AN ABSTRACT OF THE THESIS OF
Worawut Wangwatcharakul for the degree of Master of Science in Industrial
Engineering presented on October 19, 2001. Title: Development of a Passive
Micro-ball Valve.
Redacted for privacy
Abstract approved.
Brian K. Paul
A novel design, material, and fabrication method are presented to fabricate a
passive micro-ball valve. Microvalves are critical components in microflow
control devices used to control the fluid flows in microchannels. These micro flow
control devices can be integrated with microsensors to form micro analysis
systems. Glass/silicon-based fabrication is complicated and expensive. Therefore,
other materials and fabrication methods have been proposed. In this research,
Melinex 453, a polyester film, and pressure sensitive adhesives were used to
fabricate a micro-ball valve by a microlamination method.
The valve was designed to have a 450 tm diameter glass ball floating inside a
chamber size of 800 tm. The ball will permit flow in the forward direction and
impede flow in the reverse direction. The fabrication method consists of three
steps: patterning, registration and bonding. The patterning step was accomplished
using laser micromachining. Registration and bonding were performed with the use
of a pin-alignment fixture. Pressure sensitive adhesive was used in the bonding step
using double-sided acrylic adhesive tape. The micro-ball valve has advantages over
other microvalves in terms of little dead volume, simple design, disposability, low
operating pressure in forward direction, and low leakage in reverse direction.
The microbal1 valve was characterized by pressure drop testing at different
flow rates from 1 to 7.5 mi/mm. The experimental results tend to agree with a
simple theoretical model of the pressure drop through an orifice. Moreover, an
average pressure drop diodicity of at least 2980 has been achieved.
©Copyright by Worawut Wangwatcharakul
October 19, 2001
All Rights Reserved
Development of a Passive Micro-ball Valve
by
Worawut Wangwatcharakul
A THESIS
Submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Presented October 19, 2001
Commencement June 2002
Master of Science thesis of Worawut Wangwatcharakul presented on October 19,2001
APPROVED:
Redacted for privacy
Major Professor, representing Industrial Engineering
Redacted for privacy
Head of Department of Industrial and Manufacturing Engineering
Redacted for privacy
Dean of GraduMé School
I understand that my thesis will become part of the permanent collection of Oregon
State University libraries. My signature below authorizes release of my thesis to
any reader upon request
Redacted for privacy
Worawut Wangwatcharakul, Author
ACKNOWLEDGEMENTS
1 would like to thank my adviser, Dr. Brian Paul, who supported and guided
me throughout my graduate work. His guidance has contributed much to this work
and my professional development. I would like to thank Dr. Dean Jensen for
encouraging me to put more time and effort on my experiment in order to get better
results. Appreciation is also extended to Dr. Thomas Plant and Dr. Toshimi
Minoura for participating as members of my Graduate committee.
I would like to thank my colleague, Carl Wu, for being my good partner. His
ideas and advice have improved the quality of my work. I'm grateful to Steve
Etringer for his help in making a fixture and giving some suggestions on the test
loop. I would also like to thank Kannachai Kanlayasiri and Wasana Viratyosin for
sharing uncomfortable feelings throughout this process.
To my good friends, Seth and Brent, thank you very much for your support
and friendship. Your friendship has given me the perspective that" it is not a
matter of where you are from, but who you are". To Trina and Cathy, thank you
for your patience helping me improve my English. The English Learning Center is
one of my favorite places at OSU.
Finally I would like to thank my family, cousins, and friends in Thailand
whose love and support have made this journey a memorable one.
TABLE OF CONTENTS
Page
1. ABSTRACT
2. INTRODUCTION ............................................................
. 1
3
3. LITERATURE REVIEW ................................................... 6
3.1 Valve Designs ............................................................. 6
3.2 Material Selection ........................................................ 7
3.3 Fabrication Method ...................................................... 9
4. VALVEDESIGN ............................................................
11
4.1 Passive Valve Design................................................... 11
4.2 Microlamination Technique ............................................ 13
4.3 Valve Characterization .................................................. 14
4.4 Device Fabrication ....................................................... 15
5. EXPERIMENTAL ........................................................... 18
6. RESULTS AND DISCUSSION ............................................ 22
7. CONCLUSIONS .............................................................. 29
BIBLIOGRAPHY .................................................................. 30
APPENDICES ........................................................................
35
APPENDIX A: Data ................................................ 36
APPENDIX B: Pictures ............................................. 52
APPENDIX C: Calculations ....................................... 59
LIST OF FIGURES
Figure
1.
Page
The micro-ball valve design .................................................... 12
2. Cross sectional side view of the microvalve in reverse flow ............... 12
3. Micro-ball valve .................................................................. 15
4. Schematic diagram of the test loop ............................................ 17
5.
Test station ........................................................................ 19
6.
Testing device fixture ............................................................ 19
7. Measurement variation of the test ioop ........................................ 21
8. Average pressure drop versus flow rate of each valve ...................... 23
9.
The defective micro-ball valve ................................................. 23
10. Experimental and theoretical pressure drop and flow rate .................. 26
11. % Error of experimental and theoretical pressure drop vs. flow rate ...... 26
12. Response time vs. flow rate ...................................................... 28
LIST OF TABLES
Table
1.
Page
The average forward pressure drop of each valve at different flow
rates ............................................................................... 22
2. ANOVA table of testing the difference of valve #2, 3 and 4 ............. 24
3. ANOVA table of testing the difference of the five valves................ 25
4. Pressure diodicity of each valve at the flow rate of imi/min.............. 27
Development of a Passive Micro-ball Valve
1. ABSTRACT
A novel design, material, and fabrication method are presented to fabricate a
passive micro-ball valve. Microvalves are critical components in microflow
control devices used to control the fluid flows in microchannels. These micro flow
control devices can be integrated with microsensors to form micro analysis
systems. Glass/silicon-based fabrication is complicated and expensive. Therefore,
other materials and fabrication methods have been proposed. In this research,
Melinex 453, a polyester film, and pressure sensitive adhesives were used to
fabricate a micro-ball valve by a microlamination method. The valve was designed
to have a 450 tm diameter glass ball floating inside a chamber size of 800 pm.
The ball will permit flow in the forward direction and impede flow in the reverse
direction. The fabrication method consists of three steps: patterning, registration
and bonding. The patterning step was accomplished using laser micromachining.
