μ-Brewery: A Lab-On-a-Chip Solution for Developing Better Breeds of Yeast
ME 8254 Fundamentals of MEMS
By: Donald Horkheimer
ID #: 2132334
Instructor: Prof. Tianhong Cui
Teaching Assistant: Dongjin Lee
2007-04-28
Abstract: There is increasing interest in substituting a large amount of the country’s gasoline
usage with ethanol. Developing better breeds of yeast could result in a breed that digests a
greater variety of feed-stocks and improve the efficiency of the production process. Bioengineering of yeast breeds to improve ethanol production will require a simple and cost
effective means to test small samples of new yeast breeds under a variety of conditions.
The μ-Brewery is a cheap and easy to use MEMS based lab-on-a-chip for developing better
strains of yeast. The device incorporates a Magnetohydrodynamic (MHD) pump with a noninvasive laser based ethanol concentration sensor and mixing chamber. The main functional
systems of the device is constructed on a silicon wafer and then anodicly bonded between two
glass wafers and finally packaged in a Leaded Chip Carrier (LCC).
The Reynolds Number of flow within the device is approximately 0.31. The total power
consumption of the device is 0.61 W. The area of the μ-Brewery die is 1 cm^2. The device is
expected to be two to three orders of magnitude cheaper then existing research fermeters.
Introduction: Currently, ethanol fermentation faces two limitations. There are a limited number
of practical feedstocks to generate ethanol from, mainly corn or sugar cane. The efficiency of the
overall ethanol production process means a great deal of energy is expended to produce ethanol.
[1] Yeast cells ultimately poison themselves by the ethanol waste they generate as a by product
of their metabolism. Ethanol concentration is naturally limited by the fragility of yeast. Further
refinement of ethanol requires energy intensive distillation. Improved yeast breeds could be
developed that could ferment a wider range of crops and more resilient yeasts could result in
energy savings.
Main Body: The μ-Brewery represents the convergence of several areas of technology. It
incorporates advances in micro-fluidics, biotechnology, micro-technology, and smart systems to
address the problem of how society will develop sustainable forms of energy. [6, 15]
The features of the μ-Brewery are built on a silicon wafer. The device uses a
magnetohydrodynamic (MHD) pump to move test solution around the device. The MHD pump
electrodes are made by using a PVD process to apply Titanium and Platinum to the wafer. After
the electrodes are made a silicon dioxide film is formed on the exposed silicon wafer to protect
the silicon and to act as an electrical insulator. The μ-Brewery uses a fiber optic cable to
measure ethanol concentration. The fiber optic cable uses surface plasmon resonance to measure
the index of refraction of the solution to determine ethanol concentration. The wafer is bonded
between pieces of glass and is packaged in a ceramic package.
BACKGROUND AND CUSTOMER NEEDS – Current research fermenters suffer from several
drawbacks. Generally, research fermenters are large and can occupy a great amount of space in a
laboratory. They are often complicated and require skilled labor to operate and maintain. Many
of the sub-systems that support the fermenter are not well integrated or purpose built for the task
of growing yeast and as such tend to be very costly. See Figure 1 below for examples of
conventional research fermenters.
2
Figure 1. Examples of Conventional Research Fermenters
Looking at conventional research fermenters, it is possible to generate a list of customer needs
that cover different aspects of what a μ-Brewery should be and do. Specific need areas include
functional, safety, quality and manufacturing as well as economic and ecological.
Functional Needs: The device needs to be physically small, approximately the size of a CD/DVD
case. The device should not have any moving parts. The device needs to mix yeast and glucose
solution together in order to produce a homogenous mixture. The device needs to have a vent to
release carbon dioxide generated during fermentation. The energy requirements for the device
should be no greater then that which would be commonly available in a laboratory, ie 120 VAC,
15 Amps, 1-Phase. The device cannot damage the yeast cells and cannot adversely effect the
yeast’s test environment. The device needs to output information detailing ethanol
concentration, living yeast cell concentration, and glucose concentration. Thermal control of the
device can be external, but otherwise require very little external support. The materials need to
be bio-compatible and resist corrosion.
