Novel Micro System for Accelerated Determination of Diffusion Coefficient 
 
by 
 
Kirn Augusta Cramer 
 
 
 
 
A thesis submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of 
Master of Science 
 
Auburn, Alabama 
December 8, 2012 
 
 
 
 
Keywords: Micro System, Micro mixer, Diffusion, Taylor Dispersion 
 
 
Copyright 2012 by Kirn Augusta Cramer 
 
 
Approved by 
 
Jong Wook Hong, Chair, Associate Professor of Materials Engineering 
Jeffrey W. Fergus, Professor of Materials Engineering 
Barton C. Prorok, Associate Professor of Materials Engineering 
 
 
ii 
 
 
 
 
 
 
 
Abstract 
 
 
 Diffusion plays a paramount role in many scientific areas.  In the scientific field, 
the term diffusion coefficient, D, is generally used as the parameter for quantifying the 
diffusion phenomena. At present, diaphragm cell, chromatography or optical based 
methods are commonly employed to determine the D value of various solutions. 
However, these methods have major disadvantages; they use bulky equipment and 
require a lengthy experimental time.  In the past, to overcome these disadvantages, many 
research groups have tried to reduce the size of the instrument, as well as decrease the 
performance time, by using microfluidic-based devices. This study will address the 
problem of achieving quick quantification of diffusion coefficients by using a novel 
micro system fluidic device. The major advantages of this device include minimum 
sample and device size, short experimental testing time, and user-friendly programming 
allowing for acceleration of determining a diffusion coefficient.    
 
 
 
 
 
 
 
 
 
 
 
 
 
 
iii 
 
 
 
 
 
 
 
Acknowledgments 
 
 
 The author would like to acknowledge her most sincere appreciation towards her 
advisor Dr. Jong Wook Hong, for his continued encouragement, support, enthusiasm and 
guidance. The author is deeply thankful to her committee members, Dr. Jeffrey W. 
Fergus, and Dr. Bart Prorok, for their valuable support, teachings and assistance during 
the course of this study. The author would like to also thank Mr. Charles Ellis, Mr. 
Shakib Morshed and Mrs. Tamara Isaacs-Smith of Alabama Microelectronics Science 
and Technology Center (AMSTC) for permission and assistance in using the clean room 
for microfabrication.  
The author would like to express her deep gratitude and gratefulness to Mr. Chance 
Tara, Mr. Sachin Jambovane, Mr. Hoon Suk Rho and Dr. Morgan Hamon, for passing on 
their knowledge and assistance during the course of these projects. The author would like 
to also share her warmest appreciation for Mr. Chance Tara for his invaluable MATLAB 
programming assistance and Mr. Sachin Jambovane for providing the theoretical Fourier 
concentration profile equation. The author would like to thank the following individuals 
for their assistance and collaboration on various projects: Dr. Jeyhoon Khodadadi, Mr. 
Mahmoud Sedeh, Mr. Cihan Uzunpinar, and Dr. Maria Auad.  The author would also like 
to thank the company of her current and past research group members: Dr. Morgan 
Hamon, Dr. Woon Seob Lee, Dr. Jae Young Yun, Mr. Sachin Jambovane, Mr. Hoon Suk 
Rho, Mr. Jing Dai, Miss Tina Chen, Mr. Austin Adamson, Mr. Chance Tara, Miss Lauren 
 
 
iv 
 
Bradley, Mr. Xiaoyun Yang, Miss Jing Zou, Miss Hye Young Sim, Mr. Ryan Khodadadi, 
Miss Oxana Katalevskaya, Mr. Samuel Thompson, and Mr. Andy Hanna.  
The author would also like to thank to her family and friends, Joyce, Al, Anna, Kam, 
and JJ Cramer, Sam Raymond, Emily and Ty Stafford, Steve Moore and Christen May, 
for their continuous love, support, encouragement and patience. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
v 
 
 
 
 
 
 
Table of Contents 
 
 
Abstract ............................................................................................................................... ii 
Acknowledgments ............................................................................................................. iii 
List of Tables ................................................................................................................... viii 
List of Figures .................................................................................................................... ix 
List of Abbreviations ...........................................................................................................x 
Chapter 1 Introduction  ........................................................................................................1 
 1.1     Background   ..................................................................................................1 
 1.2     Microfluidic platform  ...................................................................................2 
 1.3     Multilayer soft lithography   ..........................................................................3 
 1.4     Pneumatic control systems   ...........................................................................7 
 1.4.1     Pneumatic valves   .............................................................................7 
 1.4.2     Pneumatic mixer   ..............................................................................9 
 1.5     Diffusion study on a chip   ...........................................................................12 
 1.6     Scope of the study   ......................................................................................16 
Chapter 2      Literature review ..........................................................................................17 
2.1    Introduction   .................................................................................................17 
 2.2     Conventional methods    ..............................................................................18 
 2.3     Segmented flow microfluidic systems    ......................................................22 
 2.4     Static and dynamic microfluidic systems    .................................................23 
 
 
vi 
 
 2.5     Refractive index gradient detected microfluidic systems    .........................24 
 2.6     Summary    ...................................................................................................25 
Chapter 3     Development of the diffusion chip  ...............................................................26 
3.1    Introduction   .................................................................................................26 
 3.2    Device design   ..............................................................................................27 
3.2.1    Diffusion chip design version I   .......................................................30 
3.2.2    Diffusion chip design version II   .....................................................33 
3.2.3    Diffusion chip design version III   ....................................................37 
3.3    Mold fabrication  ..........................................................................................42 
3.4    Chip fabrication   ..........................................................................................45 
3.5    Experimental setup and operation  ................................................................53 
3.6    Results and discussion   ................................................................................57 
 3.6.1    Introduction   .....................................................................................57 
 3.6.2    Equation validation   .........................................................................58  
 3.6.3    Data analysis   ...................................................................................63 
 3.6.4    SPSS analysis   ..................................................................................64 
 3.6.5    MATLAB analysis     ........................................................................67 
 3.7    Conclusions   .................................................................................................69 
Chapter 4     Summary and conclusions .............................................................................71 
4.1   Conclusions of the research   .........................................................................71 
References   ........................................................................................................................72 
Appendix I MatLab Code   ................................................................................................75 
 
 
 
 
vii 
 
 
 
 
 
 
 
List of Tables 
 
 
Table 3.1 Soft lithography chip making procedures ..........................................................46 
Table 3.2 SPSS regression analysis results ........................................................................66 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
viii 
 
 
 
 
 
 
 
List of Figures 
 
 
Figure 1.1 Chemical structure of silicone rubber or polydimethylsiloxane .........................5 
Figure 1.2 Cross-sectional view of the process flow for multilayer soft lithography..........6 
Figure 1.3 Cross-sectional schematic of a valve closing .....................................................7 
Figure 1.4 Diagraph of valve closing for rectangular and rounded channels. The dotted 
lines show the contour of the PDMS membrane as pressure is increased. ..............9 
 
Figure 1.5 Sequence of valve operation of pneumatically operated peristaltic micro mixer 
inducing fluidic flow ..............................................................................................10 
 
Figure 1.6 Schematic of working of a pneumatically operated peristaltic micro mixer ....11 
Figure 1.7 Schematic of rotary pump and appropriate variable labeling ...........................11 
Figure 1.8 Basic principles of diffusion .............................................................................13 
Figure 1.9 Schematic of Taylor dispersion of long tube related to a closed tube chamber 
on a microfluidic system ........................................................................................15 
Figure 2.1 Simple diaphragm cell, a Northrop-Anson cell ................................................19 
Figure 2.2 Apparatus presented by Taylor used for observing dispersion in a tube ..........21 
Figure 2.3 Sample dispersion study device using piezoelectric bending disc actuator and 
fiber optic detection ...............................................................................................23 
Figure 3.1 Cup and cone progression model .....................................................................27 
Figure 3.2 Basic design with detail of a reaction chamber and valve close/open key .......30 
Figure 3.3 Chip design version I ........................................................................................31 
Figure 3.4 Concentration versus time data corresponding to the ROI within reaction 
chamber. The green line indicates the release of the center valve, thus the start of 
the experiment and the blue line indicates 4 seconds later. ...................................33 
 
 
ix 
 
Figure 3.5 Chip design version II ......................................................................................34 
Figure 3.6 Device fabricated of design version II. No evidence of channel collapsing but 
shut off valves for reagent metering interferes with reagent flow .........................35 
Figure 3.7 Device fabricated of design version II.  Center valve with 28 psi pressure 
shutting valve with reaction chamber filled with air from chip fabrication ..........36  
Figure 3.8 Chip design version III .....................................................................................37 
Figure 3.9 A fabricated chip of design version III of a good chip .....................................38 
Figure 3.10 Device fabricated of design version III. Center valve pressure not 
disengaging properly affecting fluid flow drastically. 50.922 seconds after 
releasing the center valve .......................................................................................40 
Figure 3.11 Chip design progression ? reaction chamber detail view, version I (a), version 
II (b), and version III (c) ........................................................................................41 
Figure 3.12 Schematic of mold fabrication process...........................................................47 
Figure 3.13 Microfluidic chip made of design III filled with food dye for visualization of 
structure, connected to Tygon tubing and includes a quarter for size comparison 53 
Figure 3.14 Schematic of experimental setup ....................................................................54 
Figure 3.15 Schematic of experimental operational procedures ........................................55 
Figure 3.16 MATLAB plot of theoretical concentration versus time profile give the 
Fourier concentration profile and experimental and known values .......................60 
Figure 3.17 Concentration versus time profile of two experiments at 5Hz, standard 
mixing sequence of water and dye .........................................................................62  
Figure 3.18 Average peak and valley points from test 1, 2 and 3 from Figure 3.17 .........63 
Figure 3.19 SPSS regression analysis curves for the average peaks .................................65 
Figure 3.20 SPSS regression analysis curves for the average valleys ...............................66 
Figure 3.21 MATLAB output results of the peak value analysis of water and dye ..........68 
Figure 3.22 MATLAB plot of the peak value analysis of water and dye ..........................69 
 
 
 
 
x 
 
 
 
 
 
 
 
List of Abbreviations 
 
 
CE Capillary/microchannel electrophoresis 
LOC Lab on a chip 
PCR Polymerase chain reaction 
PDMS Polydimethylsiloxane 
MEMS Micro electro mechanical systems 
DRIE Deep reactive ion etching 
SFB Surface fusion bonding 
ECR Electron cyclotron resonance 
CTMS Chlorotrymethylsilate 
?TAS Micro total analysis system 
AMSTC Alabama Microelectronics Science and Technology Center 
DPI Dots per inch 
ROI Region of interest 
SPSS Statistical Package for the Social Sciences 
NMR Nuclear magnetic resonance  
 
 
1 
 
 
 
Chapter 1 
Introduction 
1.1     Background   
 Microfluidic systems allow for the study of the behavior and response of 
controlled fluidics within a confined, by design, system.  For a definition the following 
will be used: microfluidics is the science and technology of systems that process or 
manipulate small (10-9 to 10-18 liters) amounts of fluids, using channels with dimensions 
of tens to hundreds of micrometers.[1] It is possible to scale down a complicated system 
to a microfluidic system.   By doing so, microfluidic systems use minimum sample 
volumes, can precisely meter samples, and can achieve quick response and experiment 
times.  All these things considered increase the throughput of a microfluidic system 
experimentally compared to many of its predecessor techniques.  
 The field of microfluidics is a multidisciplinary field including chemical 
engineering, biological studies, physics, civil and materials engineering, to name a few.  
It also includes the ever growing study of biological interactions with drug candidates. 
Continuing advances in micro fluidic devices has opened the door to innovative micro 
scale analysis allowing technical barriers to be left by the wayside.  Diffusion is the 
process by which matter is transported from one part of a system to another as a result of 
random molecular motions.[2]  The ability to quickly and accurately measure diffusion 
coefficients is important to assessing and interpreting the quality of experimental results 
obtained from liquid chromatography and capillary/microchannel electrophoresis 
 
 
2 
 
(CE).[3]  This information can be valuable in drug, biological and other applications. By 
using a microfluidic system to determine diffusion coefficient, experimental times and 
sample size are significantly smaller compared to conventional methods, yet still as 
accurate.   
 