Registration and bonding were performed with the use of a pin-alignment fixture.
Pressure sensitive adhesive was used in the bonding step using double-sided acrylic
adhesive tape. The micro-ball valve has advantages over other microvalves in terms
of little dead volume, simple design, disposability, low operating pressure in
forward direction, and low leakage in reverse direction. The micro-ball valve was
characterized by pressure drop testing at different flow rates from 1 to 7.5 ml/min.
2
The experimental results tend to agree with a simple theoretical model of the
pressure drop through an orifice. Moreover, an average pressure drop diodicity of at
least 2980 has been achieved.
2. INTRODUCTION
The miniaturization of mechanical and electrical devices has been developed
over the past few decades. These micro-scale devices have been used in various
applications, both in individual components and integrated systems. The benefits of
scale reduction of these devices are improved efficiency, reduced dead volume,
faster response time, increased speed and accuracy, lower power consumption,
portability and cost-effectiveness.
Microfluidics is a promising application in miniaturization. The
miniaturization of fluidic components, such as valves and pumps is required to
enable portable microfluidic systems. These systems consist of microvalves,
micropumps, microchannels and sensors. Microfluidic systems deliver and
manipulate small amounts of fluid both liquids and gases in microchannels with
cross-sectional dimensions on the order of 10-100 pm. Examples of devices
requiring microfluidic systems include drug delivery systems, diagnostic systems,
blood and DNA analysis in medical and biomedical applications (Shoji, 1999),
heavy metal detection systems and water pollution analysis in environmental
monitoring applications (Suzuki, 2000), detection of exhaust gases in automotive
applications (Refaei et al.,2000), and toxic chemical detection systems in military
applications (Igbal, 2000).
Toxin detection in foods and environmental diagnostic systems are promising
applications of microfluidics in biotechnology. The micro-scale sensors used in
these applications are called biosensors. Biosensors are analytical devices using
immobilized agents, enzymes, antibiotics or cells to monitor biological conditions.
An example of a biosensor being developed at Oregon State University is the SOS
(Stochastic Optical Signals) Cytosensor. It is a micro-scale biological sensor that
detects environmental hazards by monitoring the condition of cliromatophore cells.
The chromatophore cells are highly pigmented, toxin-sensitive cells extracted from
the fins of Betta fish. These cells have the ability to change color in response to
environmental stimulation. In order to live, the cells must be immersed in fresh,
aqueous media. A microfluidic system is needed for this purpose to support the
SOS Cytosensor. In particular, it is the objective of this thesis to develop a
microvalve suitable for supporting the microfluidic system for the SOS Cyto sensor.
Microvalves can be categorized into two classes, passive and active valves.
Passive valves have no actuation principles to control fluid flow. They are commonly
used as check valves for applications in pumping and compression. Active microvalves
use actuation principles to open and close microvalves. Each actuation scheme has
advantages and drawbacks. The selection of an actuation scheme depends on the
particular requirements of each application. To select the proper actuation scheme,
power consumption, force generated, size, materials and fabrication process used are
factors that need to be taken into consideration. The actuation principles developed and
used in microvalves are pneumatic (Hosokawa et al., 2000), thermopneumatic (Henning
et al., 1997), piezoelectric (Roberts et al., 2000), electrostatic (Babaei and Kwok, 1999),
electromagnetic (Sadler et al., 1998), electromagnetic and electrostatic (Bosch et al.,
1993), bimetallic (Messner et al., 1998) and shape memory alloy (Kohl et al., 1999).
The first commercial active microvalves using thermopneumatic actuation were
fabricated by Redwood Microsystems, Inc. Ti/Ni pneumatic microvalves are also
commercially available at TiNi Alloy Co. The performance of active microvalves is
characterized by power consumption, actuation, speed, force generated, cost, and
package size (Barth, 1995). The comparisons of design, size, flow range, response time
and actuation scheme of active microvalves was shown in the literature (Yuen et al.,
2000).
To operate the SOS Cytosensor, mentioned earlier, there is a need to integrate
passive microvalves with a micropump to administer reagent onto the biosensitive cells
within the chamber of the device. The specific characteristic requirements and operating
conditions of the microvalves needed in this application are as follows.
1. Low leakage (at least 100:1)
2. Small dead volume
3. Fast response time
4. Operating pressure up to 15 psi.
5. Transparency and biocompatibility properties
6.
Operating flow rate of about 10 jill mm
7.
Integration with microlamination architecture
8. Inexpensive
3. LITERATURE REVIEW
3.1 Valve Designs
For silicon-based passive microvalves, there are a variety of mechanical
structures associated with them depending on fabrication methods used (bulk and
surface micromachining) and their applications. A summary of the moving part
structures of passive silicon microvalves such as ring mesa, cantilever, v-shape,
membrane, float and disk was presented in the literature (Shoji and Esashi, 1994).
A diaphragm is one of the most common moving part structures in microvalves.
However, it might cause clogging problems. These problems can be reduced by
different valve designs or increasing the size of the valves. However, the larger the
valve size, the more power is required to drive the valve (Shinozawa et al., 1997).
Consequently, the size, ease of fabrication, power consumption, pressure needed,
complexity, and amount of fluid sample required must be taken into account to
design microvalves in microfluidic systems.
Not only are the silicon microvalves expensive compared with polymer
microvalves, but also they are not compatible with the microlamination architecture
needed in the Cytosensor application. In non-silicon microvalves, microflapper and
microfloat valve designs using stainless steel and microlamination methods have
been presented in the literature (Paul and Terhaar, 2000). However, these valves
were reported to have limited performance and quite low average pressure
diodicities of 4.08 and 12.76, respectively.
7
In this work, a new micro-ball valve design is presented. The ball will permit
the fluid to flow in the forward direction, but will impede flow in the reverse
direction. It is expected that this design should be simple to fabricate, yet produce
very high diodicity (forward to reverse pressure drop ratio) and leak-tight seals.
The basis of these expectations is that the functional geometry of the ball valve (a
sphere fitting into a cylindrical nozzle) commonly occurs even at small scales (e.g.
capillary tubing and powder particles).
3.2 Material Selection
With attractive mechanical and electrical properties, single crystal silicon has
been the most successful material in micromachining technology. Therefore, most
micro mechanical structures have been created in silicon. Polycrystalline silicon
has been used as a base material for a sacrificial layer in surface micromachining.