Safety Needs: The device needs to be transparent for ease of inspection. The device needs to be
easily handled by human operators without requirement for extensive training or precautions.
The device needs to be durable enough to deal with conventional laboratory sterilization
methods. The basic materials need to be bio-compatible. The material should not be permeable
to various gases and liquids. Likewise the material should not retain or absorb any chemicals
from previous tests.
Quality Needs: The device needs to be easily visually inspected and contain continuous built-intest capability to verify device function. The materials used in the device need to resist corrosion
caused by water, ethanol, and simple sugars. In addition the materials need to be hydrophilic for
ease of pumping or at least accept a hydrophilic coating or treatment.
Manufacturing Needs: The device needs to be predominately 2D in construction with the intent
of minimizing process steps and complexity. The device shall not be a hybrid design with
electronic (“brains”) processed alongside the MEMS components on the same wafer.
Manufacturing needs to use “Green” (environmentally sound) production techniques.
Economic Needs: The device needs to be self contained and require little if any additional
equipment to be purchased by the end user. The design needs to be done with open source tools
3
if possible. The device electronics needs to be built around an FPGA and off the shelf
components wherever possible.
Ecological/Life-Cycle Needs: The device needs to be reusable and recyclable. Hazardous
materials need to be avoided in the design.
With knowledge of the customer’s needs it becomes easier to generate detailed design
requirements.
REQUIREMENTS – The following requirements were drawn up based on customer needs and
background research. In the final design it was not possible to meet all the requirements, but it is
believed that failing to meet these requirements does not greatly diminish the value the customer
would find in using the μ-Brewery product. It was not possible to meet Requirement #4 for in
order to get the Reynolds Number high enough the flow velocity would have to be substantially
greater which would put large power demands on the MHD pumping system and probably lead
to heat rejection issues. Requirement #11 and #12 will not be met as it was not possible to
incorporate proper sensors into the μ-Brewery design to measure these quantities. Table 1 shows
a detailed breakdown of μ-Brewery design requirements.
4
Requirement No.
Importance
Rank (1-10,
10 most
important)
Units
Lower
Marginal
Value
Upper
Marginal
Value
Lower
Ideal
Value
Upper
Ideal
Value
10
degC
15
45
0
50
8
degC
-
121
121
140
8
kPa
97
103
95
105
10
Re
-
10
-
100
4
Description
Operating
Temperature
Non-Operating
Temperature
Non-Operating
Pressure
Operating Fluid
Reynolds Number for
Chaotic Advection
Device
5
Sample Fluid Volume
10
μL
-
1000
-
200
6
Device Diameter
9
in
4
6
0.5
1
7
Device Thickness
Handling shock, HalfSine, 0.5 ms
6
in
0.5
1
0.1
0.25
6
g
-
1500
-
3000
8
in
-
35
-
72
10
ppm
-
10000
-
100
6
ppm
-
10000
-
500
3
cells/mL
13
Handling Drop Height
Ethanol Concentration
Resolution
Glucose Concentration
Resolution
Yeast Cell
Concentration
Fluid Network Control
Valves/System
10
List
-
-
-
-
14
No moving parts
7
List
-
-
-
-
15
Transparent Materials
Bio-compatible
Materials
Green Manufacturing
Process
MEMS Mask Feature
Tolerance
Reconfigurable
"Brains" with FPGA to
reduce cost
Reusable Device
RoHS, Hg, Pb free
Recyclable
6
List
-
-
-
-
10
List
-
-
-
-
6
List
-
-
-
-
3
μm
-
20
-
50
3
9
8
4
List
Cycles
List
List
100
-
-
1000
-
-
1
2
3
8
9
10
11
12
16
17
18
19
20
21
22
5x10^8
1x10^5
Table 1. Design Requirements
RISKS AND SOLUTIONS – The design of a lab-on-a-chip MEMS device to develop better
breeds of yeast faces three main technical problems:
 Moving organic/biological fluids through the device
 Measuring yeast performance/ethanol yield
 Utilizing bio-compatible materials in the design of the MEMS device
5
Yeast/sugar water/ethanol solution needs to be transported throughout the μ-Brewery in order to
accomplish several tasks essential to the operation of the lab-on-a-chip. Many different means of
