion and contraction expels a single droplet from the nozzle.
16
H-bridge circuit An H-bridge is a type of electronic circuit that can reverse the
polarity of an input voltage through the use of electronic switching elements. The
H-bridge circuit used in this droplet generator design takes the voltage from the DC
power supply as an input, then outputs it at a positive or negative polarity depending
on what stage of the droplet generation process is occurring.
The timing of the
polarity switches is controlled by an Arduino program, and the time duration between
polarity switches essentially determines the pulse width of the driving waveform shown
in Figure 2-4.
Arduino microcontroller
Arduinos are microcontroller boards commonly used
for rapid prototyping projects. A standard Arduino board has multiple input and
output pins that can communicate with a variety of sensors, motors, and actuators.
The H-bridge circuit in this electrical set up is connected to two digital output pins of
the Arduino Uno, and an Arduino program controls all of the timing for the voltage
waveform output by the H-bridge circuit. The clock frequency of the Arduino Uno is
rated as 16 MHz, so the program is capable of sending commands with very precise
timing. The two electrical control parameters are thus the amplitude (voltage) and
the duration (pulse width) of the square pulse. The pulse width of the piezoelectric
driving waveform can be controlled with a resolution as fine as 1 ps. This simple
electrical system eliminates the need for a pulse generator and amplifier as is typically
used in similar experiments [14, 11, 15, 18].
2.2
Experimental set-up
The primary variable of interest in all experiments is droplet diameter, as the original
motivation for the generator design was a system capable of repeatedly producing
droplets of the same size. High speed imaging techniques are used to capture images
of and extract diameter data from generated droplets.
The droplet generator is placed between a light source and high speed camera
system capable of capturing images at a rate of up to 1000 frames per second at full
17
resolution. The full camera system consists of a Phantom high speed camera, macro
lens, 2x teleconnector, and tube extension. For the purpose of diameter measurement,
a single image is captured per generated droplet. The timing of the image capture
is synchronized with the droplet generation by an external trigger signal sent to the
camera system. The external trigger pulse is generated on a third digital output
pin of the Arduino and the timing is specified in the same software. In a typical
image capture sequence, the program sends a voltage pulse to the piezoelectric piece,
waits for a specified delay time, then triggers the camera system to capture an image.
The proper delay time between the piezoelectric pulse and camera trigger pulse is
determined from a video taken of a single droplet generation where the generation is
complete and the droplet is nearly spherical. This delay time typically ranges from
around 30 ins to 60 ms after generation. Due to the high repeatability of the droplet
generation process, the delay time derived from the video can be used for all other
droplets generated under the same operating conditions, allowing large quantities of
data to be rapidly collected.
The overall operation of the droplet generator plus camera system is controlled
through a custom MATLAB GUI that communicates with the Arduino. Using the
GUI, a user can input desired operating parameters for the generator such as piezoelectric pulse width and delay time between subsequent droplets if multiple droplets
are being generated. Camera parameters such as video frame rate, video start and
end frames, and the external trigger delay time for a single image capture can also
be specified.
After image collection, droplet diameter data is extracted from the images with an
edge detection algorithm in MATLAB. The algorithm finds edges in an image based
on a specified intensity threshold value, then fits a circle to the detected edge using a
least-squares method. The diameter of the fitted circle is then output as the diameter
of the drop in pixels. Figure 2-5 shows the edge detected by the MATLAB algorithm
for a typical droplet image. The diameter measurement in pixels is converted to millimeters using the mm/pixel resolution of the image. This resolution is calculated
using a microscope calibration slide and is found to be 3.31
18
0.03 pm/pixel. The
Figure 2-5: Result of edge detection on droplet photo with MATLAB algorithm.
Droplet diameter is calculated in pixels by taking the diameter of a circle fitted
through a least-squares method.
uncertainty associated with this resolution comes from analysis of multiple calibration
photos taken during different days of testing. All future error bars for diameter measurements represent the combination of uncertainty from this calibration resolution
and actual variation in droplet diameters from a single run unless otherwise noted.
In certain cases where the error bar is not visible, the marker size is larger than the
error bar.