The fabrication processes of micro-scale devices were originally developed in the
microelectronics industry such as photolithography, thin film processing, and
etching processes.
However, the exploration of new materials has provided alternative ways to
facilitate the fabrication process. Materials other than silicon have been presented
to provide more viable properties, including biocompatibility, optical transparency
and toughness, each of which are required in biological and biomedical
applications. (Madou et al., 1999) Glass, plastics and elastomers are examples of
those new coming materials for micromachining technology.
In silicon-based surface micromachining, the selection of a sacrificial layer to
be easily etched away is a significant consideration (Xu et al., 2000). Also, the
selection of material for membrane for the valve seat is another consideration to
fabricate membrane structure (Hosokawa et al., 2000). In non-silicon
micromachining, the compatibility of material and fabrication methods has to be
taken into consideration. Yeun et al. (2000) has presented the fabrication of
plexiglass microvalves using CNC machining with a 250 tm diameter end mill for
use in blood analysis system applications. However, this fabrication method has a
restriction in terms of the size of the end mill, which might not be small enough for
some applications.
Based on the need for optical transparency and biocompatibility in many
biotechnology applications, polyester film is a good choice. Others properties such
as physical and chemical properties are also important. In silicon-based devices,
glass is typically used to provide optical access due to its compatibility with silicon.
However, glass is relatively heavy and brittle compared with polymers. In this
work, polyester sheet was used due to its attractive properties of optical clarity,
easy to patterning, light weight, and biocompatibility.
To produce microfluidic geometries, a bonding process was needed. Various
bonding techniques are available. Pressure sensitive adhesive is a bonding method,
which lends itself to a high degree of design flexibility (Aramphongphun, 2001).
This is advantageous in developing a microvalve. This fabrication method uses
adhesive film and pressure to bond each lamina together.
Pressure sensitive adhesive (PSA) is an adhesive that forms a bond between
two substrates under light pressure normally at room temperature. The doublecoated adhesive film used in this application is called FT 8311 from Avery
Dennison. It consists of three layers, the top and the bottom layer is an acrylic
adhesive film while the middle carrier is a polyester film.
3.3 Fabrication Method
Microelectromechanical systems (MEMS) have been developed since 1980
with silicon micromachining technology. The fabrication methods for silicon-based
materials are similar to semiconductor fabrication, such as photolithography, bulk
micromachining, surface micromachining, and LIGA process. These
micromachining methods the use of a high cost clean room environment.
Moreover, the equipment in some processes such as LIGA is costly. Alternative
microfabrication methods for fabricating low-cost microfluidic devices include hot
embossing or injection molding in polymeric materials (Becker and Dietz, 1999).
Thermoplastic molding was proposed to fabricate microvalves (Fahrenberg et al.,
1995). Other conventional fabrication methods compatible with metals have been
presented including EDM or CNC machining. EDM can cause irregular surfaces
after machining which can affect the fluid flow characteristics (Martin et al., 1999).
Moreover, high aspect ratio structure is one of the restrictions for these
conventional methods. Therefore, microlamination has been developed to
overcome this problem and provide an ability to fabricate complicated high aspect
10
ratio micro-scale devices at low costs (Paul and Peterson, 1999). Another
advantage is that this method can be used in a greater variety of materials including
metal, ceramics and polymers.
On the basis of the literature review, most microvalves were generally silicon-
based microvalves, which required clean room environment and high cost
equipment during the fabrication process. Apart from specific requirements in each
application, ease of fabrication and system integration are other essential factors
needed to take into account. In this research, the focus is on fabricating a
microvalve to meet the specific requirements in the SOS Cytosensor application
mentioned earlier. The microvalve will be used as a check valve in micropump
application to administer reagents to the biosensor. Therefore, the micro-ball valve
design is presented and a microlamination technique was used with pressure
sensitive adhesive to fabricate this microvalve.
This fabrication method will make the microvalve readily available to integrate
with other components in a microlamination architecture in future work.
11
4. VALVE DESIGN
4.1 Passive Valve Design
The micro-ball valve consists of three components: valve seat, chamber and
end plate as shown in Figure 1. Each component has the same outside structure of
l"x 1" square. Dupont Melinex 453 127 I.lm thick was used to fabricate the valve
seat and the end plate. A 325 tm orifice was designed as a nozzle in the valve seat.
The chamber consists of seven laminae; three laminae of Melinex, and four laminae
of two-sided adhesive tape, FT831 1 (104 tm thick) from Avery Dennison. The
pattern for the Melinex laminae is an 800 pm diameter hole. The pattern for the
PSA laminae was designed to be 150 tm in diameter larger than the Melinex
patterns. This was to help keep the PSA from squeezing into the valve chamber and
causing the valve to function improperly. The total chamber depth from the seven
laminae is 797 tm. The last pattern is the left end plate. The left end plate structure
consists of four 240 jim diameter holes. To control misalignment during the
bonding process, a pin-alignment fixture has been used in the registration step.
Therefore, two 3.4 mm diameter alignment holes in the top-left and bottom-right
corners were included in each lamina design. These simple designs make this valve
easy to fabricate. The 450 jim diameter glass ball was used as a moving part in the
microvalve. In conclusion, the microvalve was designed to have a glass ball
floating inside the chamber and direct the fluid to flow in only one direction. The
ball will impede flow in the reverse direction as depicted in Figure 2.
12
Figure 1. The micro-ball valve design
157
325
Reverse Flow
End Plat
Chamber
Valve Seat
I
Figure 2. Cross sectional side view of the microvalve in reverse flow
13
4.2 Microlamination Technique
Microlamination is a process for fabricating micro and meso-scale devices
having intricate arrays of components interconnected within a single block of metal
or polymeric material (Paul and Peterson, 1999). Microlamination has been
developed by researchers at Pacific Northwest National Laboratory and Oregon
State University. The technique consists of three steps: 1) lamina patterning, 2)
laminae registration, and 3) laminae bonding
The patterning step was completed using a laser micromachining system,
model ESI-4420, which employed a q-switched NdYAG laser. This UV laser has a
266 nm wavelength. The laser setting was used at a frequency of 4.5 kHz, a bite
size of 1 tm and an average power of 150 mW. Once each lamina was patterned,
the lamina was cleaned using a standard cleaning procedure, AMD (Acetone,
Methanol and Deionized water) to get rid of grease, dust and residue. This cleaning
step is extremely significant in pressure sensitive adhesive techniques, which
require clean surfaces to strengthen the bond.