pumping the test solution through the device were researched. Selection was driven by the
design requirements. Possible ranked solutions are (lowest rank is most feasible, highest rank is
least feasible):
1. AC Magnetohydrodynamic (MHD) Pump [5, 11]
2. Surface/Channel Acoustic Wave Pump [7]
3. External Rotation Centrifugal Pumping [20]
4. MEMS Positive Displacement Pumps [13]
5. DC Magnetohydrodynamic Pump [18, 19]
6. Electrophoretic Pumps [4, 10, 17]
To determine the effectiveness of a given yeast breed it is essential that one can measure ethanol
concentration at a minimum. Additionally, it may be desired to measure yeast concentration and
glucose and fructose levels. Many different means of sensing properties of the test solution
through the device were researched. Selection was driven by the design requirements. Possible
ranked solutions are (lowest rank is most feasible, highest rank is least feasible):
1. Fiber Optic Refractive Index Measurement [12]
2. Pulsed Amperometic Detection Using Microelectrode Array [16]
3. Change in Fluid Impedance Measurement [8]
4. Change in Fluid Capacitance Measurement [9]
5. Monitoring Redox Reaction of Dye Tracer Caused by Yeast Using Electrodes [3]
6. Using Fourier Transform Mid-Infrared Spectrometer Able to Measure Attenuated
Total Reflectance [2]
The lab-on-a-chip structure benefits from judicious choice of materials. Several MEMS
materials were considered for the device. Selection was driven by the design requirements.
Possible ranked solutions are (lowest rank is most feasible, highest rank is least feasible):
1. Silicon substrate with a SiO2 coating
2. Glass
3. Polydimethylsiloxane (PDMS)
4. Parylene
COST COMPARISON – Current research fermenters are often very large, complicated, and
costly pieces of equipment. In contrast MEMS based tools for researching yeast will be small,
highly integrated, and inexpensive. Figure 2 below illustrates a Lambda Laboratory bench top
fermenter that is considered to be inexpensive by conventional fermenter standards. The
complete Lambda Laboratory fermenter costs $11,620. Based on the size and relative
complexity of the proposed μ-Brewery in comparison to other MEMS devices, the estimated cost
of the μ-Brewery will probably be two orders of magnitude less expensive, i.e. ≈$100. If a one
time use μ-Brewery can be developed the price maybe three orders of magnitude less expensive,
i.e. ≈$10. A one-time use system also eliminates the need for having research labs perform nonvalue added work such as having technicians clean lab equipment between tests which means
even greater savings for the customer.
6
Figure 2. Lambda Laboratory Fermenter Minifor™
MODELING – The μ-Brewery is composed of a mixing channel and an MHD pump channel.
The two channels are parallel to one another and form a loop through connections at the ends of
the channels. For purposes of modeling the mixing channel is essentially a Y-mixer with two
individual streams of different composition coming together in parallel and mixing. The
modeling does not take into account any chaotic advection due to mixing enhancing obstacles in
the mixing channel. The sensor to measure ethanol concentration is located after the mixing
channel, but before the MHD pump.
The dimensionless number that characterizes the mixing process is the Fourier Number shown
below in Equation 1. The variables of the Fourier Number contains D the diffusion coefficient,
 the mixing time and L a characteristic mixing length and define the diffusion mixing process of
a system. The characteristic mixing length is assumed to be the width W and height H of the
channel, in other words the cross sectional area, A . Generally the Fourier Number is between
0.1 and 1 for liquid microflows.
Fo 
D
D
D


L
W * H Achannel
2
Mixing
Eq. 1
The mixing time can be easily solved for by rearranging Equation 1.

FoA
D
Eq. 2
Next, assuming the two fluids to be incompressible and given the desired flow rates, Q and
channel cross section, A it is possible to calculate an average flow velocity u in Equation 3.
u
Q A  Q B
A
Eq. 3
Then utilizing Equations 2 and 3 it is possible to calculate the channel length.
L  u
Eq. 4
Next, the pressure drop through the two equal-length channels is calculated using Equation 5.
