ece 678 introduction to biomems fall 2011 final report · pdf file1 ece 678 introduction to...

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ECE 678 Introduction to BioMEMS

Fall 2011

Final Report

Group B

Woohyuck Choi

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1. Introduction

Microfluidics is a growing field of study that has become a significant part of both research

and industry. A couple of primary benefits to microfluidic mixing are that it consumes small

amounts of valuable reagents and it mixes quickly. There are many applications for micromixers

that include: lab-on-a-chip devices, cover micro arrays, DNA sequencing, sample preparation

and analysis, cell separation and detection, and also environmental monitoring [1],[2]. Due to

this wide range of applications and many other potential applications, improving micromixers is

an important area of research.

Types of micromixers:

In general, there are two types of micromixers, active micromixers and passive micromixers.

Active Mircomixers:

The mixing process utilizes the disturbance generated by the external fields. External

disturbances like pressure, temperature, electrohydrodynamics, dielectrophoresis, electrokinetics,

magnetohydrodynamics and acoustics can be used in active mixers. The advantages of active

mixers are that mixing length is short, and they can be activated on demand. For the working of

active mixers, external power sources are required which makes the integration of mixers in a

microfluidic system challenging and expensive. Hence passive mixers are commonly used [2].

Passive Micromixers:

These mixers do not require an external energy source, and they totally rely on channel

geometry to increase vorticity and cause mixing. The types of passive mixers are: parallel

lamination, serial lamination, injection, chaotic advection and droplet. The advantages of using

passive mixers are that fabrication is simple, cost is low and they are less likely to damage

biological samples. However, passive micromixers require longer mixing lengths and have

longer mixing times than their active counterpart [2].

Methods of Mixing in Passive Micromixers:

There are two primary methods of mixing in passive micromixers which are molecular

diffusion based and chaotic advection based [2]. Increasing the contact area of the two fluids in

the channel and decreasing the diffusion path are the ways to improve molecular diffusion based

mixing [2]. Two primary methods to decrease the diffusion path are making narrow channels and

using hydrodynamic focusing. Hydrodynamic focusing is where a fluid is introduced tangential

to the initial fluid in the channel such that the width of the initial fluid is decreased [3]. Chaotic

advection involves manipulating the laminar flow in a channel such that one is forcing fluids

across their natural boundary in the channel [2]. The simplest way to achieve this is by adding

specific 3-D obstacles to the channel [2].

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2. Design and Modeling

Purpose:

The purpose of this module is to optimize the performance of a microfluidic mixer by

changing the dimensions of the channel. The objective is to obtain the highest percent mixing,

which means the lowest σ value, while keeping the pressure drop of the entire channel below

1Kpa/mm.

Introduction:

Previous to this exercise our group has already decided on a basic design for our channel.

We have also identified three variables with five different values for each variable which we will

manipulate in order to attempt to optimize our mixer. An image of a single unit of our mixer can

be seen in Figure 1 and a table of the optimization variables can be seen in Table 1.

Figure 1: One unit of the “serpent” mixer Table 1: A list of the different values for optimization.

showing the three variables we Five distinct levels were chosen for each

altered. variable. The initial values set for each variable

are highlighted in red.

The values for optimization were chosen based on one initial experiment that was run using the

initial values denoted in Table 1. The model was run in CFD-ACE+ in two dimensions instead of

three in order to be able to use a finer, more accurate, mesh and to lower simulation times. The

model was run with a 3um triangular mesh for Re=1. The results of this simulation at the outlet,

4910um, were 92.83 percent mixing and a pressure drop of 6569Pa. The pressure drop was too

high (greater than 1KPa/mm) thus we knew we needed to lower the pressure drop of our channel.

We knew that increasing the dimensions of the channel would lower the pressure drop. This is

why most of the optimization values chosen are larger than the initial values.

Procedure:

The method that we chose in order to best optimize our channel is to change one variable

at a time and optimize that variable. Then for the second variable we set the first variable to its

optimized value, and optimized for the second variable and so on. We felt that this would give us

good optimization without having to run too many models, as one would have to do in factorial

optimization.