A pressure sensitive adhesive is a sticky, viscous material that adheres to a
surface when pressure is applied to it. It tends to have good adhesion on high
surface energy materials such as metals, glass and plastics. Therefore, adhesive-
bonding techniques can be applied to a variety of materials. Moreover, another
advantage is that they permit lower temperature processing compared with anodic
and eutectic bonding (Maas et al., 1994). In order to eliminate the use of elevated
14
temperatures during processing, pressure sensitive adhesive bonding was used in
this work to bond the polyester film.
4.3 Valve Characterization
One requirement of the valve is that it has low pressure drop in the forward
direction. In order to predict the pressure drop across the valve, a simple fluid
mechanics model was developed. In this model, it was assumed that the major
contribution to pressure drop was across the orifice of the valve seat. In order to
model the pressure drop across the orifice, it was necessary to determine the type of
flow across the orifice. The type of fluid flow can be determined by the Reynold's
number, Re, which is the ratio of inertial force to viscous force.
Re=
(1)
/1
where p is the fluid density at output (kglm3), v is the flow rate (mis), L is the
length of channel in flow direction (m), and p is the fluid viscosity (kg/m s)
If the Reynold's number is low, the flow will be laminar. The typical
Reynold's number in macroscopic pipe flow for transitioning from laminar to
turbulent is between 2000 and 2300 (Gravesen et al., 1993). In microfluidic
systems, the transitional Reynold' s number
Ret
is somewhat lower than the
Ret
in
macrofluidic systems. In order to develop the model, some assumptions were made,
including that the fluid was incompressible, and the viscosity was independent of
the dimension of the flow channel, temperature and pressure. Moreover, as
15
expressed above, in order to simplify the analytical model, it was assumed that the
viscous friction losses are mainly due to the flow through the orifice of the valve
(i.e. the friction losses in the valve chamber are negligible). The fluid flow models
of flow rate and pressure drop for incompressible liquids as well as the transitional
Reynold' s number (Ret) under these conditions can be seen in the literature
(Gravesen et al., 1993). In this research, the pressure drop across the valve is
mainly from the flow through the orifice of the valve seat, and the ratio of the
orifice length and diameter (L/D = 0.39) is less than 0.5. Thus, the transitional
Reynold's number is 15 as shown in the literature (Gravesen et al., 1993). The
Reynold's numbers associated with flow rate of 1-7.5 mi/mm were calculated (See
Appendix C). The results were from 25.5 to 191.Therefore, the flow was turbulent.
The theoretical model of the pressure drop and flow rate is
o(Q2
(2)
2AJ
with
=2.6 for orifice flow (Gravesen et al., 1993).
where Q is the volumetric flow (m3/s), A is the cross sectional area of flow path
(m2), p
is the fluid density at output (kg/m3,
is the pressure loss coefficient and
zp is the pressure drop (N/rn2).
4.4 Device Fabrication
The patterning step in microlamination was accomplished by using laser
micromachining. It is fast and easy to cut polymeric materials, as well as adhesive
tape, using the laser. A UV laser with the wavelength of 266 nm was installed on a
16
laser micromachining system model ESI 4420, which was set at a frequency of
4500 Hz, a bite size of 1 tm and an average power of 150 mW. After the cutting
process, each lamina was cleaned to get rid of contaminates (greases, debris, etc)
which might occur during the laser micromachining process.
The registration process began with placing the end plate into the pinalignment fixture. Next, four laminae of adhesive and three laminae of Melinex
were interleaved in the fixture to produce the chamber. After each lamina was
registered and aligned on the fixture, pressure was applied. A dial torque wrench
was used to measure the pressure applied to the fixture. Based on past experience, a
pressure of 180 inch-pounds was applied to the fixture for 10 seconds. With those
parameters, a reasonable level of alignment was maintained, the adhesive material
was not squeezed out into the chamber, and the bond was strong enough for the
biological application. This procedure was repeated for each lamina until the last
lamina (valve seat). Once the chamber part had been completely built, a 450 tm
diameter glass ball was placed into the chamber. Finally, the valve seat was bonded
on top of the chamber. Figure 3 shows the chamber, endplate, valve seat and the
ball under a microscope after the micro-ball valve was completely made.
17
Figure 3. Micro-ball valve
18
5. EXPERIMENTAL
To validate the theoretical model, the pressure drop across the valve was
characterized. A pressure drop test loop, as shown in Figures 4 and 5, was used to
characterize the microvalves. Each microvalve was placed on the fixture and Viton,
a gasket material, was used to prevent leakage while testing as shown in Figure 6.
Deionized water was used as the medium fluid. A syringe pump (model KDS200
from Kd Scientific) was used to pump the fluid through the system and control the
fluid flow at low flow rates with an accuracy of 1%. A pressure gauge was used to
determine the pressure before the fluid entered the test device. A differential
transducer (model px2300-25di from Omega Engineering Inc.) and readout were
used to measure the pressure difference between the inlet and outlet of the test
device with an accuracy of 0.25%. Due to the limitation of the pressure transducer,
the pressure readout can measure up to a maximum of 25 psi.
Syringe
Pump
Outlet
Resevior
Pressure
Ljransducer
Device
Pressure
Gauge
Figure 4. Schematic diagram of the test loop
19
Figure 5. Test station
Figure 6. Testing device fixture
20
Leakage across the fixture was tested by putting gasket material between the
two halves of the fixture, pressurizing it to 60 psi, and turning off the inlet flow of
gas. After leaving the testing device in this condition for two hours, the system
pressure was still at the original value of 60 psi. Therefore, the testing setup proved
to be leak-proof. To characterize performance of the microvalves, the pressure drop
across the valves in both forward and reverse directions was measured at the flow
rates of 1, 2.5, 5, and 7.5 mi/mm. The microvaives allowed the fluid to flow
through easily in the forward direction. The relationship of flow rate and pressure
drop across the valve was observed.