7
P  2 * Re fu
L
Eq. 5
2 Dh2
Re is the Reynolds Number and is equal to
 Dh u
, f is the Darcy Friction Factor and is equal to

Re
4A
,  is the dynamic viscosity, and Dh is the hydraulic diameter and is equal to
.
64
2WH
Then the characteristics of the MHD pump can be modeled as shown in Equation 6. The pump
is assumed to be an AC pump where the electric field and magnetic fields have a constant and
equal frequency and phase angle. A DC MHD pump was not considered because the electrodes
generate gas bubbles and tend to wear out faster.
P  J  B L 12 cos 
Eq. 6
J is the current density, B is the magnetic flux density, L is the channel/electrode length, and
 is the phase angle between the electric and magnetic fields. A representation of a MHD pump
can be seen below in figure 3.
Figure 3. Conceptual Representation of MHD Pump Duct
Some assumptions were made during the simulation. The diffusion properties of the μ-Brewery
system solution were assumed to be representative of a water-sucrose mixture. This is a
conservative assumption as water-glucose and water-ethanol both have higher diffusion
coefficients. The electrical conductivity of the solution was assumed to be equivalent to tap
water 1.2x10^-3 S/m, this level of conductivity is greater then a pure water or pure ethanol
solution, but is lower then sucrose solution. The magnetic flux density was assumed to be a
constant 1.5 T, this is a reasonable flux density for an electromagnet. The Fourier Number is
assumed to be 0.5. The MATLAB code used in the simulation is shown in the Appendix.
Preliminary simulations showed that system’s pressure drop and power consumption to be
heavily dependent on the flow channel cross section and average flow velocity. See figure 4. To
keep power consumption at a reasonable level the channel cross section would have to be large
and the flow velocity small.
8
Figure 4. Results of MHD Pump and System Simulation
Adjusting the channel cross section area and flow velocity a feasible design was developed for
the μ-Brewery with the following parameters.
Channel Height and Width: 0.0003 m
Total Channel Length: 0.08 m
Flow Velocity: 0.0009 m/s
Volumetric Flow Rate: 0.00001 L/min
Channel Reynolds Number: 0.31
Channel Pressure Drop: 46.9 Pa
Voltage Draw: 32.5 V
Current Draw: 0.018 A
Power Consumption: 0.61 W
Channel length and power consumption could be reduced by passing the fluid through the device
multiple times and by adding flow mixing devices inside the channel.
FABRICATION – Figure 5 illustrates the preliminary process flow used in manufacturing the μBrewery.
9
Clean
Silicon
Wafers
Using RCA1
and RCA2
Wet Clean
Solutions
Apply Photoresist
and Softbake
Resist Film
Deposit Metal
Electrodes for
MHD using PVD
Strip Away
Photoresist
Repeat Photoresist,
Build Chaotic Ni
Mixers, Strip Resist
Expose &
Develop
Photoresist
Hardbake
Plasma Etch
μ-Brewery
Channels
Strip Away
Remaining
Photoresist
Grow Thermal
SiO2 Electrical
Insulating Layer
Repeat
Photoresist
Process
Anodic Bond Si
Wafer Between 2
Glass Substrates
Ultrasonically
Drill Fluid Inlets
and Electrical
Contacts
Remove Quartz
Core Fiber Optic
Jacket and Clad
with H2SO4
Wash Bare Core
With Acetone and
Methanol
PVD Thin Gold
Film onto Fiberoptic Cable
Coil, Assemble,
Install Fiber
Optic Alcohol
Sensor into μBrewery
Package
μ-Brewery
Wafer Probe
Continuity Check
Dice μ-Brewery
Install
Electromagnetic
Coil for MHD
Test MHD Pump
and Fiber Optic
Alcohol Sensor
Figure 5. Fabrication and Test Process Flow
10
PACKAGING AND TESTING – The packaging process begins after the silicon wafer is
sandwiched between two layers of glass by anodic bonding. The assembled wafer is then
ultrasonically drilled for fluid vias and finally diced into individual die. The dies are then
bonded into ceramic packages using a coating of epoxy between the μ-Brewery and the package
base. A ceramic package was chosen because of its durability over temperature in comparison to
plastic packages. Figure 6 below is an example of a leaded ceramic package. If future designs
lead to a one time use μ-Brewery then cost drivers would dictate the use of a low cost plastic
package. Signal wire connections are then wire bonded into place between the μ-Brewery and the
leaded chip carrier. Heavier gauge wire bonds are used to connect the chip leads to the
electrodes of the μ-Brewery Magnetohydrodynamic (MHD) pump.