1.2     Microfluidic platform   
 Microfluidics belongs to an area of study called micro total analysis systems 
(?TAS), also called ?lab on a chip? (LOC). Within the ?TAS or LOC, the goal is to 
house the full testing system within a single device. This field crosses a variety of 
disciplines including chemistry, biology, bioengineering, physics, electronics, 
clinical/medical science, chemical engineering and materials science. It has been able to 
grow due to advances in semiconductors and micro electro mechanical systems (MEMS).  
As these systems are at the forefront of technology, it seems only appropriate that 
chemical screening and analysis should also advance by miniaturization, resulting in 
faster response time and automated sample handling.   
The field of microfluidics or ?TAS has grown rapidly since its beginnings in the 
early 1990s. The very beginning can be traced back over 35 years to the development of a 
the first analytical miniaturized device, a gas chromatographic analyzer, fabricated on 
silicon chip base.[4, 5] Despite its rapid separation capabilities and minute size, the 
response within the scientific community to this first silicon chip device was almost 
nonexistent, most likely due to the lack of technological experience dealing with this type 
of device.[6] Despite the low effects at the time, between 1990 and 1993 there was an 
emergence of advances and studies performed in the ?TAS field. During this time, Manz 
 
 
3 
 
and colleagues presented a novel miniaturized open-tubular liquid chromatography on a 
silicon wafer[7] and presented the concept of ?miniaturized total chemical analysis 
system?.[8]  These advances led to others studying and making exciting developments in 
micropump systems[9, 10], sample injector systems[11, 12] and even the use of 
microfabricated chambers to carry out DNA amplification, also known as Polymerase 
chain reaction (PCR).[6, 13]  Since then many researchers have used microfluidics for 
numerous studies, utilizing different elemental systematic tools possible by the advances 
within the fabrication techniques.  New methods of fabrication systems and of systematic 
components have become essential elements of mircochemical ?factories? on a chip.[1]  
Such systematic components include microchannels that serve as pipes, and other 
structures that form valves[14, 15], mixers[16-18] and pumps. 
 
1.3     Multilayer soft lithography   
 These micro systems are designed to have all three dimensions of the structure on 
the microscale, producing fluid volumes in the nanoliter or picoliter scale.  There are 
various methods of producing these systems.  When talking on a small scale such as 
micro and nanometer, we must consider the fabrication method. Microcontact printing 
creates the pattern of the structure out of self-assembled monolayers (SAMs) on the 
submicrometer scale as a viable method.[19] There are also many micromachining 
methods for creating microstructures including deep reactive ion etching (DRIE)[20] and 
surface fusion bonding (SFB) and electron cyclotron resonance (ECR) source to produce 
high-aspect-ratio narrow?gap silicon devices.[6]  Another method is mircotransfer 
molding, in which a large areas of micrometer scale structures can be created by filling 
 
 
4 
 
microchannels of an elastomeric mold with precursor, curing the precursor, and then 
removing the mold to reveal a system of micro structures.[21]  
Soft lithography is a low-cost technique for microfluidic devices led the way by 
Whiteside, Xia and Zhao from Harvard University.[22]  This method allows for rapid 
prototyping (it does not need a clean room for fabrication) and requires simple equipment 
for fabrication. Easy fabrication methods allow users with basic, high school scientific 
laboratory experience to be able to create reproducible, complex micro systems.   Soft 
lithography uses soft, organic materials such as polymeric materials to create 
microstructure patterns from negative patterned molds.  By using a single elastomer 
material such as polydimethylsiloxane (PDMS), these microstructure patterns can be 
visible, allowing for countless number of studies that can be performed.  PDMS has 
become the polymer of choice for soft lithography fabrication, as it has great optical 
transparency and is a very flexible polymer, and therefore can be manipulated easily and 
has good biocompatibility.[23]  
PDMS is produced by GE Silicones and Momentive Performance Materials as a 
two-component silicon rubber, RTV 615 (room temperature vulcanizing), also known as 
silicone RTV.  The two components come as a kit of the two solutions by a 10:1 weight 
ratio.  Component A contains the PDMS monomer, while component B is a cross linking 
agent.  When mixed at a 10:1 ratio (A:B, respectively) the compound can cure, according 
to GE Silicons technical data sheet of RTV 615, in either 1 hour at 100?C or 15 minutes 
at 150?C, insuring that the compound will be cure within 24 hours at 25?C.  Figure 1.1 
shows the chemical structure of PDMS [24], while equation 1.1 shows the reaction 
mechanism of covalent bonding in two component addition-cure PDMS. 
 
 
5 
 
 
 
Figure 1.1 Chemical structure of silicone rubber or polydimethylsiloxane.  
Source: [(Callister 2003)]  
 
? ? ? ? ? ? ? ? ? ?3 2 3 3 2 32O C H S i C H C H H S i C H O O C H S i C H S i C H O?? ? ? ? ? ? ??? ? ? ? ?     
(1.1) 
  
 By decreasing the ratio of cross-linking agent, the resulting PDMS has an increase 
in flexibility.  We are then able to produce various layers of PDMS at different ratios.  
Multilayer soft lithography (MSL) combines the principles of soft lithography 
fabrication, as introduced by Whiteside, Xia and Zhao, and the flexibility of various 
ratios of PDMS to create multiple layers of microstructures within PDMS and bond the 
layers together.  Figure 1.2 shows a cross-sectional representation of the fabrication 
process flow of a MSL. The top layer, as seen on the left, is first cured onto the mold then 
removed and bonded to the cured layer on the second mold.  The final system can be 
removed from the bottom mold and bonded to a substrate, glass slide, and operated.   
C H
3
S i O
C H
3
S i O S i O
C H
3
C H
3
C H
3
C H
3
n
 
 
6 
 
 
Figure 1.2 Cross-sectional view of the process flow for multilayer soft lithography. 
Source: [(Unger et al. 2000)]  
 
 With the introduction of multilayer soft lithography by Unger et al.[25] in 2000, 
this technique for creating and manipulating microstructures has expanded the 
possibilities of applications in microfluidics.  This allows scientists to design microfluidic 
devices even more similar to the in vivo subjects than before. This gives great potential 
for advances to be made within the biotechnology field.  
 
 
 
M o l d
S u b s t r a t e  -  G l a s s
 
 
7 
 
1.4     Pneumatic control systems   
1.4.1     Pneumatic valves   
 With the introduction of the MSL by Unger et al.[25] the interaction between two 
overlapping microchannels can be studied.  By designing for different layers? 
microchannels to overlap at certain locations, we can create areas of interaction.  This 
allows structures such as on-off valves, switching valves, and pumps to be produced 
within the the PDMS structure.  There are two types of valve orientations; the control 
layer containing the valves can either be above or below the fluidic layer that is to have 
the fluid flow controlled.  Figure 1.3 illustrates a cross-sectional view valve shutting off a 
control valve below the fluidic microchannel layer. 
 
 
Figure 1.3 Cross-sectional schematic of a valve closing. 
Source: [(Unger et al. 2000)]  
C h a n n e l  f o r  
c o n t r o l l e d  r e a g e n t  f l o w
C o n t r o l  v a l v e
F l u i d i c  L a y e r
C o n t r o l  L a y e r
S u b s t r a t e  -  G l a s s
F o r c e d  
d i r e c t i o n a l  f l o w
O p e n  v a l v e
C l o s e d  v a l v e
P r e s s u r i z e d  v a l v e
P r e s s u r e  a p p l i e d  
t h r o u g h  t h e  i n l e t  
o f  t h e  p n e u m a t i c  
v a l v e  c h a n n e l
 
 
8 
 
 If the control valve is above the fluidic, then pressure is needed to push down on 
the membrane of PDMS between the two layers.  Generally, the microchannels are 100 
?m wide and 10-15?m high, allowing for a 100 ?m x 100 ?m interaction area. The 
amount of pressure needed to push down on the membrane depends on the membrane 
thickness.  Fabrication methods can control the membrane thickness, usually needing 
about 30 ?m with the previous mentioned dimensions.   
 With the control layer below and a glass substrate below the control layer, this 
decreases the response time to activation, which can be critical depending on the device.  
The shape of the flow channel can also affect the valve performance. The channel cross 
sections and heights are a result of the mold fabrication process.  Unger et al.[25] 
discussed three different shapes of the fluidic channel: rectangular, trapezoidal and 
rounded.  A rectangular or trapezoidal shaped channel requires more pressure to cause the 
membrane to touch the roof of the channel than a rounded channel requires.  Still, 
rectangular and trapezoidal channels will not fully close when the membrane is being 
pushed down due to the corners of the walls.  Channels with a rounded cross section 
above a control valve close completely because as the pressure is applied, the force 
transfers to the membrane from the edges to the center, resulting in a complete closure.  
Figure 1.4 demonstrates the difference between pushing up (b) and pushing down (a) 
similar as that suggested by Unger et al. [25] in 2000.  Also, we can see the difference of 
the contour of the PDMS membrane as pressure is applied to a rectangular cross section 
(a) and a rounded cross section (b). 
 
 
 
9 
 
 
Figure 1.4 Diagraph of valve closing for rectangular and rounded channels. The dotted 
lines show the contour of the PDMS membrane as pressure is increased.  
Source: [(Unger et al. 2000)]  
 
1.4.2     Pneumatic mixer   
 To realize the full potential of micro systems enabling a full LOC in 
microfluidics, some obstacles must be overcome.  In micro systems, due to the small 
channel dimensions, reagents observe low Reynolds numbers.  Laminar flow occurs at 
low Reynolds numbers. In laminar flow, mixing of fluids is mainly done by diffusion, 
which is good for our study, however mixing can be very slow.  To improve the mixing 
time of reagents, sequential control of pneumatic valves can induce flow.  Such flow was 
first studied by Chou, Unger and Quake in 2001 as a microfabricated rotary pump.[26]  
By operating valves in series of a closed loop, the valves can function as a peristaltic 
pump.  A peristaltic pump, or roller pump, is a positive displacement pump that pushes 
fluids through flexible tubing as rollers apply pressure to the fluids and rotate, thus 
moving the fluid in the direction of the rollers rotation.  To realize this on a micro system 
device, at least three pneumatic valves are placed in series and operated sequentially, thus 
creating directional flow.  Figure 1.5 shows a three-step sequence of pneumatically 
operated peristaltic micro valves inducing fluidic flow. 
 
( a ) ( b )
 
 
10 
 
 
Figure 1.5 Sequence of valve operation of pneumatically operated peristaltic micro mixer 
inducing fluidic flow.   Source: [(Chou et al. 2001)]  
 
When a peristaltic pump operates in a loop, an active mixer is created.  Thus, if 
we design at least three pneumatic valves in series of a closed loop and operated 
sequentially.  We create flow and the interfaces between the fluids will be stretched 
which improves mixing.  To have well developed and steady flow it is important to have 
even spacing of the valves.  Figure 1.6 shows a schematic of working of a pneumatically 
operated peristaltic micro mixer with 60? valve separation.   
P r i o r  t o  a c t i v a t i n g  s e q u e n c e
S e q u e n c e  # 1
S e q u e n c e  # 2
S e q u e n c e  # 3
 
 
11 
 
 
Figure 1.6 Schematic of working of a pneumatically operated peristaltic micro mixer. 
Source: [(Chou et al. 2001)]  
 
 Along with valve degree separation, other design parameters are important to 
determine the working functions of the micromixer.  Figure 1.7 shows the outline of a 
rotary pump necessary for determining the working function of the pump, such as 
velocity.   
 
Figure 1.7 Schematic of rotary pump and appropriate variable labeling. 
Source: [(Chou et al. 2001)]  
V a l v e  3
V a l v e  2
F l o w  d i r e c t i o n
V a l v e  1
h
R
r
o
U
o
r
 
 
12 
 
  Equation 1.2 shows how the angular velocity can be calculated according to the 
designed rotary pump.  
 
 21o
o o
U rRr? ??????????
????
 (1.2) 
 
Equation 1.2 can be used to determine the angular velocity as Uo is the maximum 
velocity at the center of the channel, ro is half the width of the channel and R is the radius 
of the ring.  The mixing time in the microchannel closed loop is directly proportional to 
the linear velocity of the fluid inside the microchannel. 
 
1.5     Diffusion study on a chip   
Diffusion is the transport process in which the concentration gradient over 
distance of one solute affects the flux of a second solute.[27]  The diffusion coefficient, D 
is the constant at which a unit concentration gradient spreads out over an area per unit of 
time, standard unit m2/s.  Figure 1.8 illustrates how two solutions, initially separated (a), 
will over time diffuse into one another (c) and how each solutions? flux will change as the 
concentration changes (b) and (d). 
 
 
13 
 
 
Figure 1.8 Basic principles of diffusion.  Source: [(Callister 2003)] 
 
When concentration, location and time are all considered Fick?s second law of 
diffusion explains their relationship to one another. According to Fick the change in 
concentration c per change in time t is proportional to the diffusion coefficient D 
multiplied by the change in concentration c per change in length, x.   
 