In fact, from the prototype experiment, the flow rate of 1 Opi/min was used to
characterize the valve. After the device was left for 20 hours in the reverse flow
test, it still did not reach the steady state. However, the pressure drop from the
pressure readout was still increasing slowly. This showed that the valve was
working. To accelerate the tests, a flow rate on the order of mi/mm was used
instead.
To deal with the precision of the testing device and the reproducibility of
the fabrication methods, five microvalves were fabricated with the same design.
Each microvalve was tested three times. Therefore, fifteen pressure drop tests were
performed randomly to cope with uncontrollable variations during testing. The
forward and reverse pressure drops were recorded in each different flow rate on
each test.
21
In order to validate the data collection methods, six separate tests were
performed at each of two flow rates using valve #4. The pressure drop results of
valve #4 at these flow rates are depicted in Figure 7. An ANOVA was performed to
determine if the two sets of data were different, and it showed that the two sets of
data were significantly different with the p-value of 1.1 6E-07. Variations in the
data might have resulted from environmental factors such as temperature. However,
the resolution of the measuring technique was found to be acceptable.
Forward Pressure drop of valve #4
025
02
E015
2.5m1/min
R5m1/min
01
0_os
01
0
2
4
6
8
10
12
index
Figure 7. Measurement variation of the test ioop.
14
22
6. RESULTS AND DISCUSSION
The results of the pressure drop tests of each valve are shown in Appendix
A. Table 1 shows the results of average forward pressure at four different flow
rates. It can be observed visually from the graph in Figure 8 that the pressure drops
of valves #1 and #5 were higher than those of #2, #3 and #4. After observing
microvalves #1 and #5 under the microscope, it was found that one of the laminae
was misaligned as shown in Figure 9. The misaligned layer blocked the fluid flow
in the forward direction resulting in higher pressure drop.
Table 1. The average forward pressure drop of each valve at different flow rates
No
Flow rate
Forward Pressure Drop (psi)
(mLlinjn)
Valve #1 Valve #2 Valve #3 Valve #4 Valve #5
1
1
0.053
0.017
0.013
0.013
0.063
2
2.5
0.120
0.050
0.047
0.067
0.190
3
5
0.207
0.170
0.177
0.177
0.263
4
7.5
0.377
0.373
0.310
0.370
0.447
23
Pressure Drop vs. Flow rate
0.5
_ 0.4
Valve#1
I
Va1ve#2
0.3
IAValve#3
0.2
X Valve#4
0.1
IX Valve#5
I________
*
0.0
I
0
2.5
5
7.5
Flow rate(ml/min)
Figure 8. Average pressure drop versus flow rate of each valve
Figure 9. The defective micro-ball valve
10
24
The repeatability of the fabrication methods was determined by making five
microvalves with the same design and procedure. At first glance, it appeared that
valves #1 and #5 had problems. Therefore, two hypothesis tests were carried out to
test whether: a) the mean values of pressure drop of valves #2, 3 and 4 were
different, and b) the mean values of pressure drop of at least one of five valves
were different from the others. The ANOVA tables of all the tests are shown in
Appendix A. Here, the ANOVA tables of the tests at the flow rate of 1 mi/mm are
shown in Table 2 and 3. The results of the first ANOVA (Table 2) show that there
is no difference between the mean values for values #2, 3 and 4. The results of the
second ANOVA (Table 3) show clearly that at least one of the valves has a
significantly different diodicity when compared with the other valves. This
indicates that the fabrication procedure may not be robust.
Table 2. ANOVA Table of testing the difference of valves #2, 3, and 4
ANOVA
F
P-value F crit
Source of Variation
SS
df
Between Groups
0.00002
2
0.00001 0.16667 0.85027 5.14325
Within Groups
0.00040
6
0.00007
Total
0.00042
8
MS
25
Table 3. ANOVA Table of testing the difference of the five valves
MS
Source of Variation
SS
df
BetweenGroups
0.00711
4
Within Groups
0.00133
10 0.00013
Total
0.00844
14
F
P-value
F crit
0.00178 13.3250 0.00051 3.47805
The Reynold's numbers associated with flow rates from 1 to 7.5 mi/mm
were calculated. The results ranged from 25.5 to 191, which indicate turbulent
flow through the orifice as assumed in Equation 2. Valve #4, one of the good
performing valves, was chosen to validate the theoretical model. The theoretical
and experimental data were compared graphically. The theoretical data can be
seen in Appendix C. The graphical comparisons of the theoretical and
experimental data for valve #4 are shown in Figure 10. The error bars of the
accuracy of the testing devices were also included at each point of experimental
data. The graph indicates a reasonable agreement between the theoretical and
experimental results, as the slope and shape of these two curves are similar. The %
errors of experimental and theoretical pressure drop at different flow rates are
shown in Figure 11. From the graph, the average error of the experimental data
from the theoretical data is 13.7%. It can be seen from the theoretical model in
Equation 2 that pressure drop has a quadratic relationship with flow rate, and those
variables from the experimental data are correlated in similar fashion.
26
This indicates that the pressure drop through the orifice is the largest contribution
to the pressure drop in the current design.
Pressure Drop vs. Flow Rate of Valve #4
2.5
-
//
1.5
) Theory
:
Experiment
-1
;
C)
0
2.5
5
7.5
10
12.5
15
17.5
20
Flow Rate (mi/mm)
Figure 10. Experimental and theoretical pressure drop vs. flow rate
% Error of Experimental and Theoretical Pressure
Drop vs. Flow Rate
50.00
40.00
E
30.00
20.00
.
10.00
.
.
.
0.00
0
5
10
15
20
Flow rate (mI/miii)
Figure 11. % Error of experimental and theoretical pressure drop vs. flow rate
The pressure diodicity was also calculated to characterize the valve. Pressure
diodicity is the ratio between pressure drop of fluid flow across the valve orifice in
the forward and backward direction at a given flow rate. Due to limitations of the
digital pressure gauge, the reverse pressure drop cannot be measured above 25 psi.
Therefore, the analog pressure gauge was used to measure the reverse pressure
drop. However, the syringe pump stops automatically at system pressure of 42 psi.
From the experiments, the reverse pressure drop of every microvalve was higher
than 42 psi for every flow rate used, which is confirmation that the valve is
reasonably leak tight in reverse flow. The summary of pressure diodicity of the
microvalves at the flow rate of 1 mi/mm is shown in Table 4.