Figure 6. Example of Leaded Ceramic Package without Glass Lid
The glass lid is then bonded to both the glass covering of the μ-Brewery and the ceramic
package. The glass lid is predrilled with holes to connect the μ-Brewery fluid connections to the
outside world. Figure 7 gives an approximate sketch of the packaged μ-Brewery. Possible
suppliers of the ceramic package could be Kyocera or NGK.
Vias
Signal
Leads
MHD
Power
Leads
Figure 7. Example of Leaded Ceramic Package with Glass Lid
After packaging the μ-Brewery would be mounted on a board in ZIF socket between two
electromagnets with one above and one below the board. The electromagnets are used by the
MHD pump.
Testing first begins with verifying the function of the MHD pump system. The resistance of the
electromagnet coil is checked and compared against the nominal design specification.
11
Next, a fluid with known conductivity and viscosity is injected into the chip and the MHD pump
is turned on. The fluid is seeded with several glass micro-beads. MHD pump current and
voltage draw is compared against the specification and visual tracking of the glass beads is used
to determine the velocity of the fluid.
After verifying the MHD pump functions properly additional fluid is added to the reference fluid
to change refractive index of the mixture to verify that the alcohol concentration sensor is
working properly.
PRELIMINARY MASK LAYOUT – Below are the preliminary masks to be used in the
photolithography process for creating the features of the μ-Brewery.
MHD Pump
Channel
Solution
Inlets/Outlets
Area for Fiber
Optic Sensor
Mixing
Channels
Figure 8. Channel Mask: Apply Positive Photoresist, Anisotropic Plasma Etch 300 µm Depth
MHD
Electrode
Channels
Figure 9. Depositing Electrode Conductor Mask: Apply Positive Photoresist and Anisotropicly
Plasma Etch Wafer then use PVD Process to Deposit Electrical Conductor for MHD Pump and
Reuse Electrode Conductor Mask for SiO2 Insulator Film Build-Up by Applying a Negative
Photoresist to Avoiding Building up Insulator on the Conductor
12
Chaotic Mixing
Protuberances
Figure 11. Chaotic Advection Mixer Bump Mask: Apply Positive Photoresist and Build Up
Nickel Bumps 50µm for Chaotic Mixing.
FUTURE WORK – The two areas of future work for developing the μ-Brewery are cost
reductions and additional sensors. Cost reductions can come in two competing forms either
greater levels of systems integration or greater emphasis on disposable one time use design
features. Figure 12 shows the two cost reduction approaches.
The proposed μ-Brewery design utilizes an external electromagnet for the MHD pump as well as
power regulating electronics and an external laser light source for the ethanol concentration
sensor. Potentially all these features could be miniaturized and integrated at the MEMS level. If
the die yield of these highly integrated systems can be kept high and the overall system is more
reusable then a slight increase in fabrication cost could be offset by reduced reoccurring costs
and smaller device size.
An alternative approach for reducing costs would be to incorporate features that benefit from a
one time use design mindset. With this approach complicated and costly components should be
kept external of the fermenter. The current design incorporates some of these features, for
example only the electrodes for the MHD pump appear in the fermenter. The electrodes are
created using a PVD process and do not require the complications other pumping mechanisms
require. The assembled fiber optic sensor could be replaced by an in-situ optical wave guide.
With durability less critical for disposable devices, materials other then glass should be
considered, for example Polydimethylsiloxane (PDMS). See Figure 13 for cost benefits of using
polymers instead of glass.
