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Lecture 5 Mixing in Microfluidics 2016A ! E 155! Mixing in Microfluidics! Fawwaz Habbal! 1 Reference Book “Micromixers – Fundamentals, Design and Fabrications” Author: Nam-Trung Nguyen William-Andrew Inc., 2008 2 Mixing Need to mix multiple streams of fluids in micro channels or chambers with: – short mixing length (and time) – operational simplicity Methods for Mixing Methods for mixing fluids in macro scale channels have been studied over many years. Mixing comprises three mechanisms of mass transfer: – molecular diffusion, – eddy diffusion, – bulk diffusion. Mechanisms for Mixing Macroscale: turbulence can generate large eddy and bulk diffusions while the molecular diffusion is negligible. Microscale: the molecular diffusion more important while the eddy diffusion and the bulk diffusion components are limited under the low Reynolds number condition. § Mixing at the microscale is generally slow and time inef<icient. Types of Mixing Methods Passive mixing Accomplished by driving <luids through channels with three-dimensional channel geometries. Active mixing Based on chaotic advection Achieved by periodic perturbation of the low ields. Chaos can improve the mixing ef<iciency Mixing Mixing occurs due to: • Brownian motion - Diffusion • Taylor Dispersion • Chaotic Advection 7 1 - Diffusion 8 Diffusion • Particles start moving at random • Assumption: each step is equally probable • The direction is random and is not related to the previous step 9 Diffusion Stokes - Einstein Equation Diffusion of a particle (gas, fluid), of size (a) Translational Diffusivity K BT Dt = 6πηa Rotational Diffusivity K T D = B r 8πηa3 10 Diffusion in Fluids Very short diffusion time 1 x2 τ = 2 D Or: < x2 >= 2Dτ And approximately: D = diffusion constant x = 2Dτ X = diffusion length τ = diffusion rate! 11 Diffusion in Fluids BUT: Laminar flow limits fluid mixing. Highly predictable diffusion has enabled a new class of microfluidic diffusion mixers 12 Mixing By Diffusion Time required to travel distance x by diffusion is = x2/2D Example: – For channel width of 70 µm and velocity 1 cm/s, ! fluorescein (D = 3 " 10-6 cm2/s) will take 2 seconds to mix over channel length of 2 mm – This puts an upper limit of 100 µm width for channels – Note for driven fluids:! Sample can spread out in width due to diffusion while being carried by electro-osmosis and drifted by electrophoresis 13 Mixing By Diffusion 14 2 - Taylor Dispersion 15 Taylor Dispersion It can be viewed as a driven diffusion Fluid is moving at a given speed. Motion could be caused by a pressure field 16 Taylor Dispersion In a pressure driven flow (parabolic) the fluid is stretched more in the middle of the channel, so it looks as if it is “diffusing” in the axial direction. For 2 dimensional analysis: 2h2 v2 In parallel plates (2h separation): D* = D + 105 D R 2v2 For channel of radius R: D* = D + 48D 17 Taylor Dispersion For 3 dimensional analysis: For a channel of width W much bigger than the height: W W 2 v D* = D + 0.0022 D 18 3 - Chaotic Advection 19 Chaotic Advection Chaotic: Velocity field leads to a chaotic response in the tracing particle. Advection: materials transported A flow field can be chaotic even if the flow is laminar A chaotic flow is NOT turbulent. Under chaotic advection, particles diverge exponentially and thus enhance mixing 20 Path Lines of Particles 21 Reminder – Some terms For channel of characteristic length “L” and flow velocity v, density ρ Reynolds number MassTransport ρvL Re = = MomentumTransport η Peclet number: AdvrctiveMassTransport vL Pe = = DiffusiveMassTransport D 22 More on these Numbers REYNOLDS NUMBER A dimensionless number, the value of which estimates the relative importance of inertial forces compared with viscous forces in flowing fluids. PECLET NUMBER A dimensionless number, the value of which estimates the relative importance of mass transfer by convection compared with mass transfer by diffusion. 23 Transport Equation Start from the diffusion equation, with C is the concentration and D is the diffusion constant: dC = D∇2C dt ∂2C ∂2C In 2 dimension ∇2C = + ∂x2 ∂y2 dC dC dx dx And since = = v dt dx dt and dt Then we can write: dC ∂2C ∂2C v = D( + ) dx ∂x2 ∂y2 PECLET NUMBER Transport Equation can be written as: ∂c ∂2 c ∂2c v = D( + ) ∂x ∂ x2 ∂ y2 Thus we write using dimensionless units, and the Peclet number: c x y vW C = X = Y = Pe = c0 W W D ∂C ∂2 C ∂2 C Pe = ( + ) ∂X ∂ X 2 ∂ Y 2 25 Graphical Solution to the Transport Equation using the ! PECLET NUMBER Transport Equation in dimensionless units: X ∂C ∂2 C ∂2 C Pe = ( + ) ∂X ∂ X 2 ∂ Y 2 Y The solution is complicated – even in 2 dimensions. 