 2
2ccDtx????
 (1.3) 
 
Understanding the nature of diffusion is a key advantage to the progress of multi-
reagent microfluidic systems.  With a known diffusion coefficient, minimal efforts are 
needed to determine proper concentration ratios and other parameters for applications 
such as sample analysis, medium preparation and material synthesis.  Much investigation 
has gone into segmented flow of reagents to determine diffusion coefficient.[28] 
C
o
n
c
e
n
t
r
a
t
i
o
n
 
P o s i t i o n ,  x  
R e a g e n t  1  
R e a g e n t  2  
P o s i t i o n ,  x  
R e a g e n t  1  
R e a g e n t  2  
P o s i t i o n ,  x  
R e a g e n t  1  
R e a g e n t  2  
( a )
( d )
( c )
J 2
J 1
C
o
n
c
e
n
t
r
a
t
i
o
n
 
P o s i t i o n ,  x  
R e a g e n t  1  
R e a g e n t  2  
( b )
 
 
14 
 
Segmented flow looks at how concentrations of solvent, sectioned by gas, leaves a film of 
solution within the channel walls.  This film diffuses into passing solvent and is 
explained by intra diffusion coefficient.  Intra diffusion is useful in studying how 
different concentrations of one solution diffuse into themselves, but is not as useful in the 
study of multiple liquid reagents.  With rectangular observation channels, films of solvent 
tend to collect at the walls and corners of the channel, thus altering the observed diffusion 
coefficient.  To circumvent this experience of films remaining on the walls, our device 
utilizes semicircle shaped walls created by a baking process after a master mold is 
fabricated.  This minimizes the effects of sharp edges within the testing chamber, which 
allow the formation of film deposits.  While there are many different experimental 
methods to determine diffusion coefficients, the diaphragm cell is one of the most basic 
in principle. A diaphragm cell can be used for diffusion coefficient measurements in 
which the device initially separates two reagents or two different concentrations.  The 
concentration gradient with respect to time is evaluated to calculate the diffusion 
coefficient.  While this method is theoretically simple, it can utilize hundreds of 
milliliters of reagents, it is time consuming, and requires certain amount of skills to 
perform the experiment properly to produce precise measurements.[29]  
We can rearrange Taylor dispersion, one of the principals of diffusion, to 
determine diffusion coefficients in an economical and timely manner.  Taylor dispersion 
is the chromatography method of observing the diffusion of one solution into another.  
This technique uses a pulse of dye solution injected into a slow stream of solvent within a 
narrow tube. The observation of the color moving along the tube as a symmetrical 
column of slowly increasing length allows one to determine the diffusion coefficient 
 
 
15 
 
given the concentration change, distance traveled and time lapse.  By transforming the 
long, undisturbed tube from the Taylor dispersion theory into one continuous circular 
tube, the study of diffusion of a length of tube can be related to the diffusion over time 
and rotations around the circular tube.  When two reagents are initially separated and 
allowed to diffuse into each other, the phenomenon relies on fluidic pressures and 
reagents? relative diffusion coefficient. Using microfluidic valves, a three step sequential 
operation will force the reagents to travel within the enclosed chamber in a hydrodynamic 
nature.  Upon fluidic interface of two reagents, unless the two are immiscible of each 
other, the reagents will diffuse into one another due to low interfacial tension between the 
two reagents.[28] By making the chamber circular, the turbulent flow, induced by forces 
on the reagent, is converted into laminar flow allowing the dispersion theory to take 
effect.  Microfluidic valves induce laminar flow within the compact device, enabling 
Taylor dispersion theory to be applied to a smaller testing area.  
 
    
Figure 1.9 Schematic of Taylor dispersion of long tube related to a closed tube chamber 
on a microfluidic system.  Source: left drawing[(Taylor 1954)]  
 
 
A B
 
 
16 
 
1.6     Scope of the study  
 The focus of this study is to design and evaluate a micro system device that is 
capable of being a tool to determine, optically, the diffusion coefficient of the two 
solutions.  The integrated microfluidic device will allow reagents to be handled, metered, 
mixed and optically evaluated.  Through this study, various designs are considered, 
evaluated and compared.  Review of previous researchers? studies and mathematical 
models are studied and reviewed. Details pertaining to data analysis and handling are 
presented.  Discussion of results and further study are presented. 
 This device is a novel approach to determining a diffusion coefficient using a 
micro system and has many advantages over conventional and other microfluidic 
systems.  The advantages include a very low sample amount (less than 10 picoliters, per 
reagent) and experiments are quick, generally less than 5 minutes.  The device is also 
reusable; washing and drying of the system allows for repeatable experiments. 
 
 
 
 
 
 
 
 
 
 
 
 
17 
 
 
 
Chapter 2 
Literature Review 
2.1    Introduction   
 As discussed previously, the definition for diffusion which will be utilized in this 
study is the transport process in which the concentration gradient over distance of one 
solute affects the flux of a second solute.[27]  Diffusion can also be described as the 
diffusion of one liquid into another, a solid into a liquid or the transfer of heat or 
electricity from one system to another.[29]  All four examples of transfer involve flow of 
materials from one or both systems to another creating gradients of concentration, heat or 
current.  The correlation between heat flow and diffusion was first presented by 
Berthollet in 1803 in his book entitled (roughly translated from French to English) 
Testing of Static Chemical.[30]  Berthollet describes the mechanism of dissolution of a 
salt crystal into water.  Fourier in his 1878 work on theory of heat flow presents that heat 
flow is a linear function of the temperature gradient.[31]  In 1855 Fick developed what is 
now known as his second law of diffusion, equation 1.3.[32]  The force responsible for 
diffusional flow is the gradient of concentration.  With Fick?s evaluation of Fourier?s 
treatment of heat conduction problem, he simply replaced the temperature gradient in 
Fourier?s equation by the concentration gradient,[29] thus allowing us to use equations 
for heat flow and relate them to concentration flow and diffusion.  In Crank?s second 
addition of The Mathematics of Diffusion[2] he explains  in detail how conversion of 
heat flow to diffusion solutions can be done given Fick?s second equation and the theory 
 
 
18 
 
of heat flow.  Looking at Fick?s second law, equation 1.3, we see the flux of the system is 
proportional to the concentration gradient multiplied by the diffusion coefficient.  The 
diffusion coefficient, D is the constant at which a unit concentration gradient spreads out 
over an area per unit of time, standard unit m2/s.  Since the time of Berthollet, Fourier and 
Fick all answers on diffusion have not been obtained as we are still interested in the 
movement of concentrations across systems.  This can be accomplished this 
quantitatively by comparing diffusion coefficients.  How to determine the diffusion 
coefficient must be known.  As technology and our knowledge of diffusion has advanced, 
so have conventional experimental methods.  In this chapter, conventional experimental 
methods will be discussed, compared with one another and micro system methods for 
determining diffusion coefficient.  
 
2.2 Conventional methods 
The effects of mixing due to thermal and mechanical disturbances are difficult to 
factor out when studying concentration flow due to diffusion.  However, in very narrow 
diffusion columns with capillaries, these unwanted effects, such as thermal and 
mechanical, are minimal. Methods of this nature were considered steady-state methods.  
Northrop and Anson[33] introduced the diaphragm cell method in 1929, in which 
a diluted solution and a concentrated solution are separated by a glass capillary, with the 
diluted solution on top in a diaphragm, usually maintained horizontally.  Diffusion was 
allowed to occur above and below and was assumed to be linear and by natural 
convection.  Many adjustments were possible, including adding stirrers and different 
materials for dividing capillary and cell containers. Diaphragm cell has the advantages of 
 
 
19 
 
simplicity, low cost, and, when used correctly, precision.  However, the experiments are 
usually time-consuming, approximately 24 hours for one experiment and reagent 
consuming, and the smallest volume mentioned was 33 mL per solution. Another 
disadvantage is that for calibration, the apparatus must be tested with a system of known 
diffusivity.  Figure 2.1 shows the simplest of diaphragm cells, a Northrop-Anson cell. 
 
 
Figure 2.1 Simple diaphragm cell, a Northrop-Anson cell.  Source: [(Tyrrell 1984)]  
 
Graham[34] introduced ?layer analysis? in 1861 for restricted diffusion analysis.   
For this method, a concentrated solution is introduced below a column of a less 
concentrated solution in a tall narrow container.  The solutions are allowed to diffuse 
completely, then the column is separated into even layers and analyzed separately. 
Another optical technique studies how a beam of light passes through a diffusion 
column and the resulting bend of the beam.  The bend angle is proportional to the 
refractive index gradient, and if the diffusion boundary is symmetrical can produce a 
time-dependent pattern.  Such pattern is parallel to the angle of the beam introduced to 
x
2
x
1
C
2
C
1
 
 
20 
 
the diffusion column and shows the interference in fringes.  These fringes are called 
Gouy fringes and the diffusion coefficient can be obtained from the pattern of the fringes 
produced. In 1879 Louis Georges Gouy first showed the broadened slit image consisting 
of bands, alternating from light to dark.[35], thus the fringes earned their name.  Another 
optical method is the study of Rayleigh fringes, which are similar to Gouy fringes in 
experimental setup and results.  However, Rayleigh fringes are produced by a double slit 
in the vertical direction of the light while Gouy has a single slit.  While precise optical 
studies of interdiffusion have been conducted, with both Gouy and Rayleigh 
interferometers both producing fringe patterns,[29] these systems can be costly and 
proper setup can be time consuming. 
Electrochemical methods for diffusion coefficient determination involve 
electroactive materials and electrode surface interaction.  Diffusion coefficients of 
electroactive species can be measured, given the electroactive species present in a 
solution contain a large excess of a backing electrolyte whose ions are not themselves 
electroactive.[29]  The rate of migration towards an electrode surface can be determined 
only by diffusion and is governed by Fick?s law.  An exact analysis in this method is 
difficult, and this method can only be used for electroactive materials and thus is not ideal 
for a baseline diffusion method to be used for many solution combinations. 
Nuclear magnetic resonance (NMR) spin-echo technique has advantages over 
other techniques because it is capable of measuring diffusion coefficients over several 
orders of magnitude and requires small samples. The basic apparatus necessary for pulsed 
NMR spectroscopy consists of a high-field magnet, pulse programmer, pulse transmitter, 
sample probe, receiver, amplifier and data recorded, along with magnetic field coils, 
 
 
21 
 
current generator and thermostat to control the sample?s temperature.[29]  The equipment 
needed for setup creates a disadvantage of this method as the equipment can be costly 
and space consuming.    
Diffusion coefficient values can be obtained from chromatography, also known as 
Taylor dispersion. In 1953 Taylor[36] explained that for a liquid in laminar flow there is 
a parabolic distribution of velocities over any cross-section normal to the tube axis.  
Therefore, the fluid at the center of the tube moves at twice the average fluid velocity. 
This method is performed when a dye solution is pulse injected into a slow stream of 
solvent confined within a narrow tube.  The color is found to move along the tube as a 
symmetrical column of slowly increasing length.  The patch of color is not distorted as 
the mass transport by the bulk flow of the liquid is supplemented by diffusion. The 
concentration distribution within the solute column as it passes can be used to determine 
the interdiffusion coefficient of a two-component system.  Figure 2.2 shows a schematic 
of a Taylor diffusion apparatus in which A is the injected dye and B is the solvent. 
 
 
Figure 2.2 Apparatus presented by Taylor used for observing dispersion in a tube.  
Source: [(Taylor 1954)] 
A B
 
 
22 
 
While this apparatus and analysis of this method is accurate and easily obtainable, 
again a large solvent volume size is needed and considerably longer experimental time as 
compared to our micro system device we are studying.  
 We chose to pursue an optical measurement for a conventional testing 
comparison. This method is noted to be central to almost all optical methods of studying 
diffusion and has been documented since the 1950s and 1960s.[29]  
 
2.3 Segmented flow microfluidic systems 
 An interesting article by Kreutzer et al.[28] in 2008 used flow segmentation to 
reduce unwanted axial dispersion within a microfluidic device.  By creating a second 
phase, separate reaction chambers of liquid, separated by gas, were used to study the 
diffusion flow. These pulse-broadening experiments utilized a PDMS device with fluidic 
cross-section channels 300 ?m wide by 300 ?m in height.  A tracer is injected into carrier 
liquid and gas flow is controlled by a piezoelectric bending disc.  Then the segmented 
solutions travel around a racetrack shaped microchannel that is 1.2 m or 1.77 m long. The 
need for the racetrack shaped microchannel is to allow large sampling as the 
concentration of the tracer in each segmented carrier liquid is measured by transmission 
spectroscopy near the outlet of the device using two polished fiber ends.[28]  Figure 2.3 
shows the device design and labeled components.   
 
 
23 
 
 
Figure 2.3 Sample dispersion study device using piezoelectric bending disc actuator and 
fiber optic detection.  Source: [(Kreutzer 2008)] 
 
 One advantage over other methods this device has is with the long microchannel 
to the detection point; a large sample size can be obtained and compared insuring ease in 
statistical sampling.  However, using piezoelectric bending disks and fiber optics for 
detection, this device is hardly a simple microfluidic device.  Also, with such a long 
microchannel to the detection point, this device requires constant pressures and bending 
of the disk along with a considerable sample size. 
 
2.4 Static and dynamic microfluidic systems 
 Culbertson et al.[3] in 2002 used a microfluidic platform to determine diffusion 
coefficient for electrochemical solution for a static and three dynamic methods. The three 
dynamic methods (stopped flow, varying applied potential and varying detection length) 
result in 11% larger diffusion coefficient values than static tests.  Devices were fabricated 
using soda-lime glass and standard photolithographic techniques with depths from 10 to 
15 ?m and half-depth ranging from 30 to 46 ?m.  The design of the microchannels was a 
 
I n l e t s  ( g a s ,  
t r a c e r ,  r e a g e n t )
F i b e r  
o p t i c s
G a s  o u t l e t
L i q u i d  o u t l e t
 
 
24 
 
simple T-structure where a buffer was introduced at the top of the T. Analyte is 
introduced on one side of the T and the waste is pushed by the buffer down the T out the 
other side.  Detection was down the length of the T-microchannel.  While this structure is 
simple in that only one layer of microchannels is needed and the volume size can be 
wasteful yet is within reason for the quickness of these testing methods.  On the other 
hand, the detection method for the dynamic tests uses a common laboratory camera while 
the static method uses more complex detection system with a laser.  All this adds the 
necessary equipment and complexity of this system. 
 