Another source of error associated with the diameter data is variation in camera
focus. Due to the highly magnified nature of the images, even very small changes in
lighting or camera position can change the focus of an image. Images slightly out of
focus have blurred edges that lead to inaccuracies in measured droplet diameters with
the edge detection algorithm. To prevent variation in camera operating conditions,
the lens aperture is opened as wide as possible, and the focus setting is fixed so that
the focal plane is as close to the camera as possible. These settings create the most
magnified image possible with a shallow depth of field, which helps limit variation in
the camera to droplet spacing. Having the aperture on the largest setting also lets
in the maximum amount of light and allows for the use of shorter exposure times. A
shorter exposure time prevents streaked images from droplet motion, and an exposure
time of 50 ps is used for all images.
At least 1000 images are captured and analyzed for each diameter measurement
19
presented in the following sections. Droplets are generated at a frequency of 5 Hz.
,
All experiments are conducted with 100% pure silicone oil of density p = 950 kg/m3
20
0.1 cSt.
.
surface tension a = 0.0206 N/m, and kinematic viscosity v = 20.9
Chapter 3
Experimental results
3.1
Droplet generation regime dependence on pulse
width and voltage
A successful DOD generation event occurs when a single droplet is ejected from the
nozzle outlet. In an undesirable event, liquid may fail to exit the nozzle entirely, or
multiple droplets may be ejected. A full sweep of the piezoelectric driving waveform
pulse width and amplitude was conducted with a 0.90 mm nozzle to quantify the
operating regimes where successful droplet generation could occur. For each voltage,
it was found that there is a lower pulse width limit below which no droplet generation
occurs, and an upper pulse width limit above which satellite droplet formation begins.
In between these pulse width limits, a single droplet is successfully generated. Figure
3-1 shows images of droplet generation in these three different regimes at a constant
waveform amplitude of 30 V.
In Figure 3-1(a), a pulse width of 0.41 ms is too short for droplet generation to
occur, and the piezoelectric expands and retracts the fluid before pinch off can occur.
More fluid is ejected from the nozzle with a pulse width of 0.55 ms in Figure 3-1(b),
and successful droplet generation occurs. When the pulse width is increased to 0.67 ms
in Figure 3-1(c), too much liquid is ejected from the nozzle, and a secondary droplet
pinches off from the tail of the primary droplet. A very interesting intermediate case
21
t=4ms
t=5ms
t=6ms
t=7ms
t=8ms
t=9ms
t=9ms
t=11ms
t=12ms
t=9ms
t=llms
t=15ms
(a)
t=4ms
t=6ms
t=8ms
(b)
t=4ms
t=6ms
t=8ms
(c)
Figure 3-1: (a) Droplet generation sequence for a 0.90 mm nozzle and 30 V with a 0.41
ms pulse width. No droplet is generated. (b) Successful droplet generation occurs for
the same operating parameters but with a 0.55 ms pulse width. (c) Satellite droplet
formation begins when pulse width is increased to 0.67 ms.
22
is also observed for pulse widths right below the lower pulse width limit. In this
case, a droplet pinches off from the nozzle, but the retraction of the fluid imparts
a negative velocity component to the droplet. After ejection, the droplet actually
reverses direction and is reabsorbed back into the fluid chamber.
As seen in Figure 3-2, lower operating voltages require longer pulse widths for
successful droplet generation but have a larger range of acceptable pulse widths. The
lower voltage range also shows larger inconsistencies between upper and lower pulse
width limits from different trials, and voltages below 12 V are unable to sustain
consistent droplet generation.
6
5
-
Satelite droplet(s)
2.
1*
010
No droplet
20
30
40
50
60
70
Voltage (V)
Figure 3-2: Upper and lower pulse width limits for each operating voltage. Successful
droplet generation occurs in the regime in between the limits.
An optimal operating voltage can be determined from the results presented in Figure 3-2. Ideally, the pulse width range should be large enough to allow for flexibility
in droplet generation, and the measured upper and lower pulse width limits should
remain consistent through different trials. Based on these criteria, an operating voltage of 30 V is chosen for all subsequent experiments. Higher voltages show smaller
variation in measured upper and lower pulse width limits, but higher voltages are not
recommended as the piezoelectric buzzer is rated for a maximum voltage of 30 V.
23
1.6
1.4
1.6
Satellite droplet(s)
- 4 Satellite droplet(s)
1.2
1.2
0.8
0.6
..
*..---
M 0.4
0.4
0
0.4 0.6 0.8
1
No droplet
0.2_
Nodroplet
0.2
e'
.