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6

Variable 1 30um 35um 40um 45um 50um --------

Variable 2 25um 30um 35um 40um 45um 50um

Variable 3 25um 30um 32um 35um 38um 40um

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For all optimization we ran the models in CFD-ACE+ in two dimensions for the same

reasons as previously stated. All of the models were run with a 3um triangular mesh and for

Re=1. The values assigned to the simulator before each run can be seen in Table 2.

CFD-ACD+

Variable Value Assigned

Reference Pressure 100,000 Pa

Liquid Mixing Rule Water

Density (ρ) 1,000 kg/m^3

Viscosity (μ) .001 kg/m-s

Diffusivity 1E-10 m^2/s

X-Direction

Velocity

.00125 m/s (Re=.1)

.0125 m/s (Re=1)

.125 m/s (Re=10)

Dye 1 Molar Concentration in Water

No Dye 0 Molar Concentration in Water

Temperature 300K

Iterations 1500

Convergence

Criteria 1.00E-06

Minimum Residual 1.00E-18

Differencing:

Velocity Upwind

Species 2nd Order Limiter with .01 Blending

Solvers:

Velocity CGS + Pre (500 sweeps, .0001

criterion)

P Correction AMG (50 sweeps, .1 criterion)

Species CGS + Pre (500 sweeps, .0001

criterion)

Table 2: Values assigned in the CFD-ACE+ Simulator

The equation for calculating percent mixing is: %𝑚𝑖𝑥𝑖𝑛𝑔 = (1− 𝐴𝑣𝑒𝑟𝑎𝑔𝑒1 − 𝐴𝑣𝑒𝑟𝑎𝑔𝑒2 ) ×100 where Average 1 is the average molar concentration of the top half of the channel, and

Average 2 is the average molar concentration of the bottom half. The equation used to calculate

σ is:σ =(100−%𝑚𝑖𝑥𝑖𝑛𝑔 )

100×

1

2. Also the values of the pressure drop of the entire channel, and

vorticity in the channel are investigated in CFD-View.

Once we had all of the optimization data we decided to compare our mixer to a straight

“T-Mixer” of approximately the same dimensions and effective mixing length of our “serpent”

mixer. Doing this would allow us to see how well our mixer performed compared to a strictly

diffusive mixer. The dimensions of the “T-Mixer” were 40um wide and 17519um long. The

simulation was run in two dimensions with a 3micron triangular mesh for Re=1.

The X-Direction velocities were

calculated for the Reynold’s numbers of

0.1, 1, and 10 using the equation for

Reynold’s number: 𝑅𝑒 =𝜌𝑣𝐷

𝜇. This

equation is then solved for velocity:

𝑣 =𝑅𝑒𝜇

𝜌𝐷. All of the values are known

except D which is the hydraulic diameter.

The equation for hydraulic diameter is :

𝐷 =4𝐴

𝑈 where A is the area of the channel

and U is the wetted perimeter. For our

200um square inlet D=80microns. After

each simulation is run the results of the

simulation are imported into CFD-View.

In this program x-cuts are made at certain

positions along the channel and the

H20_Molar concentration at each of these

x-cuts are plotted. The x-cuts that we

made in our channel are at the following

lengths along the channel: 0um, 750um.

1790um, 2830um, 3870um, 4910um.

These values were chosen such that the

cuts would be made in the same area of

each unit. The data from these plots is

then exported to MS Excel where percent

mixing and σ can be calculated.

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After we were done with optimization the fully optimized channel was extruded in three

dimensions such that it would be 50um deep. This three dimensional model was then meshed

using a 5um triangular mesh. We attempted to use the 3um triangular mesh for the three

dimensional models since we had used this meshing for the two dimensional ones; however, the

simulator reported a memory error due to the fact that the 3um meshing created too many cells in

the three dimensional channel. The smallest meshing size we could use that did not report an

error was 5um, thus we selected this value. For the optimized three dimensional models we ran

simulations for three different Reynolds numbers: 0.1, 1, and 10. The results of these simulations

were imported into CFD-View and the %mixing, σ, pressure drop, and vorticity for the channel

were obtained in the same fashion as they were for the two dimensional models.