Cost Reductions
Greater Integration
μTAS
One Time Use/Disposable
Wave Guide
PDMS
Figure 12. Different Cost Reduction Approaches
13
Figure 13. Cost Comparison of Different Polymers and Glasses [13]
The current design is limited to monitoring ethanol concentration, but conventional fermenters
monitor additional parameters such as solution PH and dissolved oxygen and carbon dioxide.
Additional μ-Brewery sensors will enhance the development of better yeast strains.
Incorporating these sensors at the MEMS level will increase the functionality of the μ-Brewery
and help the new technology displace competing conventional solutions.
Conclusion: The μ-Brewery represents the first step in the development of a new research tool
that incorporates advances in micro-fluidics, biotechnology, micro-technology, and smart
systems to improve the process by which researchers develop better strains of yeast. The μBrewery is a simpler and cheaper means of doing what once required skilled technicians,
complicated and costly equipment and a great a deal of lab space to accomplish with
conventional fermenters.
References:
1. Addison, Keith., “Is ethanol energy-efficient?” 20 April 2007.
http://journeytoforever.org/ethanol_energy.html
2. Bellon, Veronique., “Fermentation Control Using ATR and an FT-IR Spectrometer.” Sensors
and Actuators B 12 (1993): 57-64.
3. Chunxiang, Xu., et. al., “Microbial Sensor for On-Line Determination of Microbial Population
in a Fermenter.” Sensors and Actuators B 12 (1993): 45-48.
4. Doh, Il., and Cho, Young-Ho., “A Continuous Cell Separation Chip Using Hydrodynamic
Dielectrophoresis (DEP) Process.” Sensors and Actuators A 121 (2005): 59-65.
5. Eijkel, J. C. T., et. al., “A Circular AC Magnetohydrodynamic Micropump for
Chromatographic Applications.” Sensors and Actuators B 92 (2003): 215-221.
14
6. Gad-el-Hak, Mohamed. Flow Control: Passive, Active, and Reactive Flow Management.
Cambridge: Cambridge University Press, 2000.
7. Hawkes, Jermey J. and Coakley, W. Terence., “Force Field Particle Filter, Combing
Ultrasound Standing Wave and Laminar Flow.” Sensors and Actuators B 75 (2001): 213-222.
8. Krommenhoek, E. E., “Monitoring of Yeast Cell Concentration Using a Micromachined
Impedance Sensor.” Sensors and Actuators B 115 (2006): 384-389.
9. Kalinowski, T., et. al., “An Advanced Micromachined Fermentation Monitoring Device.”
Sensors and Actuators B 68 (2000): 281-295.
10. Lee, Sang-Wok and Tai, Yu-Chong., “A Micro Cell Lysis Device.” Sensors and Actuators A
73 (1999): 74-79.
11. Lemoff, Asuncion V. and Lee, Abraham P., “An AC Magnetohydrodynamic Micropump.”
Sensors and Actuators B 63 (2000): 178-185.
12. Mitsushio, M., Higashi, S., and Higo, M., “Construction and Evaluation of a Gold-Deposited
Optical Fiber Sensor System for Measurements of Refractive Indices of Alcohols.” Sensors and
Actuators A 111 (2004): 252-259.
13. Nguyen, Nam-Trung and Wereley, Steven T. Fundamentals and Applications of
Microfluidics. Boston: Artech House, 2006.
14. Oosterbroek, R. Edwin, and Albert van den Berg, Eds. Lab-on-a-Chip: Miniaturized Systems
for (Bio)Chemical Analysis and Synthesis. New York: Elsevier, 2003.
15. Tay, Francis E. H., Ed. Microfluidics and BioMEMS Applications. Boston: Kluwer
Academic Publishers, 2002.
16. Warriner, K., et. al., “Modified Microelectrode Interfaces for In-Line Electrochemical
Monitoring of Ethanol in Fermentation Processes.” Sensors and Actuators B 84 (2002): 200-207.
17. Yang, Lung-Jieh., “The Micro Ion Drag Pump Using Indium-Tin-Oxide (ITO) Electrodes to
Resist Aging.” Sensors and Actuators A 111 (2004): 118-122.