.
0.8
G0.6
I
0.4 0.6 0.8 1
1. 2 1.4 1.6 1.8
Nozzle diameter (mm)
1.2 1.4 1.6 1.8
Nozzle diameter (mm)
(a)
(b)
Figure 3-3: (a) Upper and lower curves represent the upper and lower pulse width
limits for nozzle diameters 0.60 mm - 1.60 mm. (b) Measured droplet diameters for
each nozzle evaluated at upper and lower pulse width limits.
3.2
Droplet size dependence on nozzle diameter
Ten different nozzles ranging from 0.60 mm to 1.60 mm in diameter were fabricated
and tested with the droplet generator. The upper and lower pulse width limits as
defined in section 3.1 were found for each nozzle, and diameter data were taken at both
limits. Figure 3-3(a) shows the upper and lower pulse width limits for each nozzle,
and Figure 3-3(b) shows the measured droplet diameters at those limits. Based on the
definition of the upper and lower pulse width limits, droplet diameter measurements
taken at these limits presumably represent the largest and smallest achievable droplets
for a given nozzle.
As expected, droplet diameter is roughly determined by the nozzle diameter[11];
however, variation of the pulse width can lead to droplets smaller or larger than the
nozzle diameter. Smaller nozzles appear more capable of generating droplets larger
than the nozzle diameter, while larger nozzles are more capable of generating droplets
smaller than the nozzle diameter. Overall, the range of achievable droplet diameters
appears to increase with increasing nozzle diameter, and this increase is accompanied
by an increase in pulse width range.
In general, droplet diameters ranging from
approximately 80% to 110% of the nozzle diameter were achieved from variation of
24
the pulse width alone. This is significant because a large range of droplet diameters
can then be generated without having to constantly switch nozzle sizes.
3.3
Droplet size dependence on pulse width
The variation in droplet diameters measured at the upper and lower pulse width
limits for a given nozzle suggests that when all other parameters are held constant,
droplet size is directly dependent on pulse width. To test this, a finer pulse width
sweep was conducted with a 0.90 mm nozzle. The 0.90 mm nozzle was chosen for
testing because, based on the nozzle sweep test in section 3.2, droplets ejected from
this nozzle have diameters that fall directly in the middle of the desired 0.50 mm to
1.30 mm diameter range for the walking droplet experiments.
0.94
0.92
0.9
p0.9.
0.88
0.86
'
0.84
.0.82
0.8
0.78
0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6
Pulse width (ms)
Figure 3-4: Effect of pulse width on droplet diameter with a 0.90 mm nozzle and
amplitude 30 V.
Figure 3-4 shows that droplet diameter increases monotonically with increasing
pulse width. At the lower pulse width limit, measured droplet diameter is at a minimum of 0.778 0.008 mm. Similarly, measured droplet diameter reaches a maximum
of 0.935 0.008 mm at the upper pulse width limit. These results are in accordance
with the operating principle of the piezoelectric element. The pulse width dictates the
length of time the piezoelectric is held in a contracted state, so a longer pulse width
25
allows for more fluid to be ejected from the nozzle before the piezoelectric returns to
its expanded state. Although not measured, the velocity of the ejected droplet tends
to increase with pulse width as well. This was observed qualitatively through camera
delay times that decreased with increasing pulse width.
3.4
Effect of reservoir height adjustment
0.9
0.89-
0.880.87
0.86
0.84
-3
-
0.85-
-2.5
-2
-1.5
-1
-0.5
Ah (mm)
0
0.5
1
1.5
Figure 3-5: Effect of reservoir height adjustment on droplet diameter. Ah = 0 arises
when the fluid in the reservoir is at the same height as the nozzle outlet.
As discussed previously, the pressure at the outlet of the nozzle must be carefully maintained in order to ensure consistent droplet generation. Instead of a single
equilibrium, however, there is a window of nozzle outlet pressures in which successful
droplet generation can still occur. To explore the effect of changing the nozzle outlet
pressure, diameter measurements were taken for droplets from a 0.90 mm nozzle at
various fluid reservoir heights. Since the peristaltic pump keeps the height of the fluid
in the reservoir constant, the reservoir height is isolated as the only parameter having
an effect on the pressure at the nozzle outlet.
