ENMA490 Capstone: Design of Microfluidics Mixer By: Elyse Canosa, Josh Davis, Colin Heikes, Gao Li, Pavel Kotlyarskiy, Christina Senagore, Maeling Tapp, Alvin Wilson
Outline Motivation for Microfluidic Mixing Background on Fluid Dynamics and Mixing Targeted Design Goals Definition of Channel Geometry Description of Fluent Program Used for Simulations Proposed Prototype Testing Societal Needs Simulation Results Conclusions/Future Work
Motivation MEMS devices are desired for: biotechnology chemical engineering pharmacology energy production MEMS for chemical analysis need microfluidics DNA purification and amplification Mixing is needed in microfluidic devices Laminar flow regime minimizes interfacial area
Background Fluid Dynamics Reynolds number Above ~4000 turbulent viscous flow Below ~2000 laminar viscous flow Typical 10 micron channel size Reynolds number is 10E-2 Our 1mm size channels have Reynolds numbers ~1000 Conservation of Mass Navier Stokes Equation Simplified for non-circular Pouiselle flow No Slip condition For rectangular tube Darcy-Weisbach equation ρvl VL μ Re =, ν = μ ν ρ Dρ + ρ V Dt dp * 1 2 Δp * = ( ) L = f ( ρv ) dx 2 Δp (Re = ( D D h ) f = 0 p* p ρg R μvl ( ) 2b * 2 2 h b) L D h Area D h 4 Perimeter
Background Cont d Mixing Dominated by inter-diffusion Taylor diffusion Fick s 2 nd Law in a moving coordinate system t c 2 + u c = D In order to increase diffusion increase area of unit volume by stretching Define mixing efficiency Uniformity of spatial variation in concentration c
Design Goals Design a microfluidic mixing channel Determine relationship of following on mixing efficiency and pressure drop number of rows spacing radius of curvature of stars nozzle angle size of stars/density of stars Channel must have a pressure drop value that gives a minimum outflow rate: 1microL per second Optimize mixing efficiency Defined with standard deviation Develop theoretical understanding of the determined relationships We will discuss normalized values for mixing efficiency and pressure drop We divide by length Both values are linear with channel length as shown
Parameters Spacing in x and y Size/Density of stars Radius of curvature of stars Number of rows Nozzle angle Nozzle Angle Zoomed In Mesh
Overview of Results Most important parameters for mixing will be Number of Rows of stars Star Size/Density Largest contributions to Pressure drop will be Number of Rows of stars Star Size/Density
X Spacing
Y Spacing
Star Size/Density
Radius of Curvature
Number of Rows
Nozzle Angle
How Fluent Works How does it find an answer? Equations Boundary Conditions Convergence Limitations Shape Grid Size
Finite-Volume Method Fluent runs conservation of mass and momentum equations at each point of a grid that was set up for a mesh, assuming each side of a particular rectangular cell sums up to zero in mass flow This is how Fluent calculates mass flow rate through complicated meshes Zoomed In Mesh
Boundary Conditions Defined at the inlet, walls, and outlet Allows Fluent to solve the conservation equations at these locations and interpolate the results in between
Convergence Once the reduced residuals are 10-3 or less, the solution has converged If the reduced residuals do not reach this level, then the program stops after a user defined number of intervals All of our results converged
Shape Fluent and Gambit have the ability to make shapes that are more finely resolved than their counterparts in real life Radius of curvature investigated to ensure that lithography limitations would not impact Fluent results
Grid Size Needs to be sufficiently big to include all regions accurately We tried different grid point densities and they did not have a noticeable effect on results Larger grid = longer computation time 1pt every 10 microns along features 1 pt every 5-205 microns in bulk
Design of Mixer Prototype created from Fluent simulations Two inlets with one outlet Channel features from optimized results
Design of Mixer: Fabrication of Mixer Create CAD drawing from Fluent SU-8 8 photoresist mold Spin-coating of SU-8 Soft lithography Polydimethylsiloxane channel Pre-polymer and curing agent Dessicator Plasma treatment to join glass slide
Design of Mixer: Testing of Prototype Gravity pump set-up to create adequate pressure (1/5 atm) Two Inlets with metal couples Fluorescent aqueous solution in one inlet Laser-Scanning Microscope imaging of mixing Resolution of nm Generated from intensities and reconstructed into a graphical image Expect steady-state state condition
Societal Needs Development of smaller and efficient passive micromixers will enhance the success of many MEMS that incorporate these components lab-on-a-chip idea, a proposed goal for microfluidic systems integrate various aspects of modern biology and chemistry labs on a single microchip Miniaturization of their processes leads to: Reduction of sample size Decrease of assay time Minimization of reagent volume needed Examples of certain biological/chemical procedures that will benefit DNA analysis Enzyme assays
Societal Needs DNA Analysis DNA purification is a necessary step involved in conducting effective DNA analysis Micromixer: the cellular structure to create a lysate (contents released from cell) Mixes the solution that contains the DNA sources with a buffer solution, which attacks the cell membranes Releases the DNA from its host cells Enzyme Assays Conducted to determine an enzyme s s reaction kinetics Cell lysis, protein extraction by diffusion and detection by fluorescence Passive microfluidic mixer in this process is beneficial for the cell lysing procedure.