Results:

Optimization:

The results for the optimization of variable 1 can be seen in Figure 2 below. A table of

the values obtained can be seen in Table 3. For this optimization variable 2 and variable 3 were

set to be 30um while variable 1 was adjusted.

For this variable we chose 40um as our optimized value due to the fact that is achieved the

highest percent mixing while being below the 5KPa limit.

For variable 2 we set variable 1 to be 40um and variable 3 to be 30um and varied variable

2. Figure 3 shows the graphical results of this optimization and Table 4 shows the values.

0

0.1

0.2

0.3

0.4

0.5

30um 35um 40um 45um 50um

σ

Variable Value

σ for Variable 1 at Outlet

0

0.1

0.2

0.3

0.4

0.5

25um 30um 35um 40um 45um 50um

σ

Variable Value

σ for Variable 2 at Outlet

Variable Value

Percent Mixing σ

Pressure Drop (Pa)

30um 92.83 0.035865 6569

35um 91.16 0.044183 5634

40um 89.07 0.054644 4989

45um 87.01 0.064927 4536

50um 85.48 0.072621 4180

Variable Value

Percent Mixing σ

Pressure Drop (Pa)

25um 89.84 0.050798 5449

30um 89.07 0.054644 4989

35um 87.78 0.061084 4712

40um 86.72 0.066408 4523

45um 86.66 0.066713 4390

50um 86.73 0.066375 4302

Figure 2: A plot of σ vs. variable value for variable 1.

All values are taken at the outlet (4910um)

Table 3: Values used in Figure 2. The value in red is

the selected value for optimization.


All values are taken at the outlet (4910um) Table 4: Values used in Figure 3. The value in red is


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We chose 30um as the optimized value for this variable since it had the highest percent mixing

while also fulfilling the pressure requirement.

For variable 3 we set variable 1 to be 40um and variable 2 to be 30um and varied variable

3. The graphical results of this optimization can be seen in Figure 4. A table of the values is

given in Table 5.

We chose 30um as the optimized value for variable 3 due to the highest percent mixing while

remaining below the pressure drop cap.

T-Mixer:

The results at the outlet of the “T-Mixer” were: 91.4% mixing and 8333Pa pressure drop.

Optimized Serpent Mixer:

Now that we had all of the levels for all of the variables we made our optimized mixer.

An image showing all of the dimensions of a single unit of the optimized mixer can be seen in

Figure 5.

Figure 5: Dimensions of optimized channel. All numbers shown are in microns

0

0.1

0.2

0.3

0.4

0.5

25um 30um 32um 35um 38um 40um

σ

Variable Values

σ for Variable 3 at OutletVariable

Value Percent Mixing σ

Pressure Drop (Pa)

25um 89.54 0.05231 5100

30um 89.07 0.054651 4990

32um 88.60 0.056992 4882

35um 88.13 0.059333 4802

38um 87.43 0.062871 4724

40um 86.80 0.065992 4683


All values are taken at the outlet (4910um)

Table 5: Values used in Figure 4. The value in red is


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The graphical results the optimized channel under the Re=.1 conditions can be seen in

Figure 6. Table 6 shows the values obtained from this simulation.

The results of the optimized channel under the Re=1 condition are graphed in Figure 7

and shown in Table 7.

The results of the optimized channel under the Re=10 condition are graphed in Figure 8 and

shown in Table 8.