26
As defined in section 2.1.1, Ah is the difference between the reservoir height and
nozzle plane, and Ah = 0 when the fluid in the reservoir is perfectly aligned with the
nozzle outlet. The droplet generator is normally operated with the reservoir at this
equilibrium height, but successful droplet generation can still occur if Ah is varied
slightly. A change in fluid height of 1 mm corresponds roughly to a change in pressure
at the nozzle outlet of pgAh = 9.3 Pa.
Droplet diameter measurements were taken for a range of Ah's using a constant
pulse width of 0.50 ms. As seen in Figure 3-5, a positive Ah causes droplet diameter
to increase, and a negative Ah causes droplet diameter to decrease. A minimum
droplet size of 0.849 0.008 mm occurs at a height 2.54 mm below the equilibrium,
and a maximum droplet size of 0.886 0.008 mm occurs at a height 1.27 mm above the
equilibrium. Heights further away from equilibrium in either direction cause either
uncontrolled fluid dripping or air bubble formation. These results demonstrate that
the fluid reservoir height could potentially be used as a parameter to control droplet
diameter, a possibility that has not been explored by other systems.
3.5
Day-to-day repeatability of the droplet generator
One of the original criterion in designing the droplet generator was that the droplet
generation process be as repeatable as possible. Based on results from previous tests,
the generation process is very repeatable for a single run. Diameter measurements
of over 1000 droplets generated with the same operating parameters typically have
standard deviations of less than 0.5% of the mean droplet diameter.
Another repeatability that must be taken into account, however, is the day-today repeatability of the droplet generator. This parameter is generally not assessed in
other DOD studies, but it is important to quantify the variation in droplet generation
across multiple days. During a day of testing, it is not uncommon that the generator is
bled, the reservoir height is adjusted several times, or some other part of the generator
27
0.905
0.9
0.895
0.89
0.8851
g
0.88
0.8750.87
0.865
0.86
i_
1
2
Day I
3
2
3
Day 2
2
3
Day 3
Trial number
Figure 3-6: Day-to-day repeatability of droplet diameters generated from a 0.90 mm
nozzle with a pulse width of 0.50 ms and voltage of 30 V. Between each measurement,
air was introduced into the chamber and the bleeding procedure was repeated.
set up is disturbed. The droplet generator operation should remain impervious to
such temporary disturbances, and minimal change in operating parameters should be
required from day-to-day to produce droplets of the same diameter.
To test this day-to-day repeatability, an air bubble was purposefully introduced
into the fluid chamber by raising the height of the chamber relative to the reservoir
and lowering the pressure at the nozzle outlet. The chamber was then bled following
the process described in section 2.1.2. This process was repeated three times over
three different days of testing, and the results are shown in Figure 3-6. The operating
conditions of the droplet generator were kept consistent through all trials with a 0.90
mm nozzle and 0.50 ms pulse width.
The variation in droplet diameter within a single day after bleeding was approximately t1.2%, and the overall variation in droplet diameter across all three days was
28
also approximately
1.2%.
The uncertainty in these measurements is dominated,
however, by the calibration uncertainty. For a better assessment of the day-to-day
variation, a calibration photo should be taken each day to separate this uncertainty
from the true variation in droplet diameter measurements.
Fluid pump requirement
0.906
0.914
0.903 ..N~
0.912
0.896
-0.
0.885
0
.
.
.
.
1
2
3
Droplet number
0908
0.902
4
5
3
xlO
-
3.6
0
1
2
3
3
Droplet number
(b)
(a)
Figure 3-7: Comparison of droplet generation (a), with pump, and (b), without a
pump.
Without the peristaltic pump to keep the height of the fluid in the reservoir
constant, the fluid height will gradually decrease as more droplets are ejected. To
compare the operation of the generator with and without the pump, 5000 droplets
were generated while the pump was running, and 5000 more droplets were generated
with the pump turned off. Both runs were performed with a 0.90 mm nozzle and 0.55
ms pulse width.
A comparison of Figure 3-7(a) and Figure 3-7(b) demonstrates that there is an
unmistakable decline in droplet diameter without the use of the pump. This agrees
with the results of section 3.4, as lowering the reservoir height has essentially the same
effect as decreasing the amount of fluid in the reservoir. The decrease in measured
diameter is only less than 2% after 5000 droplets, however, so the pump is likely not
necessary for most applications requiring the generation of a relatively small number
29
of droplets. Of course, increasing the diameter of the fluid reservoir will also offset
the rate of fluid height depletion with droplet generation.
