MEMS Fabrication Laboratory Report - University of …hork0004/ME8254microbrewery.doc · Web...

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μ-Brewery: A Lab-On-a-Chip Solution for Developing Better Breeds of Yeast

Transcript of MEMS Fabrication Laboratory Report - University of …hork0004/ME8254microbrewery.doc · Web...

μ-Brewery: A Lab-On-a-Chip Solution for Developing Better Breeds of Yeast

ME 8254 Fundamentals of MEMSBy: Donald Horkheimer

ID #: 2132334Instructor: Prof. Tianhong Cui

Teaching Assistant: Dongjin Lee2007-04-28

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. Bio-engineering 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 non-invasive 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.

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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-in-test 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

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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.

Require-ment No. Description

Importance Rank (1-10, 10 most important) Units

Lower Marginal Value

Upper Marginal Value

Lower Ideal Value

Upper Ideal Value

1Operating Temperature 10 degC 15 45 0 50

2Non-Operating Temperature 8 degC - 121 121 140

3Non-Operating Pressure 8 kPa 97 103 95 105

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Operating Fluid Reynolds Number for Chaotic Advection Device 10 Re - 10 - 100

5 Sample Fluid Volume 10 μL - 1000 - 2006 Device Diameter 9 in 4 6 0.5 17 Device Thickness 6 in 0.5 1 0.1 0.25

8Handling shock, Half-Sine, 0.5 ms 6 g - 1500 - 3000

9 Handling Drop Height 8 in - 35 - 72

10Ethanol Concentration Resolution 10 ppm - 10000 - 100

11Glucose Concentration Resolution 6 ppm - 10000 - 500

12Yeast Cell Concentration 3 cells/mL   5x10^8 1x10^5

13Fluid Network Control Valves/System 10 List - - - -

14 No moving parts 7 List - - - -15 Transparent Materials 6 List - - - -

16Bio-compatible Materials 10 List - - - -

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17Green Manufacturing Process 6 List - - - -

18MEMS Mask Feature Tolerance 3 μm - 20 - 50

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Reconfigurable "Brains" with FPGA to reduce cost 3 List - - - -

20 Reusable Device 9 Cycles 100 - 1000 -21 RoHS, Hg, Pb free 8 List - - - -22 Recyclable 4 List - - - -

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

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 coating2. Glass

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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 non-value added work such as having technicians clean lab equipment between tests which means even greater savings for the customer.

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 the diffusion coefficient, the mixing time and a characteristic mixing length and define the diffusion mixing process of a system. The characteristic mixing length is assumed to be the width and height of the channel, in other words the cross sectional area, . Generally the Fourier Number is between 0.1 and 1 for liquid microflows.

Eq. 1

The mixing time can be easily solved for by rearranging Equation 1.

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Eq. 2

Next, assuming the two fluids to be incompressible and given the desired flow rates, and channel cross section, it is possible to calculate an average flow velocity in Equation 3.

Eq. 3

Then utilizing Equations 2 and 3 it is possible to calculate the channel length.

Eq. 4

Next, the pressure drop through the two equal-length channels is calculated using Equation 5.

Eq. 5

is the Reynolds Number and is equal to , is the Darcy Friction Factor and is equal to

, is the dynamic viscosity, and is the hydraulic diameter and is equal to .

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.

Eq. 6

is the current density, is the magnetic flux density, 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

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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.

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 mTotal Channel Length: 0.08 mFlow Velocity: 0.0009 m/s

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Volumetric Flow Rate: 0.00001 L/minChannel Reynolds Number: 0.31Channel Pressure Drop: 46.9 PaVoltage Draw: 32.5 VCurrent Draw: 0.018 APower 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 μ-Brewery.

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Figure 5. Fabrication and Test Process Flow

Clean Silicon Wafers Using RCA1 and RCA2 Wet Clean Solutions

Apply Photoresist and Softbake Resist Film

Expose & Develop Photoresist Hardbake

Plasma Etch μ-Brewery Channels

Strip Away Remaining Photoresist

Grow Thermal SiO2 Electrical Insulating Layer

Remove Quartz Core Fiber Optic Jacket and Clad with H2SO4

Package μ-Brewery

Install Electromagnetic Coil for MHD

Test MHD Pump and Fiber Optic Alcohol Sensor

Repeat Photoresist Process

Repeat Photoresist, Build Chaotic Ni Mixers, Strip Resist

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Deposit Metal Electrodes for MHD using PVD

Strip Away Photoresist

Anodic Bond Si Wafer Between 2 Glass Substrates

Ultrasonically Drill Fluid Inlets and Electrical Contacts

Wafer Probe Continuity Check

Wash Bare Core With Acetone and Methanol

PVD Thin Gold Film onto Fiber-optic Cable

Coil, Assemble, Install Fiber Optic Alcohol Sensor into μ-Brewery

Dice μ-Brewery

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.

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.

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MHD Power Leads

Signal Leads

Vias

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.

Figure 8. Channel Mask: Apply Positive Photoresist, Anisotropic Plasma Etch 300 µm Depth

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

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MHD Electrode Channels

MHD Pump Channel

Solution Inlets/Outlets

Mixing Channels

Area for Fiber Optic Sensor

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.

Figure 12. Different Cost Reduction Approaches

Cost Reductions

Greater Integration One Time Use/Disposable

Wave Guide PDMSμTAS

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Chaotic Mixing Protuberances

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 μ-Brewery 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.

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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.

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Abbreviations and Variables:

AbbreviationsLCC = Leaded Chip CarrierFPGA = Field Programmable Gate ArrayMHD = MagnetohydrodynamicμTAS = Micro Total Analysis SystemPDMS = PolydimethylsiloxanePVD = Physical Vapor Deposition

Variables Area [m^2]

Magnetic Flux Density Vector [T] Diffusion Coefficient [ ] Hydraulic Diameter [m]

Dynamic Viscosity [kg/ms] Fourier Number [ ] Darcy Friction Factor [ ] Height [m] Current Flux Density Vector [A/m^2] Length [m] Pressure Drop [Pa] Volumetric Flow Rate [m^3/s] Reynolds Number [ ] Phase Angle [rad] Mixing Time Constant [s] Flow Velocity [m/s] Width [m]

Appendix:

%Donald Horkheimer%ME8254, 2007-03-28%Modeling and Scaling of micro-Brewery Matlab Code for i =1:1:10Fo(i) = 0.5; %D*tau/L^2 = Fourier NumberW(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]QdotA(i) = (20e-9)/60*(2*(1/i)); %Flow rate of water [m^3/s]

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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 Droptau(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 Numberf(i) = 64/Re(i); %Darcy Friction FactordelP(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 DropJ(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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