2.5 Refractive index gradient detected microfluidic systems 
 Costin[37] used a microchip based device and measured the refractive index 
gradient between adjacent laminar flows at different positions along a microfluidic 
channel to determine diffusion coefficient and molecular size using dual-beam mode of a 
micro-scale molecular mass sensor as the detector.  The device mobile phase inlet 
dimensions were 500 ?m wide by 200 ?m deep with analysis channel of 3.5 cm long 
while the sample inlet dimensions were 100 ?m wide by 200 ?m deep and 1 cm long.  
While this device was accurate, it required a great deal of reagents. Polyethylene glycol at 
various molecular weights and sugar solutions were evaluated using this method.  This 
system also requires the use of fiber optic splitter and fiber coupled laser diode along 
with positive sensitive detectors, taking the simple T-structure into a complicated analysis 
method. 
 
 
 
 
25 
 
2.6 Summary 
 Different methods for determining diffusion coefficient have been studied and 
evaluated for 100s of years.  As we advance in technology so does the validity of 
conventional methods.  With ?TAS and LOC, we can reduce the sample size needed as 
compared to the hundreds of milliliters we once needed for diaphragm cells, and we can 
now use 10 nL of reagent to determine diffusion coefficient. As compared to the 
microfluidic systems introduced here, we want to present a multilayer softlithography 
device that needs no additional equipment installed within the PDMS structure and a 
simple laboratory camera to capture the diffusion of two reagents within a single  reaction 
chamber of a total volume less than 25 nL. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
26 
 
 
 
Chapter 3 
Development of the Diffusion Chip 
3.1    Introduction   
The idea of measuring diffusion coefficient on a microfluidic platform is to 
optically observe the diffusion of two solutions into one another as related to time and 
calculate the appropriate observed diffusion coefficient.  With our basic design of two 
solutions initially separated by valves, we show the basis of diaphragm cell.  However, to 
observe diffusion like Taylor dispersion, we use pneumatic mixing valves to induce a 
directional flow of the two reagents into one another.  This flow allows us to see a clear, 
initial cup-and-cone relationship between the two solutions. This is similar to Taylor?s 
experiments in which a stream of tracer was easily seen within a steady solution.  With 
time, the cup and cone diminish and the intensity of both solutions stabilizes to show one 
final observed intensity, as a constant concentration of solutions within one another.  A 
cup and cone interfacing of the two reagents observe clear visibility of diffusion.  This 
interfacing is where the interdiffusion takes place.  From the tail of the cup and cone we 
can also determine the velocity of the reagent mixture within the chamber.  The following 
schematic in Figure 3.1 represents three stages of our proposed contained diffusion. Red 
and green colors represent two solutions that are optically distinguishable from one 
another. Figure (a) shows the two solutions initially separated, similar to a diaphragm 
cell.  Figure (b) is a step forward in time, as the two solutions start to flow about the 
reaction chamber in a counterclockwise manner.  The beginning of diffusion between the 
 
 
27 
 
two reagents is illustrated with the yellowish-orange color shown between the cup and 
cone and tail of each reagent. Figure (c) is a further step in time, if the solutions do not 
diffuse well with one another, then a clear cup and cone maybe be seen circling the full 
reaction chamber. 
 
 
Figure 3.1 Cup and cone progression model. 
 
3.2    Device design   
 
The device is constructed out of transparent and flexible PDMS and is fabricated 
through a soft lithography technique.  To design our device we used AutoCAD (Auto 
Desk) to model the structure in two dimensions.  The basis of the design and three design 
versions will now be discussed.   
 
All of the designs consist of two layers; a control layer in which the microvalves 
are constructed and a fluidic layer, top layer, in which the reaction chambers are 
positioned.  Three separate circular fluidic systems were used consisting of two reagent in 
ports, two out ports, and a wash in and out system.  The initial idea was to allow for all 
three separate reagent chambers to be examined simultaneously, given an appropriate 
( a ) ( b ) ( c )
 
 
28 
 
recording setup.  However, our current experimental setup of our microscope and camera 
limit the clear visibility of diffusion for all three separate reaction chambers at once.  
Therefore, at this time we cannot simultaneously determine three separate diffusion 
coefficients.  All three reaction chambers use the same shut off and mixing value system, 
all within series of each other.  The mixing value system consist of three pneumatic 
valves located below the fluidic layer.  Each valve is 30? separated from its neighbor 
valve.  Previous colleges have studied at length the effects of varying valve dimensions, 
angle of separation, number of valves and operational frequency.  From their studies we 
choose to use our valves for this study as follows. Various shut off control valves are 
located throughout the structure of the device to control the metering and direction of the 
fluidic reagent flow. Control channel inlets are 100 ?m in width and decrease to 30 or 50 
?m, depending on design version, near the testing system to prevent pressure interface on 
the circular diffusion chamber.  Such interface can cause decreases in the flow of the 
fluidic layer and therefore is undesirable.  These unwanted interfaces can be caused by 
large control channel widths crossing under the fluidic layer being operated at other 
locations and interfering with the flow of the fluidic channel it crosses under. Another 
way an unwanted interface can occur is by an increase of control valve pressure greater 
than necessary to shut the valves.  The differences between the three designs are based 
mainly on the size of the width of the reaction chamber and the control channels. 
 Mixing control valves are used to induce flow of the two reagents and allow the 
two reagents to diffuse into one another.  For clear visibility of diffusion, a cup and cone 
of the two reagents will show the two reagents as they diffuse into the each other in the 
direction of the flow.  When testing various designs for this project, it was important to 
 
 
29 
 
clearly see the cup and cone of the two reagents.  As the design versions? reaction 
chamber widths changed, so did the corresponding mixing and shut off control valve 
dimensions. Figure 3.2 shows the basis of the three designs and a close up of the reaction 
chamber. On the left hand side, we see the reaction chambers of the fluidic layer all 
colored in blue.  The left side of each reaction chamber has three inlets: reagent 1, water 
for washing and air for drying and one outlet, and an outlet for reagent 1 for loading.  On 
the right side of the reaction chamber, there is one inlet for reagent 2 loading and two 
outlets, one for washing and drying and one outlet for reagent 2 for loading. The three 
mixing valves are on the control layer and colored green.  There are bends in mixers 2 
and 3 channels before the first chamber and in between the following chambers. These 
bends allow for the same length of channel and thus, volume, for all three mixers to 
travel.  This insures proper response time and even pressure for the three mixers.  The 
remaining shut off values are colored in red.  SV1, SV2 and C are for valves responsible 
for metering and sectioning the solutions before each experiment. As they are a pre-test 
tool, the even channel lengths are not necessary.  The remaining valves are all involved 
with the washing and drying of the chambers. 
 
 
 
30 
 
 
Figure 3.2 Basic design with detail of a reaction chamber and valve close/open key. 
 
3.2.1    Diffusion chip design version I   
 The control widths start at 100 ?m and taper down to 50 ?m.  The reaction 
chamber has an inner and outer radius of 1000 ?m and 1200 ?m, respectively.  This 
creates a 200 ?m testing width for a clear visual  of cup and cone.  Valves were created to 
be 300 ?m long by 200 ?m wide.   
 
O p e n  
v a l v e
1  m m
C l o s e  
v a l v e
M1 M2 M3 S V - 1 C S V - 2
S V 1 - A S V 1 - B S V 1 - C S V 2 - C S V 2 - B S V 2 - A
R 1 A - I
WA
R 1 B - I
R 1 C - I
R 1 A - O
WB
R 1 B - O
WC
R 1 C - O
R 2 C - O
W C - O
R 2 C - I
R 2 B - O
W B - O
R 2 A - O
R 2 B - I
R 2 A - I
W A - O
A
u
b
u
r
n
N
a
n
o
f
l
u
i
d
i
c
s
S V - A ir
A ir B
A ir A
A ir C
A
u
b
u
r
n
N
a
n
o
f
l
u
i
d
i
c
s
S V - W
S V O - 2
S V O - 1
1  m m
1  c m
W a s h  
O u t
W a s h  
I n
R e a g e n t  1  I n l e t
R e a g e n t  2  I n l e t
S h u t  o f f  
v a l v e s
M i x e r s
 
 
31 
 
 
Figure 3.3 Chip design version I.  
 
The first experiments, preformed with this design, experienced problems with 
collapsing valves and unwanted air developing within the chamber due to great pressures 
needed to close the large control valves. Also, problems presented by simply trying to 
contain the test solutions within the reaction chamber presented pressure difficulties. All 
of these things are undesirable and needed vast testing parameter improvement. 
 
 Due to channel collapsing and control layer interference, we tried to level 
out the internal pressure of the control valves and fluidic reagent by using pressures of 15 
psi and 1.02 psi, respectively. Within the 2 Hz mixing sequence, we could observe cup 
5 0 0  ? m
 
 
32 
 
and cone of the two reagents after 4 seconds, as desired.  While we want to decrease the 
experimental test time by using the mixing valves to induce movement of the two 
reagents, we also need to observe the cup and cone clearly for several frames to 
determine the velocity.  However, any collapse of a mixer valve is evident that the 
internal pressure within the reaction chamber is still too great for the mixing valve.   
 
 This uneven internal pressure between the two layers makes the response time of 
each mixing valve subject to unreliability due to possible inconsistency.  Figure 3.4 is the 
data of an experiment using design I microfluidic device corresponding to 4 seconds from 
the releasing of the center valve according to the intensity/concentration reading at a ROI 
within the chamber valve.  We analyzed the information after the center valve release, as 
the concentration fluctuation with time evaluation is the focus of our study to determine 
diffusion coefficient.  However, the fluctuation presented here in this data is not ideal, 
compared to what we expected from the peak-to-peak relationships.  We expected 
exponentially decreasing peaks with time as the valleys exponentially increase with time 
and that both time steps are similar to each other.   
 
 
 
33 
 
 
Figure 3.4 Concentration versus time data corresponding to the ROI within reaction 
chamber. The green line indicates the release of the center valve, thus the start of the 
experiment and the blue line indicates 4 seconds later. 
 
 With the problems of the reagent chamber ceiling collapsing due to the large, 
unsupported sections of chamber, we determined it would be appropriate to decrease the 
reaction chamber width and thus decrease the needed control valve dimensions.   
 
3.2.2    Diffusion chip design version II 
 The control widths were unchanged from version I.  The reaction chamber has an 
inner and outer radius of 1140 ?m and 1200 ?m, respectively.  This creates a 60 ?m 
testing width for decrease valve sizes.  Valves were 120 ?m by 120 ?m.   
 
80 
100 
120 
140 
160 
180 
0 20 40 60 80 100 
In
ten
sity 
(A
.U.)
 
Time (sec) 
 
 
34 
 
 
Figure 3.5 Chip design version II.  
 
 For design version II changes to the reaction chamber width and valve sizes were 
made to fix the problems observed in design version I with channel collapsing. However, 
in this design it was hard to find a suitable operating pressure combination.  Figure 3.6 
shows that the design change to version II does remove the problem of channel 
collapsing.  The top mixer valve is activated in Figure 3.6; that is why it appears to have a 
darker channel outline than the other mixer valves.  In addition, the reagent inlet and 
outlet shut off valves are activated in the middle left and right of the image.  Since the 
shut off valves are filled with buffer (water) and the mixer valves are empty (nitrogen gas 
if activated) this explains the color and activated valve outline difference between the two 
5 0 0  ? m
 
 
35 
 
types of valves used in the micro system device.  While improvements from problems 
were made from design version I to design version II, other problems were present with 
this design. 
 
 
Figure 3.6 Device fabricated of design version II. No evidence of channel collapsing but 
shut off valves for reagent metering interferes with reagent flow. 
 
 At the points where both reagent control shut off valve channels cross the reaction 
chamber there is major pressure interference.  To level the internal pressures prior to 
activating the mixer sequence the following pressures were used at 1.0 Hz, 20 psi, 15 psi, 
and 3.52 psi for the control valves, mixer valves and fluidic reagent loading, respectively.  
On the left, this causes the flow in the reaction chamber to be limited by the small amount 
of blue dye above the channel.  This is a major disadvantage and must be prevented.  
 In addition, with this design version a clear cup and cone could not be seen with 
our given camera equipment because the experimental flow was so much faster than 
3 0 0  ? m
 
 
36 
 
design version I.  Thus, preventing us from determining the velocity in that manner.   As 
mentioned with design version II the needed pressure for closing the control valves has 
increased greatly from design version I.  Figure 3.7 shows a center valve requiring 28 psi 
pressure to shut, with the reaction chamber filled with air from chip fabrication. 
 