3.7
Bimodality of generated droplets
Figures 3-7(a) and 3-7(b) show a bimodal distribution of generated droplet diameters.
This effect was present in all other experiments as well, and remained an enigma for
quite some time. The difference in measured droplet diameter between the two modes
is extremely small and consistently on the order of only a few microns, but the bimodal
distribution remains glaringly present nevertheless.
It was eventually discovered that the small fluctuations in diameter were caused
by a 3-4 microsecond interrupt in the Arduino software. The digital output pins
corresponding to the H-bridge were also not being addressed in the most efficient
manner possible, causing the actual pulse width being sent to the piezoelectric to
vary in total by about 5-6 microseconds.
After fixing this issue, the bimodality
problem was solved. It is a testament to the repeatability and accuracy of the droplet
generator, however, that such a small difference in pulse width is directly observable
in droplet diameter. Removing the bimodality reduces the typical variation within a
single run from
0.5% to as small as
0.06%.
30
Chapter 4
Conclusion and recommendations
The goal of this thesis was to present and evaluate the potential of a piezoelectric
droplet generator design for use in fluids experiments, specifically those involving
walking droplets. The effects of voltage, pulse width, and reservoir height on droplet
generation were investigated, and tests were also conducted to characterize the effect
of day-to-day disturbances on the repeatability of generated droplets.
Based on the results of chapter 3, the droplet size is roughly prescribed by the
nozzle diameter, though droplets smaller and larger than the nozzle diameter can be
generated through variation of either the pulse width or reservoir height. Being able
to control droplet diameter through reservoir height adjustment could be preferable
to adjusting pulse width, as a fixed pulse width and voltage could greatly simplify
the electrical components of the generator. For a given nozzle size, however, pulse
width adjustment can produce a much larger range of droplets than reservoir height
adjustment. Pulse width adjustment is also capable of varying droplet diameter at
a much finer resolution than reservoir height adjustment; consequently, pulse width
emerges as the preferred parameter for controlling droplet size. As a result, the
reservoir translation stage is not necessary for inclusion in future designs.
Operating voltage also has an effect on droplet generation, but using a fixed voltage
can potentially eliminate the need for an adjustable DC power supply, making the
generator even more simple and low cost. Based on the pulse width and voltage
regime diagram presented in section 3.1, 30 V is a good choice for operating voltage
31
for the drop size range of interest.
If a pump is used to keep the reservoir fluid height constant, large numbers of
droplets can be generated with consistent diameters. Without a pump, droplet diameter begins to decrease as the height of the reservoir fluid decreases. For applications
requiring the generation of only a few droplets, however, this diameter decrease is
negligible. In this case, the pump could be eliminated and the reservoir refilled by
hand. The simplest possible droplet generator system design could then consist of a
piezoelectric element, fluid chamber, fixed fluid reservoir, nozzle, fixed voltage power
supply, and Arduino H-bridge circuit.
For a single run, generated droplet diameters are repeatable to within t0.5%.
The day-to-day variation in droplet generation is larger at around i1.2%, but this
uncertainty is dominated by the calibration uncertainty term. For future tests, a
calibration photo should be taken at the start of each day of testing for a more
accurate representation of the generator's day-to-day repeatability. In both cases,
this droplet generator design achieves incredibly repeatable results compared to other
designs in literature. A "first drop problem" also occurs in the designs of Yang et
al. and others, in which the first few ejected droplets are inconsistent [15, 9]. The
droplet generator design presented in this thesis has no such issue.
The high repeatability and large range of droplet diameters producible from this
generator design makes it an excellent candidate for use in walking droplet experiments. The generator is low cost, simple to manufacture, and easily reproducible for
any other fluids experiments requiring precise droplet generation.
Future work could examine the operation of the generator with fluids of different viscosities. Droplet velocity was also not investigated in this thesis, and future
experiments with droplet velocity as a variable of interest could further characterize the effect of different operating parameters on droplet generation. A redesign of
the generator for fabrication from rapid prototyping techniques such as 3D printing
could further lower the manufacturing cost, making the generator even more easily
accessible for interested parties.
32
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34