Table 4. Pressure diodicity of each valve at the flow rate of 1 ml/min
Valve # Flow rate
(mi/mill)
Forward
Pressure Drop (psi)
Reverse
Pressure Drop (psi)
Pressure
Diodicity
1
1
0.053
42.0
792
2
3
1
1
0.017
0.013
42.0
42.0
2470
3230
4
1
0.013
42.0
5
1
0.063
42.0
3230
667
As mentioned earlier, the reverse pressure drop could not be measured
precisely. The pressure diodicity in Table 4 shows the minimum pressure diodicity
of each microvaive at a flow rate of 1 ml/min. It is obvious that the defective
valves # 1 and #5 have much lower pressure diodicity than that of valves # 2, 3
28
and 4. The average pressure diodicity from valves # 2, 3,and 4 is 2980. Therefore,
the results indicate that a minimum pressure diodicity of 3230 can be reached
using the microvalve design.
Regarding the requirements of the microvalve for the SOS Cyto sensor
application, the valve will be used with an operating pressure up to 15 psi. It is
clear that the valve can stand even the pressure of 42 psi. The response time of the
valve can be simply estimated as shown in Appendix C. The response time is
dependent on the flow rate used. The graph in Figure 12 shows relationship
between response time and flow rate. With the flow rate of 10 jtl/min, the response
time is 1 .25s. The higher the flow rate, the faster the response time. Nevertheless,
the exact flow rate in this application is still unknown. The study of the effect of
fluid mechanics on the chromatophore cells is still ongoing. The dead volume of
the microvalve was calculated and shown in Appendix C. The result showed that
the dead volume of the microvalve design is 0.138 p1.
Response Time vs. Flow Rate
L!IP'j:: JUl!
1a1!!![
I
Flow Rate (il/min)
Figure 12. Response time vs. flow rate
1
29
7. CONCLUSIONS
A passive micro-ball valve has been developed using microlamination
methods. Melinex 453, a polyester film was used to fabricate simply designed,
easy-to-make, disposable microvalves. Laser micromachining was used in the
cutting process, and pin alignment fixtures were used in the fabrication process.
Pressure sensitive adhesive (in this case, double-sided acrylic tape) was used to
bond the laminae. The performance of the valve was characterized using a pressure
drop test loop. In order to predict the performance of the microvalve with respect to
flow rate and pressure drop, an analytical model of the fluid flow through the
microvalve has been developed and verified. These results indicate that the pressure
drop through the orifice is the largest contribution to the pressure drop in the entire
valve for the current valve design. Also, the maximum and average pressure
diodicity was found to be higher than 3230 and 2980, respectively. Two of the
valves that were produced were found to be defective, due to misalignment during
the registration process. This suggests that future work might investigate alternate
methods for making the micro-ball valve, including soft lithography methods.
Reaction time and dead volume of the valve were estimated to be 1.25 s and 0.138
ti, respectively at the flow rate of 10 tl/min. Overall, the micro-ball valve design
developed in this thesis was found to meet the requirements needed in the SOS
Cytosensor application. In future work, the micro-ball valve will be integrated with
an actuation principle to form a micropump to control the fluid flow in
biotechnology applications.
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35
APPENDICES
APPENDIX A: DATA
37
Experiment Order
Valves #
Random#
Order
Order
Valve #
1
0.85941862
14
1
5
2
0.28160873
2
2
2
3
0.89067267
15
3
5
4
0.50758732
6
4
1
5
0.22638646
1
5
2
1
0.55274669
9
6
4
2
0.73652423
13
7
3
3
0.61576972
10
8
5
4
0.68570634
12
9
1
5
0.53326486
8
10
3
1
0.40548694
4
11
4
2
0.49855434
5
12
4
3
0.51353475
7
13
2
4
0.63610519
11
14
1
5
0.40043255
3
15
3
38
Pressure Drop Testing Results
Test#1
Test#2
Test#3
Test#4
Test#5
V5
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.06
25
416.67
2
2.5
0.21
25
119.05
3
5
0.29
25
86.21
4
7.5
0.47
25
53.19
V2
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.03
25
833.33
2
2.5
0.05
25
500.00
3
5
0.13
25
192.31
4
7.5
0.39
25
64.10
V5
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(ml/min)
(psi)
(psi)
1
1
0.07
25
2
2.5
0.19
25
357.14
131.58
3
5
0.27
25
92.59
4
7.5
0.45
25
55.56
Vi
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.07
25
357.14
2
2.5
0.13
25
192.31
3
5
0.2
25
125.00
4
7.5
0.37
25
67.57
V2
Flow rate Forward Pressure Drop Reverse Pressure Drop
(mi/mm)
(psi)
(psi)
1
1
0.01
25
2
2.5
0.07
25
3
5
0.17
25
4
7.5
0.34
25
Pressure Diodicity
2500.00
357.14
147.06
73.53
39
Test#6
Test#7
Test#8
Test#9
Test#1C
V4 Flow rate Forward Pressure Drop Reverse Pressure Drop Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.01
25
2
2.5
0.12
25
3
5
0.17
25
2500.00
208.33
147.06
4
7.5
0.38
25
65.79
V3
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(mi/mm)
(psi)
(psi)
1
1
0.02
25
1250.00
2
2.5
0.05
25
3
5
0.17
25
500.00
147.06
4
7.5
0.32
25
78.13
V5
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(ml/min)
(psi)
(psi)
1
1
0.06
25
2
2.5
0.17
25
3
5
0.23
25
416.67
147.06
108.70
4
7.5
0.42
25
59.52
Vi
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.03
25
833.33
2
2.5
0.14
25
178.57
3
5
0.23
25
108.70
4
7.5
0.4
25
62.50
V3
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(ml/mm)
(psi)
(psi)
1
1
0.01
25
2
2.5
0.06
25
2500.00
416.67
3
5
0.21
25
119.05
4
7.5
0.35
25
71.43
Test#1 I
Test#12
Test#1 3
Test#1LI
Test#1 5
V4
Flow rate Forward Pressure Drop Reverse Pressure Drop Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.01
25
2
2.5
0.06
25
3
5
0.19
25
2500.00
416.67
131.58
4
7.5
0.38
25
65.79
V4
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.02
25
1250.00
2
2.5
0.05
25
500.00
3
5
0.17
25
147.06
4
7.5
0.35
25
71.43
V2
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.01
25
2500.00
2
2.5
0.05
25
500.00
3
5
0.21
25
119.05
4
7.5
0.39
25
64.10
Vi
Flow rate Forward Pressure Drop Reverse Pressure Drop
Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.06
25
416.67
2
2.5
0.09
25
277.78
3
5
0.19
25
131.58
4
7.5
0.36
25
69.44
V3
Flow rate Forward Pressure Drop Reverse Pressure Drop Pressure Diodicity
(mllmin)
(psi)
(psi)
1
1
0.01
25
2
2.5
0.03
25
3
5
0.15
25
4
7.5
0.26
25
2500.00
833.33
166.67
96.15
Results from pressure drop testing
VALVE# 1
Flow rate
(mi/mm)
Test#1
Test #2
Test #3
Mean
1
1
0.07
0.03
0.06
0.053
2
2.5
0.13
0.14
0.09
0.120
3
5
0.2
0.23
0.19
0.207
4
7.5
0.37
0.4
0.36
0.377
No
Forward Pressure Drop (psi)
Pressure Drop vs. Flow rate of Valvel
0.45
0.4a,
0.35
0.3
Test#1
0
0.25
a,
I-
a,
a,
C,
D Test#2
0.2-
Test#3
0.15
0.1
1
0.