 
Figure 3.7 Device fabricated of design version II.  Center valve with 28 psi pressure 
shutting valve with reaction chamber filled with air from chip fabrication. 
 
  From Figure 3.7 we can see that the valve is not fully closed.  With such a large 
pressure for the system being applied we expect that the valve would be fully closed.  
With our experimental equipment system, 30 psi is the maximum pressure setting 
obtainable.  By working at pressures of 20 psi and greater puts great, unneeded stress on 
the system.  This makes the response, consistency, and reliability of each valve a subject 
of concern.  With the problems of the reagent chamber interference from high pressures 
of control shut off valve channels and decrease in visibility of cup and cone of reagents, 
1 0 0  ? m
 
 
37 
 
we determined it would be appropriate to increase the reaction chamber width, decrease 
the control channel widths and increase the control valve dimensions to correspond with 
the reaction chamber width.  We improved the micro system from the previous design; 
however, our disadvantages led us to redesign once again. 
 
3.2.3    Diffusion chip design version III 
All the control widths start at 100 ?m and taper down to 30 ?m to prevent 
pressure interface on the circular diffusion chamber.  The reaction chamber has an inner 
and outer radius of 1100 ?m and 1200 ?m, respectively.   
 
 
Figure 3.8 Chip design version III.  
5 0 0  ? m
 
 
38 
 
 For design version III, changes to the reaction chamber width and valve sizes 
were made to fix the problems observed in design version II with pressure interference 
and cup and cone visibility.  Shut off valves could be closed at appropriate pressures, 
such as 10 to 15 psi, and no collapsing allow for a usable, working micro system device.  
Cup and cone could be seen clearly and velocity could be easily determined by frame-by-
frame movement analysis.  Control valve channel interference with the reaction chamber 
was diminished due to the appropriately sized valves and decrease in control channel 
widths.  Figure 3.11 shows a fabricated chip of design version III of a good chip.  We can 
see the cup and cone of the two reagents and no control valve channel interference.  The 
top mixer valve is activated in Figure 3.9 explaining the appearance difference in the 
valves and again the reagent inlet.  Outlet shut off valves are activated in the middle left 
and right of the image.  Like the device in Figure 3.7, the device in Figure 3.9 has buffer 
(water) in the shut off valves, and mixer valves are empty (nitrogen gas if activated), 
explaining appearance difference between the two types of valves.   
 
 
Figure 3.9 A fabricated chip of design version III of a good chip. 
3 0 0  ? m
 
 
39 
 
 Also, all of the valves are working properly. The testing parameters for the device 
in Figure 3.9 were 5 Hz mixing sequence and the following pressures: 10 psi, 15 psi, and 
5 psi for the control valves, mixing valves and fluidic reagent loading, respectively.  
Similarly, pressure combinations were tried for version I and version II, but did not allow 
for the valves to operate properly given the chamber width and valve dimensions.   
 Even with the great improvements made to design version III, other problems 
presented themselves.  A problem of dye traveling inconsistently from the center valve 
once pressure was released was undesirable.  As we want to control the fluid flow by the 
mixer valves this is a problem.  This problem was inconsistent and therefore made our 
current testing parameters unreliable.  Figure 3.10 shows a fabricated chip with the center 
valve not fully releasing its pressure after deactivation, resulting in dye solution traveling 
to both sides of the reaction chamber.  The testing parameters for the device in Figure 
3.10 was 1 Hz mixing sequence and the following pressures: 8 psi, 10 psi, and 2.04 psi 
for the control valves, mixing valves and fluidic reagent loading, respectively.  The top 
mixer valve is activated in Figure 3.19, explaining the appearance difference in the 
valves, and again the reagent inlet and outlet shut off valves are activated in the middle 
left and right of the image.  Like the device in Figure 3.9, the device in Figure 3.10 has 
buffer (water) in the shut off valves and mixer valves are empty (nitrogen gas if 
activated), explaining appearance difference between the two types of valves.   
 
 
 
40 
 
 
Figure 3.10 Device fabricated of design version III. Center valve pressure not 
disengaging properly affecting fluid flow drastically. 50.922 seconds after releasing the 
center valve. 
 
 Later it was determined that the control layer membrane was too thick.  By 
increasing the spin speed of applying the PDMS to the control wafer from 2400 rpm to 
2600 rpm, this problem was removed and not seen again.  This shows the importance of 
proper selection of chip fabrication process times and speeds. 
Chamber heights vary depending on master mold fabrication.  Typically 10.8 ?m 
maximum height of fluidic channel was observed. The resulting volume of reagents in a 
single chamber, excluding the center valve volume, is 7.53 nL.  While for Design II to 
achieve a 5 nL volume of each reagent within the reaction chamber, a height of 11.72 ?m 
would be needed or a height of 14.06 ?m could produce 6 nL per reagent. The mold 
fabricated for design version II had a height of 11.32 ?m, yielding less than 5 nL per 
reagent within the reaction chamber.  Version I mold, with a height of 15 ?m, would 
3 0 0  ? m
 
 
41 
 
produce volumes of 9.76 nL per reagent, while a height of 7.68 ?m would produce a 
reagent volume of 5 nL each.  For our purposes we wanted to stay below 10 nL for 
convincing of the device for future endeavors. Figure 3.11 shows the device design 
progression from one version to another of a single reaction chamber.   
 
 
Figure 3.11 Chip design progression ? reaction chamber detail view, version I (a), version 
II (b), and version III (c). 
 
In a side-by-side comparison, we can see the reaction chamber width change, as 
well as the mixing valve dimensions.  One minor change from design I to design II was 
the channel connection to the wash out shut off valve to the right of the chamber in (a).  
In design I, the control channel goes above the fluidic channel, while in the two following 
designs the channel goes below.  This was done to reduce the number of fluidic channels 
that each wash out shut off valve crossed on the way to its outlet from 8 to 7.  This allows 
the reagent to be loaded with less backpressure due to any control layer pressure 
interactions.  
 
( a ) ( c )( b )
5 0 0  ? m5 0 0  ? m 5 0 0  ? m
 
 
42 
 
3.3    Mold Fabrication   
Micro fluidic chips are produced by employing soft lithography method[38].  Molds 
are fabricated in Broun Hall in the Alabama Microelectronics Science and Technology 
Center (AMSTC).  The center requires a safety test for permission to use the laboratory 
space and equipment.  The center is clean room requiring proper clean room clothing and 
safety protection.  Before entering the clean room for fabrication, the AutoCad design is 
sent off to CAD/Art Services, Inc. for photo printing of the design at a 20,000 dpi (dots 
per inch).  This resolution is capable of printing a design accurate down to 10 ?m.  The 
smallest feature size on any of the three designs is 15 ?m.  Designs are printed on a 
transparent thin sheet of plastic and delivered sealed to prevent dust exposure.  
Figure 3.12 illustrates the mold fabrication process for both a fluidic and a control 
layer.  First start with clean 4? silicon wafers with 100 ? titanium coating.  Next, spin 
coat photoresist onto both wafers.  Then, expose that mask to the wafer using UV 
exposure.  Develop away excess photoresist, and the pattern remains.   
 
 
 
43 
 
 
Figure 3.12 Schematic of mold fabrication process.  
 
    Full details on the mold fabrication process now follow.  Before starting 
fabrication, once in the clean room, the mask is removed from its container and cut to 
shape.  Then the mask is taped on four corners to a clean 4 inch by 4 inch glass plate and 
set aside. To begin, photoresist AZ P4620 (AZ Electronic Materials) is spun coated onto 
a 4 inch silicon wafer with 100 ? titanium coating followed by a 90 second soft bake at 
F l u i d i c  L a y e r C o n t r o l  L a y e r
4 "  S i l i c o n  w a f e r 4 "  S i l i c o n  w a f e r
S p i n  c o a t i n g  o f  p h o t o r e s i s t S p i n  c o a t i n g  o f  p h o t o r e s i s t
U V  e x p o s u r e  p a t t e r n  f r o m  f l u i d i c  m a s k U V  e x p o s e  p a t t e r n  f r o m  c o n t r o l  m a s k
D e v e l o p  a w a y  e x c e s s  p h o t o r e s i s t  t o  
r e v e a l  m a s t e r  f l u i d i c  m o l d
D e v e l o p  a w a y  e x c e s s  p h o t o r e s i s t  t o  
r e v e a l  m a s t e r  c o n t r o l  m o l d
 
 
44 
 
110 ?C.  The titanium coating improves the adhesion of photoresist to the wafer surface 
and the lifetime of the mold.  The spin speed settings determine the height of the 
structures, with slower speed resulting in higher channels.  These molds were produced at 
a setting of 500 rpm for 5 seconds at 100 rpm/second acceleration followed by 
immediately by 1300 rpm for 35 seconds at 300 rpm/second acceleration.  Next the mask 
and glass plate are mounted into the UV exposure machine (Karl Suss MA6/BA6). The 
structure on the mask is then exposed onto the wafer by hard UV exposure. The machine 
has an intensity of 19 mW/cm2.  To copy the pattern onto the wafer, the transparent mask 
is exposed to a certain amount of UV light.  The part of the mask that does not have 
anything printed on it will be excess photoresist and removed later.  The amount of UV 
light or dose is controlled by the exposure time and light intensity.  The dose can be 
calculated as follows[39]: 
 
 22( / ) ( / ) ( s e c )d o s e m J c m i n t e n s i t y m W c m t i m e?? (3.1) 
  
As the equipment in the AMSTC clean room has an intensity of 19 mW/cm2, the 
time can be calculated according the dose wanted.  Dose sizes should be different 
according to the thickness of the desired structure; a thicker structure requires a greater 
dose. With an intensity of 19 mW/cm2 and a desired dose of 600 mJ/cm2, a 31 second 
exposure time at hard contact is appropriate.   
 The exposed photoresist is developed away by placing the wafer in a plastic bin 
and agitating it back and forth within 200 mL of AZ 400 K 1:4 diluted developer (AZ 
Electronic Materials) for 2-4 minutes.  Since AZ P4620 is red, as the photoresist is being 
 
 
45 
 
developed, the liquid will turn pink.  After developing, the wafer is then rinsed 3-5 times 
with deionized water and air-pressure dried.  Next, the wafer is inspected under the 
microscope to insure the photoresist has been fully removed.  The final step in the control 
mold making is checking the height of the structure.  Using a refileameter (Tencor) 
measure the structure at numerous locations to insure that the structure is the same height 
all around.  Once this is done, the control layer is complete. After measuring the fluidic 
layer, a final post-bake at 130 ?C is preformed for 3 minutes to round the channels.  The 
height is measured again with the refileameter and the mold is complete.  
Control mold height was observed to be on average 10.60 ?m and after a post 
baking, the fluidic mold channels were 10.8 ?m on average.    
 
3.4    Chip Fabrication   
Since the control layer?s ceiling will need to be raised as air pressure is applied to 
the channel in the control layer, the control layer needs to be more elastic than the fluidic 
layer.  Thus the fluidic layer should have a 1:10 PDMS ratio and the control layer shall 
have a 1:20 PDMS mixing ratio.  This allows for less cross-linking in the control layer 
making it more elastic. 
Table 3.1 and Figure 3.12 illustrate the chip fabrication process starting with the 
two separate layers, then with the completed chip.  First, a mold is fabricated as discussed 
in section 3.3 of this thesis.  Next, PDMS is poured and spun to the appropriate wafers.  
Then, the PDMS is cured, exposing the microchannels within the PDMS.  The inlet holes 
for the fluidic layer are punched and the fluidic layer is aligned onto the control layer.  
After proper curing, the two layers are removed from the control mold and the control 
 
 
46 
 
layer inlets are punched. Lastly, the two layers are placed onto a glass substrate covered 
with cured PDMS and the chip is complete minus a final, long curing step.  
 