0

0.1

0.2

0.3

0.4

0.5

0 750 1790 2830 3870 4910

σ

Downstream Position (um)

0

0.1

0.2

0.3

0.4

0.5

0 750 1790 2830 3870

σ

Downstream Position (um)

0

0.1

0.2

0.3

0.4

0.5

0 750 1790 2830 3870 4910

σ

Downstream Position (um(

Downstream Position

Percent Mixing σ

Pressure Drop (Pa)

0um 3.26 0.48369

1053

750um 51.61 0.241956

1790um 85.20 0.073986

2830um 95.51 0.022429

3870um 98.56 0.007187

4910um 99.58 0.002108

Downstream Position

Percent Mixing σ

Pressure Drop (Pa)

0um 3.17 0.484164

10700

750um 47.44 0.262803

1790um 77.55 0.112261

2830um 90.27 0.048634

3870um 95.81 0.02093

4910um 98.37 0.008168

Downstream Position

Percent Mixing σ

Pressure Drop (Pa)

0um 3.20 0.484011

130,800

750um 64.27 0.178647

1790um 93.13 0.034345

2830um 98.22 0.008909

3870um 99.52 0.002396

4910um 99.90 0.000504

σ vs. Downstream Position Re=.1

σ vs. Downstream Position Re=1

σ vs. Downstream Position Re=10

Figure 6: Graphical results of σ vs. channel length

for Re=0.1

Table 6: Values used in Figure 6.


for Re=1



for Re=10.


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Discussion:

There are quite a few interesting aspects of our channel that we learned by going through

this optimization process. The fist aspect to note is that as we constricted the individual

dimensions of the channel the percent mixing always increased, but so did the pressure drop.

This is what we expected due to the fact that constricting the dimensions lowered the width over

which diffusion could take place. Due to the fact that there was a maximum pressure drop of

1KPa/mm we could only constrict these dimensions so far. In order to fully optimize the channel

we chose each variable such that it was the smallest possible while still following the pressure

drop guidelines.

When the channels were extruded in three dimensions a couple of issues arose. The first

issue was that we could not use the same size meshing as we had for optimization. By having to

use a larger meshing the simulator overestimated the mixing in the channel. This is why the

values for the three dimensional models are larger than the two dimensional ones. The other

issue was that the pressure in the channel approximately doubled for the three dimensional

models. Since we had optimized for the highest percent mixing, which was also the highest

allowed pressure, in two dimensions this doubling of the pressure put us well over the pressure

limit. We were unaware that this was going to happen, and did not have sufficient time to correct

the pressure drop.

Comparing our mixer to the “T-Mixer” also provided some interesting findings. When

compared to the “T-Mixer” our “serpent” mixer was worse by 2.33% mixing but had 3343Pa

lower pressure drop. One possible reason for the lower mixing performance is that the “serpent”

mixer is not 40um all the way through the channel. It varies from 40um to 65um in each diffuser

with 30um connections between diffusers. The overall effect of this is that we sacrifice a small

amount of mixing for a significant lowering of the pressure drop. Since our mixer performed

very closely to the “T-Mixer” we modeled it suggests that our mixer is primarily a diffusive

mixer. This also makes sense from the standpoint that there were no obstacles in the channel that

would cause a split and recombination of the flow.

The results from the three dimensional model with the three different Reynolds numbers

also told us a little bit about the mixing that was occurring in the channel. The Re= 0.1 case

provided greater mixing than the Re=1 case. This further supports the idea that the mixer is

primarily diffusive in nature since we achieved better mixing for a less turbulent flow. However,

the Re=10 case had better mixing than either of the other two cases. This may be due to the fact

that for large Reynolds numbers there may be a race track effect around the corners in our

channel. However, due to the large meshing of these three dimensional models the data from

these simulations is not very accurate.

Conclusion:

The “serpent” mixer design that was simulated is a primarily diffusive mixer. However,

due to the sharp bends in the channel there is some race track effect that is occurring that

becomes more pronounced at large Reynolds numbers. According to the simulation we expect to

obtain approximately 89% mixing in our channel for the Re=1 case. This number should increase

slightly for the Re=0.1 and Re=10 cases. However, the simulator also reported that we are going

to have high pressure drops which may cause the PDMS channels to rip and or the fluid to come

out of the channel. Also due to some inherent error in the simulator and the fact that the

dimensions obtained after fabrication will not be exactly what they were when we ran the

simulator we expect to see a drop in the percent mixing when the device is actually tested.