Thoughts on Implementation Fabrication process does not impose any significant harmful effects on those that will be carrying out this procedure It will be of great benefit to implement the new design of this PDMS microfluidic mixer because of the benefit it will bring to society in improving the performance of potential lab-on-a-chip applications
Is Fluent Effective? We ran a simple rectangular channel with a width of 1mm We used the Darcy- Weisbach equation to calculate pressure drop for various aspect ratios Pressure Drop (Pa) 10000 1000 100 10 Pressure Drop vs. Aspect Ratio y = 159.22x -1.6654 R 2 = 0.9983 Pressure Drop Power (Pressure Drop ) 1 0 2 4 6 8 Aspect ratio, height/width
Simulation Results: Size of Star & Density Remember Darcy- Weisbach equation Δp (Re = ( D D h ) f μvl ( ) 2b * 2 2 h b) Figure 1a Figure 1b Higher Density of stars (smaller stars) bends flow more Higher densities (smaller stars) contribute more to f, the friction factor Figure 1c Figure 1d
Simulation Results: Radius of Curvature Figure 2a Figure 2b Figure 2c Figure 2d Expected higher mixing for more curvature Dead space developes Dead space causes more pressure drop
Simulation Results: X Spacing Remember Darcy- Weisbach equation Δp (Re = ( D D h ) f μvl ( ) 2b * 2 2 h b) Figure 3a Figure 3b Decreased spacing doesn t increase flow confinement Longer spacings give longer mfp and less resistance to flow Figure 3c Figure 3d
Simulation Results: Y Spacing Figure 4a Figure 4c Figure 4b Figure 4d Remember Darcy- Weisbach equation Δp (Re = ( D D h ) f μvl ( ) 2b * 2 2 h b) Decreased spacing doesn t increase flow confinement Longer spacings give longer mfp and less resistance to flow Pressure drop in y has less effect No slip condition
Simulation Results: Nozzle Angle Δp (Re = ( D D h ) f μvl ( ) 2b * 2 2 h b) Figure 5a Figure 5b No clear trends within error of measurements Flow is more laminar through aperture 0 degree angle has largest aperture Figure 5c Figure 5d
Simulation Results Rows of Stars Figure 6a Figure 6c Figure 6b Figure 6d Pressure Drop scales increases with more rows Combination of rows is like resistors in series Trend is opposite of expected for mixing efficiency Fluent used 2.88E- 5 m^2/s as selfdiffusivity of water Actual is 2.4E-9 m^2/s Actual for dye is 4.4 E -10 M^2/s
Before Correction look at stream lines When proper diffusivities are included our channel does increase mixing Important result Corrected Values for Diffusivity mfp of molecule diffusing compared to the channel feature spacing P = 2.76Pa ME = 9.23% P = 369.32Pa ME = 31.89%
Conclusions Most important variables for mixing are spacing/density and Number of Rows These two factors also have the largest effect on pressure drop Can have drop of 19400 Pa at 2m If mixing scales linearly with number of rows, need 44 rows for 99.87% efficiency If pressure drop is linear this corresponds to 800 Pa pressure dropd If there is increase in slope after 11 rows, drop is >1571 Pa Need to consider the strength of PDMS features Can features withstand 19400 Pa drop? Corresponds to ~1.5mN per pillar in first row for 1mm^2 cross section with 80 micron pillar Anomalous result for rows of columns illustrates limits of feature spacing Features can impede diffusion if molecules will be scattered by feature before they are scattered by media molecules Need to have feature spacings that are smaller than mfp of a unit volume of fluid in order to bend the volume to increase surface area
Future Work Characterize Fluent more effectively Only looked at matching of pressure drop with analytical results Needed to also consider the species transport The value used for water self diffusion was wrong Consider non-periodic spacings Build prototypes Stress test micron scale pillars to determine channel reliability
Acknowledgements Dr. Phaneuf Dr. English Dr. Rubloff Dean Berlin Tom Loughran Dr. Heetderks Dr. Shy-Hau Guo