Table 3.1 Soft lithography chip making procedures. 
Fluidic Layer Mold  Control Layer Mold  
Prepare RTV 615 mixture  
A : B = 10 : 1  
Prepare RTV 615 mixture  
A : B = 20 : 1  
Vacuumize RTV 615 Mixtures (2 hour)  
Covering (A:B=15g:1.5g, 1.5 hour) and Surface Treatment with CTMS* Vapor 
(10 min)  
Make Aluminum Foil Mold  Spin Coating (2600 rpm, 1 min)  
Pour RTV 615 Mixture onto 
Mold  Leveling (15~30 min)  
Keep in Oven at 80? (60 min)  Keep in Oven at 80? (45 min)  
Natural Cooling (10~15 min)  Natural Cooling (10~15 min)  
Cut, Peel, Reverse and Punch 
Holes   
Fluidic Layer is Aligned with Control Layer  
Keep in Oven at 80? (1 hour)  
Cut, Peel, Reverse and Punch Holes  
Seal Chip with Glass Slide and Keep in Oven at 80? (18 hour)  
* CTMS, Chlorotrymethylsilate 
 
 
47 
 
 
Figure 3.12 Schematic of chip fabrication process.  
M a s t e r  f l u i d i c  m o l d M a s t e r  c o n t r o l  m o l d
F l u i d i c  L a y e r C o n t r o l  L a y e r
P D M S  t h i c k  l a y e r  f r a m e d  o n t o  m o l d
P D M S  t h i n  l a y e r  s p u n  o n t o  c o n t r o l  
m o l d
F l u i d i c  p a t t e r n  c u r e d  i n t o  P D M S C o n t r o l  p a t t e r n  c u r e d  i n t o  t h e  P D M S
P u n c h  i n l e t  h o l e s  f o r  f l u i d i c  l a y e r
A l i g n i n g  t w o  l a y e r s  t o g e t h e r
P u n c h  i n l e t  h o l e s  f o r  c o n t r o l  l a y e r
C o m p l e t e  c h i p  o n  g l a s s  s l i d e
 
 
48 
 
The first step in making a microfluidic chip is preparing 2 mixtures of PDMS that 
will be used for the different layers.  For the control layer, a 1 to 20 ratio (1 part RTV615 
B-cross linking agent and 20 parts RTV615 A- silicone potting compound) of PDMS is 
needed.  It is best to measure out component B first since in both mixtures will have a 
smaller amount of component B than A.  Depending on the desired thickness of the 
control layer and adhering layer of the glass substrate (used later) a full 20 grams of A 
and 1 gram of B might not be needed.  Usually 16 grams of component A and 0.8 gram 
of component B will work.   
For the fluidic layer, the top layer where the fluid is introduced into the chip, a 
desired thickness is 5 mm.  Usually a 45 gram A and 4.5 gram B will be sufficient; the 
amount depends on how large the frame of aluminum is created around the system. 
 Measure out the B component into a small 3? plastic weighing dish and then zero 
the scale and add the A component right on top of the B component.  Use a disposable 
plastic pipette to mix the solution for 5 full minutes.  To remove any remaining PDMS 
from previous fabrication, pour a small amount, about 8 grams, of the 1:10 mixture onto 
each wafer, cover and place in the oven set at 80?C to cure.  Place the remaining PDMS 
mixtures in vacuum to remove bubbles you introduced.  Cure the PDMS on the wafers 
for at least 45 minutes.  However, we generally will cure for 60 min and vacuum for 90 
min or 90 min and 120 min, respectively. This cleaning layer of PDMS on each wafer 
prepares the wafer for use by removing any remaining PDMS or particles from previous 
fabrication use.  Wafers, if keep properly, may be used for years.  This insures 
consistency in device structure for fabrication.  Cleaning layers maybe applied and cured 
after fabrication to decrease the next fabrication prep time needed.  
 
 
49 
 
 After cure time is up, remove wafers and let cool for a few minutes (2-3).  
Remove PDMS carefully and place wafers in clean petri dishes.  Chlorotrymethylsilate 
(CTMS) treatment is optional.  However, it improves the lifetime of the photoresist on 
your wafers and prepares the surface for the PDMS.   
Under a fume hood we use a large flat beaker (see images) with a small 40 ml 
beaker sitting inside.  Tear approximately a 12 x 12 inch square of aluminum foil and 
fold it over the large beaker securely. Remove foil and place aside for the moment.  With 
CTMS, carefully remove cap and pour about 2-5 mL into the small beaker.  Make sure 
this is all done under the fume hood as the liquid is extremely flammable and vapors are 
dangerous and can cause cancer.  Put the small beaker in the middle of the large beaker.  
Next using the wafer tweezers, transport the wafer from its Petri dish to the large beaker.  
Next, position the wafers so that one part is resting on the small beaker (see picture).  Re-
cover the large beaker using the aluminum foil shaped earlier. Let wafers stay in CTMS 
treatment for 10 minutes.  Once time is up, remove aluminum foil and wafers, and let 
remaining CTMS evaporate under the hood. 
 Once vacuum is done, turn the vacuum off.  Turn on the spinner, coat the inside 
of the spinner with aluminum foil for easy clean up and turn on vacuum and nitrogen for 
spinner.  Remove the 1:20 mixture; remove any bubbles and particles (usually around the 
edges) with a disposable plastic pipette.  Place control wafer in center of spinner, apply 
vacuum, and do a test spin run to insure it is properly centered.  Using the nitrogen gas 
valve, spray off any possible dust from the wafer.  Currently I am using a program with 2 
steps: step 1, 60 seconds, 2600 rpm, 256 rpm/s acceleration; step 2, 20 seconds, 200 rpm, 
256 rpm/s acceleration.  The first step dictates the thickness of the PDMS layer, while the 
 
 
50 
 
second step is primarily used to slow down the wafer.  Start pouring the 1:20 PDMS 
mixture into the spinner bowl and then onto the wafer itself.  Start pouring PDMS away 
from the chip so that you leave less possibility for bubbles to form.  Pour most of the 
mixture onto wafer and then go back to the spinner bowl, just like the way you started.  
Next using a disposable plastic pipette, remove any bubbles and possible dust from the 
wafer.  Once that is complete, close the lid and press ?Run Stop? button.  Once spinning is 
complete, open lid, press ?Vacuum? and place wafer back into its Petri dish.  Place wafer 
on flat surface (we have levels to show the appropriate places) and allow wafer to level 
for 15 to 30 minutes.  Coating the glass slide with PDMS is optional and steps are as 
follows: Once you place wafer in leveling area, clean a glass slide using the 70% ethanol 
push bottle (30% water) and the lab wipes.  Then place the glass slide in the spinner and 
repeat the same steps for the glass slide.  However, the glass slide can level until the 
wafer is done.  Turn off the spinner and vacuum when done. 
 While the glass slide and wafer are leveling, prepare the fluidic layer for PDMS.  
Using aluminum foil, tear off about a 10? x 10? sheet, then place the fluidic wafer in the 
middle.  Fold the edges of the aluminum foil up to the wafer design leaving at least a half 
a centimeter between the aluminum walls and the outer edge of the design.  The 
aluminum foil walls should be at least one centimeter high.  Using nitrogen, spray off any 
possible dust from the aluminum foil and wafer structure and turn off nitrogen when 
done.  Press down carefully and make sure aluminum is secure to the wafer.  Remove the 
1:10 PDMS mixture from the vacuum and remove bubbles and dust using a disposable 
plastic pipette.  Slowly pour the PDMS into the aluminum frame.  Again, remove any 
possible dust and bubbles afterwards.  Place petri lid back on when done.  Now put both 
 
 
51 
 
wafers and glass slide into the oven at 80?C once the leveling time for control layer has 
completed.   
After 45 minutes remove the control layer wafer and glass slide and after 1 hour 
from original introduction, remove the fluidic layer wafer. Let the fluidic wafer cool for 
at least 5 minutes before continuing. 
 After letting the fluidic layer cool, put back on gloves and get out a ruler and the 
Exacto knife.  Clean off the ruler and Exacto knife blade with ethanol solution push bottle 
and the lab wipes.  Next, try to bend back parts of the aluminum structure that did not 
come in contact with PDMS to make the aluminum frame level with the PDMS.  You 
next want to cut the PDMS structure out into the shape of a rectangle outside of the 
rectangular parameter photoresist pattern.  Place a ruler across the PDMS and cut with 
the Exacto knife at least 0.5 cm away from the outline of the structure.  Try to make 
smooth cuts and do not try to cut all the way down to the wafer in the first cut, make 
several passes progressing in depth each time.  Do this for all four sides.  Once all sides 
are cut, carefully pull back the excess PDMS and remove the aluminum foil.  Then 
slowly peel off the fluidic PDMS layer from the wafer.  Place PDMS structure with the 
pattern up onto a cleaned glass slide.  Throw away the excess aluminum foil and PDMS. 
 Next punch inlet holes using a microscope.  The microscope we utilize is a Nikon 
SMZ 800 microscope (Model C-DS).  Press the hole punch in a indicated hole area.  
Then carefully, with the hole punch still in, remove the fluidic layer from the glass slide 
and place a finger behind the hole punch and press through.  Remove the excess PDMS 
and slowly remove the hole punch. Place PDMS structure back on glass slide, clean the 
hole puncher and repeat until done.  Once all holes are punched, clean the surface of the 
 
 
52 
 
PDMS with tape.  Cover the surface with a layer of tape and remove.  Do this until it is 
free of dust and particles. 
 Next, align the control layer with the fluidic layer, the pattern side of the fluidic 
layer should go downward.  Use the cross-hairs as aligning indicators; all plus signs on 
the control layer should align with the fluidic plus signs. Take your time and get it right.  
It takes practice to get this right and time needed can be reduced with practice. Once 
aligning is complete, clean the surface of the control layer with tape like before. Once 
done place petri dish lid back on and place in oven for 60 min, depending on chip design.   
 After the required curing time has passed, remove chip and let cool for 10 
minutes.  Use scapula knife, cleaned with ethanol solution, to cut along the edges of the 
chip.  Once that is done, slowly lift chip starting at one side to remove from wafer.   Next, 
place on clean glass slide and punch any remaining holes like before.  Once all holes are 
punched, place chip with pattern down on the spun glass slide from earlier.  It is 
important to inspect the device for any collapsing channels prior to the final curing step. 
Collapses noticed was during chip fabrication usually are due to the large surface area of 
the inlets. All of these collapses can be fixed easily by introducing small amounts of air 
into the device through the fluidic inlets to equalize the internal pressure between the two 
layers. Air is introduced through the inlet of the channels using a syringe, Tygon tubing 
and tubing-to-device needle. Make sure there is no air bubbles between the two layers.  
Place chip back into oven at 80? for at least 18 hours.  
 
 
 
 
 
53 
 
3.5    Experimental setup and operation 
The chip is operated using gas pressure to control the valves, and fluid movement 
is induced by pressure delivered from nitrogen gas.  Pressure for each channel is 
delivered from the nitrogen tank to a pressure controller (Fluidigm) to a solenoid valve 
(The Lee Co., 12 VDC, 40 psig) to the chip, through a series of Tygon tubing.  Figure 
3.13 shows a completed microfluidic chip made from design III, filled with food dye for 
visualization.  It is connected to Tygon tubing and includes a quarter for size comparison.  
Like Figure 3.2, the control layer is indicated with red, mixer channels with green and 
fluidic channels with blue food dye. 
 
 
Figure 3.13 Microfluidic chip made of design III filled with food dye for visualization of 
structure, connected to Tygon tubing and includes a quarter for size comparison.   
 
 
 
54 
 
Control valve tubes are filled with de-ionized water as a buffer solution and is 
pumped into the channel at a low pressure, approximately 2-3 psi. This is not done to the 
mixer valves; to prevent lag time of induced gas pressure to activate and deactivate the 
mixing valves, these tubes remain free of buffer (water) solution.  All miniports are 
connected to a BOB3 operating system, which is then connected to a computer operated 
by LabVIEW software.  Figure 3.14 shows a schematic of our experimental equipment 
setup. 
 
 
Figure 3.14 Schematic of experimental setup.  
 
We use LabVIEW to create a single step, repetitive mixing sequence to observe 
the oscillation of inter diffusion of the two reagents.  The mixing valve sequence as 
discussed in section 1.4.2 is as follows: (100, 010, 001).  Constant fluidic pressure is set 
to approximately 5.0 psi (? 0.05 psi) and the control valves and mixers pressure is set to 
10 and 15 psi, respectively.   
Details of the operating procedures for a single test include the following steps.  
For operation of the device, first the center valve and side wash valves, one on each side, 
are closed separating the reaction chamber into two separate but equal parts.  Next, 
N 2
T a n k
B O B 3  
C o n t r o l l e r
G a s  l i n e
P r e s s u r e  
C o n t r o l l e r
8  C h a n n e l  
M a n i f o l d
C a m e r a
C o n t r o l  s i g n a lC o n t r o l  s i g n a l
G a s  l i n e
G a s  l i n e
I n v e r t e d  
M i c r o s c o p e
I m a g e  
C a p t u r i n g
L a b V I E W
 
 
55 
 
reagents are loaded into the dry chamber parts.  It takes a matter of a few seconds to 
introduce the reagents to the chambers.  To insure even pressure throughout each half, 
reagents are allowed to flow an additional 3 minutes.  For industrial uses, this additional 
loading time may not be necessary.  Once loaded, the shut off valves to the reagent in and 
outs are activated and pressure-pushing reagents are deactivated.  Figure 3.15 illustrates 
the step-by-step operating procedures for a single reaction chamber experiment. 
 