0.05
0
I
0
2.5
I
5
Flow rate ( mm/mm)
I
7.5
10
VAL VE#2
No
Flow
rate
Forward Pressure Drop (psi)
(mi/mm)
Test#1
Test #2
Test #3
Mean
1
1
0.01
2
2.5
3
5
0.01
0.05
0.21
4
7.5
0.03
0.05
0.13
0.39
0.017
0.057
0.170
0.373
0.07
0.17
0.34
0.39
Pressure Drop vs. Flow rate of Valve2
0.45
'
O.4j
03
O.3
Test#1
0.25
0.2
co
U,
o Test#2
Test#3
0.i5-
.
0.L
0.05
00
I
2.5
5
Flow rate(mm/min)
I
7.5
10
VAL VE#3
Forward Pressure Drop (psi)
Flow rate
(mi/mm)
Test#1
Test #2
Test #3
Mean
1
1
0.02
0.01
0.01
0.013
2
2.5
0.05
0.06
0.03
0.047
3
5
0.17
0.21
0.15
0.177
4
7.5
0.32
0.35
0.26
0.310
No
Pressure Drop vs. Flow rate of Valve3
0.4
0.35
0.3
0.25
Test#1
0.2
Test#2
0.15
Test#3
0.0.05
0
I
0
2.5
5
Flow rate ( mm/mm)
I
7.5
10
VAL VE#4
Forward Pressure Drop (psi)
Flow rate
(mi/mm)
Test#1
Test #2
Test #3
Mean
1
1
0.01
0.01
0.02
0.013
2
2.5
0.09
0.06
0.05
0.067
3
5
0.17
0.19
0.17
0.177
4
7.5
0.38
0.38
0.35
0.370
No
Pressure Drop vs. Flow rate of Valve 4
0.4
._ 0.35
(0
0.
0.3
Test#1
0.25
00.2-
Test#2
A
C,
I-
t Test#3
U,
0.1°
0.05
0-4---
0
-
2.5
5
Flow rate ( mm/mm)
7.5
10
VAL VE#5
Flow rate
(mi/mm)
No
Forward Pressure Drop (psi)
1
1
Test#1
0.06
2
2.5
0.21
3
5
4
7.5
0.29
0.47
Test #2
0.07
0.19
0.27
0.45
Test #3
Mean
0.06
0.17
0.23
0.42
0.063
0.190
0.263
0.447
Pressure Drop vs. Flow rate of Valve 5
u
0.5
0.45
0.4
0.35
0.3
0.25
A
________
Test#1
Test#2
ATest#3
0.1
0.05
0
I
0
2.5
7.5
5
Flow rate (
10
mmlmin)
JI
Average Forward Pressure Drop of each valve
No
Forward Pressure Drop (psi)
Flow rate
(mL'min)
Valve #1 Valve #2 Valve#3
Valve#4
Valve#5
1
1
0.053
0.017
0.013
0.013
0.063
2
2.5
0.120
0.050
0.047
0.067
0.190
3
5
0.207
0.170
0.177
0.177
0.263
4
7.5
0.377
0.373
0.310
0.370
0.447
Pessure Drop vs. Flow rate
0.5
O.4
valve#1
Dvalve#2
Avalve#3
A
u.3
0.2
xvalve#4
Cl)
vaIve#5
Cl)
0.1
.
0.0
0
2.5
5
Flow rate(ml/min)
7.5
10
Flow rate(mllmin) Valve #
ANOVA
1,2,3,4,5
Source of Variation
SS
df
MS
F
P-value
Fcrit
Between Groups
0.00711
4
0.00178
13.32500
0.00051
3.47805
Within Groups
0.00133
10
0.00013
Total
0.00844
14
Source of Variation
SS
df
MS
F
P-value
Fcrit
Between Groups
0.00002
2
0.00001
0.16667
0.85027
5.14325
Within Groups
0.00040
6
0.00007
Total
0.00042
8
AND VA
2,3,4
Flow rate(mllmin) Valve #
ANOVA
2.5
1,2,3,4,5
Source of Variation
SS
df
MS
F
P-value
Fcrit
Between Groups
0.04444
4
0.01111
25.63846
0.00003
3.47805
Within Groups
0.00433
10
0.00043
Total
0.04877
14
Source of Variation
SS
df
MS
F
P-value
Fcrit
Between Groups
0.00069
2
0.00034
0.96875
0.43192
5.14325
Within Groups
0.00213
6
0.00036
Total
0.00282
8
ANOVA
2.5
2,3,4
4.