18. Zhong, Jihua, Mingqiang Yi, and Haim H. Bau., “Magnetohydrodynamic (MHD) Pump
Fabricated with Ceramic Tapes.” Sensors and Actuators A 96 (2002): 59-66.
19. Zhong, Jihua, Mingqiang Yi, and Haim H. Bau., “A Minute Magnetohydrodynamic (MHD)
Mixer.” Sensors and Actuators B 79 (2001): 207-215.
20. Zimmerman, William B. J., Ed. Microfluidics: History, Theory and Applications. New York:
SpringWien, 2006.
15
Abbreviations and Variables:
Abbreviations
LCC = Leaded Chip Carrier
FPGA = Field Programmable Gate Array
MHD = Magnetohydrodynamic
μTAS = Micro Total Analysis System
PDMS = Polydimethylsiloxane
PVD = Physical Vapor Deposition
Variables
A
Area
Magnetic Flux Density Vector
B
Diffusion Coefficient
D
Hydraulic Diameter
Dh

Dynamic Viscosity
Fo
Fourier Number
f
Darcy Friction Factor
Height
H
J
Current Flux Density Vector
Length
L
P
Pressure Drop
Volumetric Flow Rate
Q
Re
Reynolds Number
Phase Angle

Mixing Time Constant

Flow Velocity
u
W
Width
[m^2]
[T]
[]
[m]
[kg/ms]
[]
[]
[m]
[A/m^2]
[m]
[Pa]
[m^3/s]
[]
[rad]
[s]
[m/s]
[m]
Appendix:
%Donald Horkheimer
%ME8254, 2007-03-28
%Modeling and Scaling of micro-Brewery Matlab Code
for i =1:1:10
Fo(i) = 0.5; %D*tau/L^2 = Fourier Number
W(i) = (100e-6); %Channel Width [m]
H(i) = (100e-6); %Channel Height [m]
A(i) = W(i)*H(i); %Channel Cross Section [m^2]
HyD(i) = 4*A(i)/(2*W(i)+2*H(i)); %Hydraulic Diameter [m]
Dwater_ethanol = 1.24e-9; %Diffusion of water into ethanol [m^2/s]
Dwater_glucose = 0.67e-9; %Diffusion of water into glucose [m^2/s]
Dwater_sucrose = 0.52e-9; %Diffusion of water into sucrose [m^2/s]
nu = 8.9e-4; %Dynamic Viscosity of water [kg/ms]
rho = 1000; %Density of Water [kg/m^3]
16
QdotA(i) = (20e-9)/60*(2*(1/i)); %Flow rate of water [m^3/s]
QdotB(i) = (20e-9)/60*(2*(1/i)); %Flow rate of ethanol or glucose or sucrose
[m^3/s]
u(i) = QdotA(i)+QdotB(i)/A(i); %Flow velocity [m/s]
B = 1.5; %Magnetic Flux Density [T]
%E = %Electrode electric field [V/m]
sigma = 120e-4; %Electrical Conductivity of tap water [S/m]
phi = 0; %Phase angle between magnetic and electric fields [deg]
%Calculate Mixing Channel Length and Pressure Drop
tau(i) = Fo(i)*A(i)/Dwater_sucrose; %Channel Mixing Time [s]
L(i) = u(i)*tau(i); %Channel Mixing Length [m]
Re(i) = rho*u(i)*HyD(i)/nu; %Reynolds Number
f(i) = 64/Re(i); %Darcy Friction Factor
delP(i) = 2*Re(i)*f(i)*u(i)*(nu*L(i)/(2*HyD(i)^2)); %Pressure Drop Through
MHD Channel and Mixer [N/m^2]
%Calculate MHD System Needs to Overcome Pressure Drop
J(i) = delP(i)/(L(i)*B*0.5*cosd(phi)); %Time-Averaged Electrode Current
Density [A/m^2]
E(i) = J(i)/sigma; %Time-Averaged Electrode Electric Field [V/m]
V(i) = E(i)*W(i); %Time-Averaged Electrode Voltage [V]
I(i) = J(i)*L(i)*H(i); %Time-Averaged Electrode Current [A]
P(i) = I(i)*V(i); %Time-Averaged Electrode Power [W]
end
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