 
Figure 3.15 Schematic of experimental operational procedures.  
O p t i c a l  
D e t e c t i o n
O p t i c a l  
D e t e c t i o n
L o a d i n g  o f  r e a g e n t s  M e t e r i n g  o f  r e a g e n t s
M e t e r i n g  a n d  d e t e c t i o n  
o f  d i f f u s i o n
D i f f u s i o n  c o m p l e t e d W a s h i n g  a n d  d r y i n g
O p e n  
v a l v e
C l o s e  
v a l v e
1  m m
 
 
56 
 
Next, the camera is activated to record the following experiment.  Within our lab, 
we use a Motic 1000 1.3M camera connected to the inverted scope of our Ziess Axiovert 
40 C/CFL microscope.  Next the mixing valve sequence is started, quickly followed by 
the release of pressure to the center valve. This allows diffusion of the two solutions to 
begin.  Once testing is complete, the mixing sequence is stopped and the wash in and out 
valves are opened.  First, the chamber is washed with de-ionized water for a 
approximately two minutes at constant pressure, followed by drying with nitrogen gas at 
constant pressure. Once dry, the operation can be performed again.  All reagent, water 
and drying are at the same constant pressure to allow for constant testing parameters.  
The blue and yellow filled areas represent reagents and were used to aid in visualization 
of the devices? functions and do not indicate the color of the reagents used.   
A video is recorded at 2.5 X or 10 X magnifications using a Motic 1000 1.3M 
pixel camera and Motic Images Plus 2.0 program.  Video is started before releasing the 
center valve and stopped after approximately 3 to 5 minutes of mixing valve sequence 
operation.  The camera is mounted to a Zeiss optical microscope (Axiovert 40 CFL, 
Germany).  The videos are first separated into image sequence of each test using Virtual 
Dub, then uploaded into Image J software.  Utilizing Time Series Analyzer V2.0, a plug 
in for Image J software, a ROI, region of interest, is selected within the testing chamber 
on the reagent two side of the testing chamber and an average intensity is calculated for 
each image.  
 
 
 
 
 
57 
 
3.6    Results and discussion 
The diffusion coefficient is represented in terms of centimeters squared per 
second.  Visual light intensity is comparable to concentration because in this method we 
are looking for the change in concentration per time.  Before allowing diffusion to occur, 
the water side has a high and steady state visual intensity.  Once diffusion is allowed to 
occur, shut off valves are opened, and the blue food dye diffuses into the water 
decreasing the visual intensity value.  The visual intensity value oscillates from low to 
high as the two reagents diffuse into one another and advance around the testing chamber 
until a steady state visual intensity value is observed; this is lower than the starting water 
intensity.  The intensity change can be correlated to the concentration change of dye in 
water. 
The software Image J allows the average intensity of one area to be calculated 
given a set region of interest (ROI).  We used an oval ROI with height and width of 22 
pixel circle in 640 x 512 pixel sized image sequence, when in 2.5 magnification using the 
Zeiss optical microscope.   
All tests on chip were performed at room temperature at 25.0 (?0.2 ?C) using an 
indium tin oxide heater (Cell MicroControls, USA).  The experimental setup was similar 
to Taylor dispersion in that they introduced a tracer pulse in a fluid flowing in laminar 
flow within a circular cross section.  
 
3.6.1 Introduction  
Our plan is to validate a micro system device using optical detection of intensity 
fluctuation as pneumatic valves operate in sequence to create a peristaltic pump within a 
 
 
58 
 
closed loop.  Since the observed intensity is related to the concentration, we will use the 
two interchangeably. Using an equation, we developed for Fourier concentration profile 
we plan to match the equation to the experimental concentration versus time profile 
through data analysis and computer programming and then calculate k, apparent or virtual 
diffusion coefficient from the experimental.  Lastly, we will use an equation relating k to 
D, diffusion coefficient and determine the experimental diffusion coefficient of our 
reagents. 
  
3.6.2 Equation validation 
 Jean Baptiste Joseph Fourier was a mathematician and physicist known for 
studying applications and problems of heat transfer and vibrations.  Fourier developed 
many analytical relationships for heat transfer.  In Crank?s second addition of The 
Mathematics of Diffusion[2] he explains  in detail how conversion of heat flow to 
diffusion solutions can be done given Fick?s second equation and the corresponding 
equation for heat flow.  This is allows ?, temperature to be analogous to C for 
concentration and K, heat conductivity, with D for diffusion coefficient. This allows us to 
use Fourier?s relationship for varied movement of heat in a ring to determine the apparent 
diffusion coefficient.  We modified the original Fourier?s concentration profile equation 
from Fourier?s 1878 Analytical Theory of Heat to suit out analysis [31]. 
 
 22
21
4( , ) e x pm
n
nC x t C k tL ??
?
??? ? ???
???
 (3.2) 
 
 
 
 
59 
 
C(x,t) represents the concentration as related to distance and time, Cm is the final 
average concentration.  U is the velocity of the solution, cm/s, while L is the length of the 
system, or in our case the circumference. t is time, in seconds, and k is the apparent 
diffusion coefficient, cm2/s.  The apparent diffusion coefficient has been related to the 
diffusion coefficient relationship by Taylor 1953 [36]. 
 
 2248RUk D?  (3.3) 
 k is the apparent diffusion coefficient and D is the diffusion coefficient, both in 
units of cm2/s whereas R is the radius of the diffusion tube, as related to Taylor 
dispersion, cm, and U is velocity, cm/s.  From the these two equations we can expect our 
concentration versus time profile to look similar to Figure 3.16. 
 
 
 
60 
 
 
Figure 3.16 MATLAB plot of theoretical concentration versus time profile given the 
Fourier concentration profile and experimental and known values. 
  
 Figure 3.16 was developed by entering the diffusion coefficient value from Pratt 
et al.[40] at 1.05 x 10-5 m2/s, using our circumference of 0.7226 cm as L, half of our 
testing chamber width at 0.005 cm as R.  U and Cm we observed experimentally as 
0.0674679 cm/s and 111.037 (A.U.), respectively. n was set at 100. 
 The equation validation plan is to fit the experimental data with the theoretical 
equation, to an appropriate degree of error, and calculate the corresponding k and D 
values.  Then, compare the experimental determined k and D values with known values 
and evaluate.  Proper testing parameters such as operating pressures, mixing frequency 
 
 
61 
 
and sequence should allow for reproducible and reliable experimental microfluidic 
results.  However, the testing parameters are not known for this particular experimental 
determination and therefore will require evaluation and determination of ideal testing 
parameters.  
 To determine the proper testing parameters, we have some expectations from 
prior experience.  These expectations will now be discussed.  For control to fluidic 
pressure ratio a working ratio of 2:1 should be observed.  To accommodate this ratio, the 
internal pressure within the fluidic channels must be limited such that the thin membrane 
of PDMS from the control channel does not become collapsed to the substrate by the 
weight or pressure exerted by the fluidic channel.  Thus, no collapsing should occur 
before, during or after an experiment.  A clear cup and cone of the two reagents should be 
distinguishable at the beginning of each experiment, so that the velocity may be 
determined.  Proper selection of a mixing frequency is also needed as related to the 
mixing valve sequence of operation.  Given the same mixing valve sequence, an increase 
in frequency should result in a decrease in time to a constant concentration and vice 
versa. Also, with an increase in frequency we would expect shorter time difference 
between peaks and valleys compared to a lower frequency.  This increase may also 
induce unsteady, erratic shifts in concentration as compared to lower frequency allowing 
the concentration to steadily increase and decrease as the two reagents diffuse into one 
another.  Following these considerations, we evaluated each design version and 
corresponding data validity.  Through which, the third design proved improved 
reproducible devices with favorable response times.  Extensive testing for determining 
the proper operating parameters were evaluated.  From the testing operating procedure 
 
 
62 
 
experiment comparisons, we determined water and dye had smoother curves and 
therefore would be ideal for initial validation of the theoretical equation as compared to 
ethanol and dye experiments. Other procedures chosen were standard mixing sequence of 
(100, 010, 001), as it produced smoother curves for water and dye than compact mixing 
sequence, and 5 Hz mixing sequence, as it produced faster results.  In addition, mixer 
sequence activated before the center valve released was chosen as our results were 
inconclusive, and that was our common practice before these experiments.  Therefore we 
performed more experiments using the above testing operating procedures and reagent 
combination to give the following concentration versus time profile as seen in Figure 
3.17. 
 
 
Figure 3.17 Concentration versus time profile of two experiments at 5Hz, standard 
mixing sequence of water and dye. 
 
80 
95 
110 
125 
140 
155 
170 
185 
0 50 100 150 200 
In
ten
sity 
(A
.U.)
 
Time (seconds) 
Test 1 
Test 2 
Test 3 
 
 
63 
 
To validate the diffusion equation we chose the experimental conditions, as it 
appeared similar to our theoretical curve. The three experiments were performed using 
the same testing parameters and the same microfluidic chip, one after the other.   
 
3.6.3 Data analysis 
 From the observed intensity fluctuation trend, a relationship with the following 
equation can be used to determine the observed diffusion coefficient.  The peaks and 
valleys of the experimental data are evaluated to determine the diffusion coefficient.  For 
the baseline dye and water experiments, Figure 3.18 shows the averaged peak and valley 
points with regards to time from the three tests. 
 
 
Figure 3.18 Average peak and valley points from test 1, 2 and 3 from Figure 3.17. 
 
 All data was normalized by comparison with a standard light intensity reading 
during each test off set from the experimental diffusion area. The first valley peak was 
80 
95 
110 
125 
140 
155 
170 
185 
0 50 100 150 200 
In
ste
nsity 
(A
.U.)
 
Time (seconds) 
Average Peaks 
Average Valleys 
 
 
64 
 
chosen at the start of the experiment.  While there was no mixing occurring prior to this 
point, there was some slight variance in light intensity due to experimental setup.  To 
better reflect the true first valley point the presented point was chosen as compared to the 
smallest intensity recorded.  Figure 3.18 data of averaged peak and valley values are used 
in the remaining analysis procedures. 
 
3.6.4 SPSS analysis 
 Since we have one equation and 1 unknown (k) we choose to curve-fit of the 
exponential of the peaks and valleys to the exponential part of the theoretical equation.  
We assume that the exponential curves of the top and bottom of the theoretical equation 
will give us an appropriate approximation of k and therefore D. MATLAB curve fit 
functions were not appropriate giving poor R and R square values and curves with less 
than adequate fit.  The resulting equations were linear looking and curved slightly, in the 
opposite direction. Consequently, we used SPSS program (Statistical Package for the 
Social Sciences).  SPSS is a computer program used for statistical analysis, among other 
things (IBM company).  From the regression analysis options we choose three options 
that seemed the most promising for accurate analysis. Logarithmic, cubic and power 
regression equation analysis were chosen.  Their corresponding equations are as follow. 
 
Logarithmic SPSS regression analysis expression 
 1 ln( )oY b b t??  (3.4) 
Cubic SPSS regression analysis expression 
 231 2 3oY b b t b t b t? ? ? ? (3.5) 
 
 
65 
 
Power SPSS regression analysis expression 
 ? ? ? ? ? ?01ln ln lnY b b t?? (3.6) 
 
Using a MATLAB ?polyfit? function, we were able to get fit line expression equal 
to that of SPSS growth analysis.  Therefore, in SPSS analysis we compared the three 
expressions. Figure 3.19 and 3.20 shows the SPSS regression analysis fit curves for the 
peaks and valley averaged values Table 3.2 shows the analysis resulting values.  The 
closer R square is to 1, the better the fit of the equation.   
 
 Figure 3.19 SPSS regression analysis curves for the average peaks. 
 
 
66 
 
 
Figure 3.20 SPSS regression analysis curves for the average valleys. 
 
Table 3.2 SPSS regression analysis results.  
 R R Square 
Logarithmic 
Peaks 0.988 0.976 
Valleys 0.988 0.976 
Cubic 
Peaks 0.999 0.998 
Valleys 0.999 0.999 
Power 
Peaks 0.985 0.970 
Valleys 0.990 0.980 
 
From the SPSS regression analysis curves we see the logarithmic and power 
curves overlap each other and do not fit the data as well as the cubic curve.  These 
 
 
67 
 
observations are supported by the trend of the R2 value being greatest for the cubic.  At 
this time we will continue our analysis with the averaged peak and valley values as 
compared to the cubic analysis. 
 
 
3.6.5 MATLAB analysis 
We developed a MATLAB program to solve for k and D using the SPSS 
regression cubic equation and the exponential part of equation (3.2).  First, the program 
plots experimental averaged peaks and valleys.  Next, using the regression analysis 
equation from SPSS, MATLAB calculates the concentration given the same time range 
and time steps as the experimental and plots the curve.  Curve fit points at the same time 
as the experimental peaks are also plotted.  Then, the MATLAB program has a while 
loop that compares the concentration from the SPSS equation and the concentration found 
for the theoretical equation for every time value given a guessed k. Since n still remains 
within the exponential part of the equation, there is a for loop within the while loop.  This 
loop goes through the n values, 1 to 100, and summates the values with Cm and gives one 
Ctheoretical value per time value. The loops create the following relationship. 
 
 2210023
0 1 2 3 21
4e x p n
t h e o r e t i c a l mc u r v e f i t nC b b t b t b t C C k tL
?
?
?????? ? ? ? ? ? ? ????
?????
 (3.7) 
  
We set an error limit (a maximum) to 10%, once the error is reduced to that 
amount we are given a k value.  Next, the program plots the theoretical concentration 
curve according to the determined k value.  Also, the theoretical points at the same time 
 
 
68 
 
as the experimental peaks are plotted.  Lastly, the diffusion coefficient was determined 
according to the equation (3.3) relationship.   
Therefore, from our MATLAB program, we input a data set of averaged peaks 
and valley points per 3 tests, and SPSS cubic regression equation and its constants.  Next, 
we get k and D values along with percent error between  the concentrations calculated 
from the cubic regression equation and our diffusion equation using k.  Figure 3.21 
MATLAB output results and Figure 3.21 shows the graphic results for the concentration 
profile analyzing the data. 
 