00
Flow rate(mllmin) Valve #
ANOVA
5
1,2,3,4,5
Source of Variation
SS
df
MS
F
P-value
Fcrit
Between Groups
0.01857
4
0.00464
6.21875
0.00885
3.47805
Within Groups
0.00747
10
0.00075
Total
0.02604
14
Source of Variation
SS
df
MS
F
P-value
Fcrit
Between Groups
0.00007
2
0.00003
0.04225
0.95891
5.14325
Within Groups
0.00473
6
0.00079
Total
0.00480
8
ANOVA
5
2,3,4
Flow rate(mllmin) Valve #
ANOVA
7.5
1,2,3,4,5
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
0.01777
4
0.00444
8.43671
0.00303
3.47805
Within Groups
0.00527
10
0.00053
Total
0.02304
14
Source of Variation
SS
df
MS
F
P-value
Fcrit
Between Groups
0.00162
2
0.00081
1.55319
0.28603
5.14325
Within Groups
0.00313
6
0.00052
Total
0.00476
8
ANOVA
7.5
2,3,4
(Ji
51
Summary of Pressure Diodicity at different flow rates
Valve # Flow rate
(mI/mm)
1
1
2
3
4
5
1
1
1
1
Valve # Flow rate
1
2
3
4
5
2.5
2.5
2.5
2.5
2.5
Valve # Flow rate
1
5
2
5
3
5
4
5
5
5
Valve # Flow rate
1
2
3
4
5
7.5
7.5
7.5
7.5
7.5
Forward
Backward
Pressure Drop(psi) Pressure Drop(psi)
Pressure
Diodicity
468.78
1470.59
1923.08
1923.08
396.83
0.053
0.017
0.013
0.013
0.063
25
25
25
25
25
Forward
Pressure Drop
Backward
Pressure Drop
0.120
0.05
0.047
0.067
0.19
25
25
25
25
25
Forward
Pressure Drop
Backward
Pressure Drop
0.207
0.17
0.177
0.177
0.236
25
25
25
25
25
Forward
Pressure Drop
Backward
Pressure Drop
Pressure
0.377
0.373
0.31
0.37
0.447
25
25
25
25
25
66.31
67.02
80.65
67.57
55.93
Pressure
Diodicity
208.33
500.00
531.91
373.13
131.58
Pressure
Diodicity
120.77
147.06
141.24
141.24
105.93
Diodicity
52
APPENDIX B: PICTURES
53
The orifice of the valve
The end plate of the valve
hil
ESI 4420 Laser Machine
Dial torque wrench
Pin alignment fixture
Vise and fixture
56
Pressure drop test ioop
Test ioop fixture
57
Syringe pump
Test ioop fixture
58
Applying pressure to the fixture using torque wrench
59
APPENDIX C: CALCULATIONS
Results from the theoretical model
2A
Flow rate(mllmin)
1
2.5
5
7.5
10
12.5
15
17.5
L
0.000127
0.000127
0.000127
0.000127
0.000127
0.000127
0.000127
0.000127
D
0.000325
0.000325
0.000325
0.000325
0.000325
0.000325
0.000325
0.000325
LOW
998
998
998
998
998
998
998
998
MU
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
A
8.296E-08
8.296E-08
8.296E-08
8.296E-08
8.296E-08
8.296E-08
8.296E-08
8.296E-08
Q
1.667E-08
4.167E-08
8.333E-08
1.25E-07
1.667E-07
2.083E-07
2.5E-07
2.917E-07
V
0.2009
0.5023
1.0045
1.5068
2.0091
2.5113
3.0136
3.5158
Re
25.5
63.7
127.3
191.0
254.6
318.3
382.0
445.6
L/D
0.391
0.391
0.391
0.391
0.391
0.391
0.391
0.391
Deltap(N/m2)
52.4
327.3
1309.2
2945.6
5236.7
8182.4
11782.6
16037.4
Delta p (psi)
0.00760
0.0475
0.190
0.427
0.760
1.19
1.71
2.33
Theoretical Pressure Drop vs. Flow Rate
2.50
2.00
1.50
2
w
I-
U)
U)
C)
[11111
10
5
0
20
15
Flow Rate(mI/min)
-
_____-
---
--------------
-
I
62
Reynold's Number Calculation
Re=
'U
where p is the fluid density at output (kg/rn3), v is the flow rate (mis), L is the
length of channel in flow direction (m), and p is the fluid viscosity (kg/rn s)
Fluid = Deionized water
p = 998 kg/rn3
t
=0.001kg/ms
L= 127pm
V = 0.2009,0.5023,1.0045,1.5068 mIs
Flow
rate(mLlmin)
Q
V
8.2958E-08
l.6667E-08
0.2009
2.5
0.000127
0.000325
998
0.001
8.2958E-08
4.1667E-08
0.5023
8.2958E-08
8.3333E-08
1.0045
7.5
0.000127
0.000325
998
0.001
8.2958E-08
1.25E-07
1.5068
Re
25.4
63.7
127
191
1
p
0.000127
0.000325
998
p
0.001
L
D
A
5
0.000127
0.000325
998
0.001
63
Dead Volume Calculation
325
Reverse Flow
PSA
Melinex
U
End Plat
Valve Seat
Chamber
71
Dead Volume = [ d( h1+h2 )+
4
d1
4
(d2 - d12 )h2 J
6
d
= the diameter of Melinex laminae
d2 = the diameter of PSA laminae
d3 = the diameter of the glass ball
h1
= total channel length of Melinex laminae
h2 = total channel length of PSA laminae
In this micro-ball valve design, d1 = 800 tm, d2 = 950 jim, d3 = 450 tim,
h1381 Lm(3*127),h2=416tm(4*1O4)
Dead volume
[
0.82
( .381+.416 )+
= 0.186- .0477
=0.138 mm3 =0.l38il
(.95 -
.82
).416] -
453
Response Time Calculation
Reverse Flow
I
End Plate
Orifice
797
am
It was assumed that the fluid moved the ball and was able to flow through the
channel instantaneously in the forward flow. Therefore, the response time was
determined by the time used to move the ball from the end plate side to the orifice
side in the reverse flow. It was also assumed that the starting position of the ball in
the reverse flow was in the middle of the channel at the end plate side. The
volumetric flow rate of 10 p1/mm from the microvalve requirement was used to
calculate the response time.
65
Q=vA
Q = the volumetric flow rate
v = the flow rate through the channel
A = the diameter of the channel
Q = 10 j.il/min, A =
v=
d; d = 80O.im,
331 pm/s
A
V
t = the time used to move the ball from the end plate side to the orifice side
s = the distance from the beginning position to the orifice
v = the flow rate
s414.5 pm
v331 pm/s
414.5
t
V
331
=1.25s
The response time at the flow rate of 1 p1/mm is 1 .25s.