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3. Fabrication of Device

Mask layout in AutoCAD:

AutoCAD was used to design the mask of our mixer using the dimensions from the final

design. This AutoCAD design was then sent out for fabrication of mask. For a 3” diameter wafer

we will require a 4” square mask. SU-8 is a negative photoresist and thus to get a negative of the

AutoCAD layout we will use a dark field chrome mask.

SU-8 Master Fabrication:

SU-8 master was fabricated for PDMS casting. MicroChem’s SU-8 resist was used on a

3” silicon wafer. The substrate was cleaned with an Acetone/methanol/DI water rinse followed

by a piranha clean. Then the wafer was dehydrated for 10 min at 150oC on a hotplate. A layer of

SU-8 was spin coated with a thickness of ~50 μm. A soft bake was done, using a leveled hot

plate, at 65oC for 5 min and ramped to 95

oC for 45 min, and then was allowed to cool down to

room temperature. The exposure was done using the mercury I-line (365 nm) high pass filter at

exposure energy of 175 mJ/cm2, for 35 sec. A glycerin layer was used in between the SU-8 wafer

and mask to reduce diffraction effects. Now, a post exposure bake was done which is similar to

the soft bake. MicroChem SU-8 developer was used to develop away the unexposed resist. The

wafer was developed for 2 hrs and then an IPA rinse was performed to confirm the completion of

development process. An O2 plasma etch was then performed to etch away a small layer from the

top of the SU-8. The final wafer obtained was free of cracks and non uniformities.

PDMS Casting:

SU-8 patterned wafers were coated with Sigmacote and left to air-dry for 30 min to

facilitate mold release. Next the PDMS was mixed at a 10:1 (m/m) ratio of elastomer base to

curing agent. PDMS must be mixed until it becomes milky-white due to the air bubbles stirred in

it. Degassing of PDMS component mixture is necessary for the removal of air bubbles, which

may degrade quality of the replication. Degassing was done by using a vacuum desiccator for 15

min. Then the PDMS was poured over the patterns directly, with care taken to avoid formation of

additional air bubbles. Again a process of degassing was done to remove any air bubbles formed

while transferring PDMS. The degassed PDMS was then cured using a hotplate at 80oC for 2hrs.

The curing time is dependent on the thickness of PDMS and the curing temperature. Finally, the

cast and cured PDMS is slowly peeled away from the mold, taking care not to damage the SU-8

master.

Bonding:

Bonding with oxygen plasma is one of the best ways to bond PDMS substrate with glass.

We used a corona discharge wand which ionizes air to treat PDMS surface. Inlet and outlet holes

were made by piercing a 14 gauge syringe tip in the final mixer cast at the points of the two fluid

inlets and the single outlet, respectively. Piranha clean was performed to clean the microscope

glass slides and then it was rinsed with DI water and then dried with nitrogen gas. The PDMS

casting was also washed using DI water. With the bonding side up, the clean glass slide and the

PDMS sample were placed on a non-conducting surface. The wire electrode was moved back

and forth approximately ¼ inches above the bonding surface for 20 sec. Finally the treated

surface was pressed together and left undisturbed for 2 hrs for complete bonding to take place.

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4. Device Characterization

Structural Characterization:

The device was characterized under a microscope prior to plasma bonding. The channel

dimensions were recorded by placing the PDMS microchannel under the microscope. Figure 9

shows some of the photographs taken. It can be seen that the fabricated mixer is almost identical

to the designed mixer. There is only a few microns variation present in the final fabricated mixer

as compared to the designed one. The sharp corners turned out to be rounded as anticipated, due

to the non precise photolithography and SU-8 fabrication while working at small dimensions of

the order of 20 µm.