 
Figure 3.21 MATLAB output results of the peak value analysis of water and dye. 
 
 
 
 
69 
 
 
Figure 3.22 MATLAB plot of the peak value analysis of water and dye. 
 
3.7 Conclusions  
From Figure 3.22 the blue circles represent the average time and intensity values 
for the peak and valleys from test 1, 2, and 3.  The red lines are the standard deviations of 
each point per intensity and time range values of the three tests.  The two green dashed 
lines are the two cubic SPSS regression curves and while the two solid lines are the 
calculated curves using k. From the analysis performed on the water and dye experiments 
we get 4.35x10-4 cm2/s for k and 1.838x105 cm2/s for D values.  Using SPSS cubic 
regression analysis equation compared to our diffusion equation we calculated a 6.30% 
error in determining k and thus D.  With all things considered, we assume our method is 
appropriate for determining an estimate of diffusion coefficient and has great potential in 
expediting the determination process. 
 
 
70 
 
 We have developed a novel mirco system device capable of experimentally 
mixing nanoliters of reagents together. By optically recording the movement and 
diffusion of the two reagents into one another we can obtain an intensity versus time 
curve.  As the intensity is related to concentration, we can analyze the data to determine 
an experimental diffusion coefficient with the aid of SPSS and MATLAB analysis.  By 
comparing the valley points versus the peak points from the data, after analysis the 
resulting dispersion and diffusion coefficients were within good agreement of each other.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
71 
 
 
 
Chapter 4 
Summary and conclusions 
4.1   Conclusions of the research   
  A progress of micro system device designs has been evaluated and tested. We 
were capable of developing a micro system device induced by mircomixers within a 
series capable of experimentally mixing nanoliters of reagents together. We optically 
recorded and evaluated the resulting fluid flow of the two reagents mixing with one 
another. By improvement of baseline data analysis of the raw data, we were able to 
determine peak and valley points of the raw data and relate the change in each peak or 
valley by cubic regression analysis using SPSS software. We could determine an 
experimental diffusion coefficient using MATLAB analysis and part of an equation 
related to Fourier?s concentration profile.  By comparing the valley points versus the peak 
points from the data, after analysis the resulting dispersion and diffusion coefficients 
were within good agreement of water and dye solutions at 25.0 ?.  Further investigation 
can only improve the accuracy of the device and analysis process.  We assume our 
method is appropriate for determining an estimate of diffusion coefficient and has great 
potential in expediting the determination process. 
 
 
 
 
 
 
72 
 
 
 
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75 
 
 
 
Appendix I 
MatLab Code 
 
clear all 
clc 
  
Tp=xlsread('Data.xls','Data','A2:A20');%Peak averaged time 
Cp=xlsread('Data.xls','Data','B2:B20');%Peak averaged concentration 
Tv=xlsread('Data.xls','Data','C2:C20');%Valley averaged time( 
Cv=xlsread('Data.xls','Data','D2:D20');%Valley averaged concentration 
TsdP=xlsread('Data.xls','Data','E2:E20');%Peak standard deviation time 
CsdP=xlsread('Data.xls','Data','F2:F20');%Peak standard deviation 
concentration 
TsdV=xlsread('Data.xls','Data','G2:G20');%Valley standard deviation 
time 
CsdV=xlsread('Data.xls','Data','H2:H20');%Valley standard deviation 
concentration 
  
Cpmax=max(Cp);%A.U. 
L=0.7226;%cm 
R=0.005;%cm 
U=0.0674679;%cm/s 
% Cm=108.5084;%Etest3 AU, light intensity 
Cm=121.271; 
  
disp('The following values are with n=100') 
disp(' ') 
plot(Tp,Cp,'o')%Plot full experimentatl data as a blue line 
hold on 
plot(Tv,Cv,'o') 
hold on 
  
bp0=198.004; 
bp1=-1.393; 
bp2=0.009; 
bp3=-2.16E-05; 
Tpc=0:0.1:180.5; 
Cpc=bp0+bp1*Tpc+bp2*Tpc.^2+bp3*Tpc.^3; 
plot(Tpc,Cpc,'--g') 
hold on 
  
bv0=87.631; 
bv1=0.363; 
bv2=-0.001; 
bv3=8.71E-08; 
Tvc=0:0.1:180.5; 
Cvc=bv0+bv1*Tvc+bv2*Tvc.^2+bv3*Tvc.^3; 
 
 
76 
 
plot(Tvc,Cvc,'--g') 
hold on 
  
K=5e-4;%starting guess K 
N = [1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 
50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 
74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 
98 99 100];  
Tt = 0:0.1:180.5; 
  
Cf=Cvc; 
Ci=Cpc; 
% Ct=Cf+190; 
% avg_error_K = mean((Ct-Cf)./Cf); 
avg_error_K=.3; 
Ccal_sumv=Cm; 
Ccal_sump=Cm; 
%If the avg_error_K test value is too low, the loop will not stop 
while avg_error_K >= 0.063 
    K = K - 0.000001; 
  
    for i = 1:length(N) 
        n = N(i).^2; 
        %for Minimum peaks Ccal = ((-exp((... 
        Ccalv = ((-exp((-4.*(pi.^2).*K.*(Tt))./(L.^2))).^n); 
        Ccal_sumv=Ccalv+Ccal_sumv; 
        Ccalp = ((exp((-4.*(pi.^2).*K.*(Tt))./(L.^2))).^n); 
        Ccal_sump=Ccalp+Ccal_sump; 
      
    end 
    errorKv=abs((Cf'-Ccal_sumv')./Cf'); 
    errorKi=abs((Ci'-Ccal_sump')./Ci'); 
    MeanKv = mean(errorKv); 
    MeanKi = mean(errorKi); 
    two=(MeanKv+MeanKi)/2; 
     
    avg_error_K = mean(two); 
    max_error_K = max(two); 
    min_error_K = min(two); 
    
end 
  
disp('K value is') 
disp (K) 
disp('Final error average') 
disp(avg_error_K) 
  
Ctv=Ccal_sumv; 
Ctp=Ccal_sump; 
  
plot(Tt,Ctv,'b') 
hold on 
plot(Tt,Ctp,'b') 
hold on 
 
 
77 
 
  
disp('Diffusion coefficient directly from the above K value is:') 
D = ((48*K)/((R^2)*(U^2))) 
  
xlabel('Time (seconds)') 
ylabel('Concentration (A.U.)') 
title(['K determined = ',num2str(K),'cm^2/s','  Thus the D determined = 
',num2str(D),'cm^2/s'])%manually change n value 
% legend('Experimental','Experimental Peaks','Regression 
Logarithmic','Regression Logarithmic Peaks','Theoretical','Theoretical 
Peaks'); 
axis([0 185 80 200]) 
hold on 
  
i=1:1:15; 
A=[Tp(i)-TsdP(i), Tp(i), Tp(i)+TsdP(i)]; 
B=[Cp(i), Cp(i), Cp(i)]; 
  
x=A(1,:); 
y=B(1,:); 
plot(x,y,'r') 
hold on 
x=A(2,:); 
y=B(2,:); 
plot(x,y,'r') 
hold on 
x=A(3,:); 
y=B(3,:); 
plot(x,y,'r') 
hold on 
x=A(4,:); 
y=B(4,:); 
plot(x,y,'r') 
hold on 
x=A(5,:); 
y=B(5,:); 
plot(x,y,'r') 
hold on 
x=A(6,:); 
y=B(6,:); 
plot(x,y,'r') 
hold on 
x=A(7,:); 
y=B(7,:); 
plot(x,y,'r') 
hold on 
x=A(8,:); 
y=B(8,:); 
plot(x,y,'r') 
hold on 
x=A(9,:); 
y=B(9,:); 
plot(x,y,'r') 
hold on 
x=A(10,:); 
y=B(10,:); 
 
 
78 
 
plot(x,y,'r') 
hold on 
x=A(11,:); 
y=B(11,:); 
plot(x,y,'r') 
hold on 
x=A(12,:); 
y=B(12,:); 
plot(x,y,'r') 
hold on 
x=A(13,:); 
y=B(13,:); 
plot(x,y,'r') 
hold on 
x=A(14,:); 
y=B(14,:); 
plot(x,y,'r') 
hold on 
x=A(15,:); 
y=B(15,:); 
plot(x,y,'r') 
hold on 
  
i=1:1:15; 
A=[Tp(i), Tp(i), Tp(i)]; 
B=[Cp(i)-CsdP(i), Cp(i), Cp(i)+CsdP(i)]; 
  
x=A(1,:); 
y=B(1,:); 
plot(x,y,'r') 
hold on 
x=A(2,:); 
y=B(2,:); 
plot(x,y,'r') 
hold on 
x=A(3,:); 
y=B(3,:); 
plot(x,y,'r') 
hold on 
x=A(4,:); 
y=B(4,:); 
plot(x,y,'r') 
hold on 
x=A(5,:); 
y=B(5,:); 
plot(x,y,'r') 
hold on 
x=A(6,:); 
y=B(6,:); 
plot(x,y,'r') 
hold on 
x=A(7,:); 
y=B(7,:); 
plot(x,y,'r') 
hold on 
x=A(8,:); 
 
 
79 
 
y=B(8,:); 
plot(x,y,'r') 
hold on 
x=A(9,:); 
y=B(9,:); 
plot(x,y,'r') 
hold on 
x=A(10,:); 
y=B(10,:); 
plot(x,y,'r') 
hold on 
x=A(11,:); 
y=B(11,:); 
plot(x,y,'r') 
hold on 
x=A(12,:); 
y=B(12,:); 
plot(x,y,'r') 
hold on 
x=A(13,:); 
y=B(13,:); 
plot(x,y,'r') 
hold on 
x=A(14,:); 
y=B(14,:); 
plot(x,y,'r') 
hold on 
x=A(15,:); 
y=B(15,:); 
plot(x,y,'r') 
hold on 
  
i=1:1:14; 
A=[Tv(i)-TsdV(i), Tv(i), Tv(i)+TsdV(i)]; 
B=[Cv(i), Cv(i), Cv(i)]; 
  
x=A(1,:); 
y=B(1,:); 
plot(x,y,'r') 
hold on 
x=A(2,:); 
y=B(2,:); 
plot(x,y,'r') 
hold on 
x=A(3,:); 
y=B(3,:); 
plot(x,y,'r') 
hold on 
x=A(4,:); 
y=B(4,:); 
plot(x,y,'r') 
hold on 
x=A(5,:); 
y=B(5,:); 
plot(x,y,'r') 
hold on 
 
 
80 
 
x=A(6,:); 
y=B(6,:); 
plot(x,y,'r') 
hold on 
x=A(7,:); 
y=B(7,:); 
plot(x,y,'r') 
hold on 
x=A(8,:); 
y=B(8,:); 
plot(x,y,'r') 
hold on 
x=A(9,:); 
y=B(9,:); 
plot(x,y,'r') 
hold on 
x=A(10,:); 
y=B(10,:); 
plot(x,y,'r') 
hold on 
x=A(11,:); 
y=B(11,:); 
plot(x,y,'r') 
hold on 
x=A(12,:); 
y=B(12,:); 
plot(x,y,'r') 
hold on 
x=A(13,:); 
y=B(13,:); 
plot(x,y,'r') 
hold on 
x=A(14,:); 
y=B(14,:); 
plot(x,y,'r') 
hold on 
  
i=1:1:14; 
A=[Tv(i), Tv(i), Tv(i)]; 
B=[Cv(i)-CsdV(i), Cv(i), Cv(i)+CsdV(i)]; 
  
x=A(1,:); 
y=B(1,:); 
plot(x,y,'r') 
hold on 
x=A(2,:); 
y=B(2,:); 
plot(x,y,'r') 
hold on 
x=A(3,:); 
y=B(3,:); 
plot(x,y,'r') 
hold on 
x=A(4,:); 
y=B(4,:); 
plot(x,y,'r') 
 
 
81 
 
hold on 
x=A(5,:); 
y=B(5,:); 
plot(x,y,'r') 
hold on 
x=A(6,:); 
y=B(6,:); 
plot(x,y,'r') 
hold on 
x=A(7,:); 
y=B(7,:); 
plot(x,y,'r') 
hold on 
x=A(8,:); 
y=B(8,:); 
plot(x,y,'r') 
hold on 
x=A(9,:); 
y=B(9,:); 
plot(x,y,'r') 
hold on 
x=A(10,:); 
y=B(10,:); 
plot(x,y,'r') 
hold on 
x=A(11,:); 
y=B(11,:); 
plot(x,y,'r') 
hold on 
x=A(12,:); 
y=B(12,:); 
plot(x,y,'r') 
hold on 
x=A(13,:); 
y=B(13,:); 
plot(x,y,'r') 
hold on 
x=A(14,:); 
y=B(14,:); 
plot(x,y,'r') 
hold on