A ~1mm sliced cross section of the mixer along the z direction was used to observe and

characterize the channel cross-sectional features. The total height of the PDMS cast mixer

channel is shown in figure 9(B). It was measured to be 50.1 microns, which was only 0.1

microns larger than expected. This shows the accuracy of the recipe chosen to make the PDMS

molds. Figure 9(C) displays the fabrication of the PDMS microchannel at the regions of the

optimization variables chosen for the design. For variable one the dimensions are 40.1 microns

which is an increase by only 0.1 microns from the actual designed dimension. For variable two

the measured dimension was 33.54 microns which is more by 3.54 microns compared to the

actual design. Finally, for the third variable we got the fabricated dimensions as 30.31 microns

which is again just 0.31 microns larger than the actual design. These are very minor changes

occurring from designed micromixer to the fabricated one. This again shows the accuracy of the

SU-8 master fabrication and the PDMS casting process.

Figure 9:

(A) Channel top view

(B) Cross-sectional view of channel

wall

(C) View of the variables that were

optimized.

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Overall, the casting shows little deviation in the dimensions from the CAD designs. Channel

dimensions differed from the AutoCAD and the CFD-GEOM designs mainly due to variations in

the exposure, etching, and casting procedures.

Fluid Flow Characterization:

The mixing characteristics of the micromixer were measured using a fluorescence dye.

During testing, a syringe pump was used to deliver water to one inlet and the dye solution to the

other. For the Reynolds number equal to 1, the flow rate was calculated to be 3.75 µL/min.

Images of mixing for Re=1 are shown in figure 10. The entrance image shows the difference

between Fluorescein and water. With changes in the intensity of the two liquids, as we proceed

along the channel length, progressive mixing can be calculated. 100% mixing is achieved when

the channel appears to only have one bright fluid in it. ImageJ was used to analyze the images for

percent mixing. Intensity values at each pixel were plotted versus the width of the channel. The

data for the channel was then extracted from these plots and was used to calculate percent mixing

and σ.

Figure 10: Images of subsequent mixing through channel. At 15.8 mm we can see that ~100% mixing has occurred.

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Results and Discussion:

After fabricating the micromixer and finding out the new dimensions of the

microchannel, a new CFD-GEOM file was created with the dimensions of the final device. This

was done to compare the results obtained for the simulations run using the CFD tools and the

actual device. The conditions for this simulation were the same as before, but the mesh size used

in this case was 2 microns in order to get accurate results and save time.

At ~5 mm channel length the mixing percentage calculated from the simulated model and

the experimental data is shown in table 9.

Re=.1 Re=1 Re=10

Simulated %Mixing (2um mesh) 95.32 73.70 71.40

Experimental %Mixing 77.10 72.03 79.80

Difference 18.22 1.67 -8.40

Table 9: Comparison of % Mixing At 4910um Downstream

As seen from the table, the results from simulation and experiment for Re=1 are almost

matching. Whereas for the case of Re=0.1 the simulation results show an exaggerated percent

mixing. This error can be possibly accounted for the inaccurate simulation mathematics or

meshing layout. One unexpected result of the simulation was the percent mixing for the Re=10

case was the lowest of the three Reynolds numbers tested. In previous simulations and the

experimental results, the Re=10 case actually had a higher percent mixing than the Re=1 case.

Even though this was an unexpected and experimentally unverified result, the difference between

the simulator and the experimental data was still only 8.4% which is within acceptable range.

Figure 11 shows the graph for σ vs. downstream position for different Reynolds numbers.

Also figure 12 displays the variation in the value of σ with change in Reynolds number. It can be

seen that the mixing performance is worst for Re=1 whereas we get good mixing for Re=0.1 and

10. Good mixing at low Reynolds number is due to high amount of diffusivity between two

fluids. Also for Re=10 we get good mixing because of the race track effect present at the

curvatures as shown in Figure 13. Table 10 shows the comparison of the mixer for different

Reynolds numbers at different positions along the channel length. It also displays the y (90) for

the three cases i.e. the channel length at which the mixing percent reaches 90% and σ=0.05. The

y(90) was calculated for each channel by fitting a 4th

order polynomial to each curve and solving

this polynomial for σ=0.05.

13

In order to further investigate why the Re=10 case mixes better than the Re=1 case the

vorticity in the channel was investigated. Figure 13 shows a plot of the vorticity in the channel

and indicates that vorticity is created at each of the bends in the channel. This is likely due to the

race track effect since it is a sharp bend in the channel and the inner path is shorter than the outer

one. The race track effect causes some mixing to occur that is not purely diffusive and should be

more pronounced at higher Reynolds numbers since the flow is faster. This would explain why

the Re=10 case mixed better than Re=1.

Figure 13: Vorticity in the optimized serpent mixer with Re=1.

Distance along

channel (µm)

Re = 0.1 Re = 1 Re =10

750 48.14% Mixing 53.40% Mixing 45.40% Mixing







y (90) 10895 µm 12642 µm 10729 µm

Figure 12: Plot for σ vs. different Reynolds numbers

Figure 11: Plot for σ vs. downstream position

Table 10: Percent mixing for different Reynolds numbers at different distances along the channel. The calculated

distance at which 90% mixing will occur is also shown.

Figure 11: Plot for σ vs. downstream position

14

5. Conclusion

The “serpent” mixer was initially designed and tested using the CFD software in order to

see what the expected performance of the channel would be. From these simulations we

discovered that we would achieve approximately 89 percent mixing at five millimeters into the

channel for Re=1 and a pressure drop of approximately 10.7 KPa. Due to meshing constraints,

inherent error in the simulation software, and potential deviation in dimensions due to fabrication

we expected that the actual performance of our mixer would be lower by up to 20 percent.

The SU-8 master fabrication and PDMS casting techniques were very precise. The

fabricated model only deviated from the mask dimensions by a few microns. It was also noticed

that the sharp corners in the device got rounded slightly. Neither of these issues will cause a

significant deviation from the simulated mixer results.

Once the exact dimensions of the fabricated channel were known the geometry file was

changed to match these dimensions and simulated again. The results of this simulation were

compared with the actual experimental data and it was found that there was a maximum

deviation of approximately 18 percent from simulated to experimental data which is close to

what we estimated the difference would be. For the experimental results at 1.06 cm into the

channel the maximum percent mixing that we achieved was 86.55% for the Re=0.1 case. This

was followed by Re=10 and the worst mixing was seen in the Re=1 case. The fact that Re=0.1

had the highest percent mixing suggests that the mixer is primarily diffusive but at higher

Reynolds numbers there is the race track effect that increases the mixing.

The performance of the “serpent” mixer was fairly good. At one centimeter into the

channel for approximately the same Re and Pe values the staggered herringbone mixer achieved

approximately σ=.04 which corresponds to about 92% mixing [4]. Under the same conditions the

“serpent” mixer achieved approximately 87% mixing, which is only a 5% decrease in mixing.

However, the staggered herringbone mixer uses complicated 3-D obstacles to cause chaotic

advection in the channel [4]. The “serpent” mixer is a purely planar design which makes it easier

to fabricate and it achieves almost the same mixing. More testing would need to be done to

determine how well the mixer would perform under different circumstances, such as adding

particles to the fluid, but all signs indicate that the “serpent” mixer is a very effective

microfluidic mixer.

15

References

[1] J. Ottino and S. Wiggins, "Designing optimal micromixers," Science (New York, N.Y.), vol.

305, pp. 485, 2004.

[2] N. Nguyen T. and Z. Wu, "Micromixers - a review," Journal of Micromechanics, vol. 15,

2005.

[3] S. Hardt, K. S. Drese, V. Hessel and F. Schonfeld, "Passive micromixers for applications in

the microreactor and μTAS fields," Microfluidics and Nanofluidics, vol. 1, pp. 108-118, 2005.

[4] A. D. Stroock, S. K. W. Dertinger, A. Ajdari, I. Mezic, H. A. Stone and G. M. Whitesides,

"Chaotic Mixer for Microchannels," Science, vol. 295, pp. 647-651, January 25. 2002.

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