26 Mixing Methods 27 MIXING with MICROPILLARS 28 Structure 29 Micropillers • When is this a good method? • Low Re or high? • Is it better to have aligned or misaligned posts? 30 Micropillers – Calculations When is this method good? • Low Re or high? • Relatively high • Is it better to have aligned or misaligned posts? • Aligned 31 Rough Channels 32 Rough Channels Cross section Versus 33 Rough Channels – Effectiveness? Cross section Only when there are “choking points” 34 Mixing by! Split-and-Recombine (SAR) 35 Split and Recombine 36 Split and Recombine 37 Split and Recombine- Effectiveness 38 T and Y Mixers 39 T Mixer 40 T an Y Mixers Mixing is based on diffusion 41 Y Structure 42 Self Circulating 43 Self Circulating Chamber Y-C Chung et al 44 Velocity Field and Re 45 Simulations 46 Experiments Fluorescence stereomicroscopic image Re = 150 Re = 50 47 ! Focusing of Mixing Stream! 48 Hydrodynamic Focusing 49 Mixing In Microfluidic Design Goals: Fast mixing time (< 10 µs) Low sample consumption Mixing is diffusion driven Reduce diffusion length Low Re, laminar flows Hydrodynamic focusing ~ 400 nsec mixing (Pabit/Hagen ‘02) Design (e.g. see Knight et al. 1998) Small nozzle dimensions Integrated filters Large velocities > 1m /sec 50 Mixing • Important to integrate mixing function on many microchips • Design of contact areas for more than one fluid • Effect of Diffusion on mixing • Effect of type of Fluid flow on mixing: “turbulence” is not helpful in microchannels - can lead to “dead volumes” • Specific geometric designs of flow tubes for better mixing v Arrow junctions v Small radius & curved tubes v Zigzag shaped channels 51 Serpentine Mixers 52 Serpentine Mixing Create a Serpentine Channel Serpentine Mixing Serpentine Mixer 55 Serpentine Mixer Simulations by Students with ! Prof. Bruce Finlayson University of Washington, Chem Engineering http://courses.washington.edu/microflo/ 56 Efficiency of Serpentine Mixing Evolution of the concentration at several down-channel positions after 1, 2, 3, 4, 5, and 10 period at the four Reynolds numbers, a Re = 0.01, b Re = 10, c Re = 30, and d Re = 50 A more Complex One Tae Gon Kang Mrityunjay K. Singh, Patrick D. Anderson Han E. H. Meijer Microfluid Nanofluid (2009) Volume 7, pages 783–794 Microfluid Nanofluid (2008) Volume 4, pages 589–599 Chaotic Mixers 59 Chaotic Mixers These are passive micromixers with no moving parts. Concept: Geometries are designed to create a flow that stretch and fold volumes of fluid over the cross section of the channel. § Chaotic mixing uses periodic and aperiodic sequences of mixing protocols. 60 T and U 61 Examples for High Re 62 Chaotic Mixer Stroock etal., Science 295. 647 (2002) Yang etal., (2006) Simulation of Concentration Evolution 64 Different Geometries 65 A Promising Idea § A new method presented by David Ross and Laurie Locascio (National Institute of Standards and Technology) that provides highly efficient mixing, even at very high flow rates. • Information was presented in the MIT enterprise forum of Washington – Baltimore The Method The Building Block Slanted wells redirect flow and cause fluids to fold over each other - like kneading bread. Microfluidic Mixing 70 μm The Method Slanted wells redirect flow and cause fluids to fold over each other like kneading bread. Rapid microfluidic mixing 440 μm Rapid microfluidic mixing 440 μm Rapid microfluidic mixing 440 μm Rapid microfluidic mixing 440 μm An Example for Mixer Fabrication A) Deposition of Si B) Photolithography C) And D) RIE Etching E) PDMS Replica F) PDMS Bonding - by plasma Activation Another Geometry Another Geometry Another Geometry Another Geometry Tesla Mixer Intermediate Re 80 Recycling Mixer 81 Droplet Mixing 82 height Fluids Geometry width Flow Control complex designs (oil, water) l = m /m i o (pressure-driven flow) Q , Q Wettability Additives oil water (surfactants, polymers) - dynamics Emulsion Design in - rheology Microfluidic Devices Morphology Drop Size Volume Fraction Rheology of Emulsions Size Distribution Coalescence/Stability f = Qw/(Qw+Qo) 83 Dynamic Contact Angle Know the contact angle for a static droplet: θs When a fluid is flowing, the contact angle is related to the capillary and viscous forces. The relative importance is related to the capillary number ηv Ca = γ Dynamic Contact Angle 94 Ca θd = θs ± 2 3 θ s advancing receding Can alter contact angles by an applied field Mixing Internal recirculation induced by turns Stretch and Fold Striation thickness related to the number of steps (n) which depends on the velocity, the dimensions ACTIVE Mixers 90 Active Mixing Based on chaotic advection Achieved by periodic perturbation of the low ields. Chaos can improve the mixing ef<iciency Chaos can improve the mixing ef<iciency Several <luid actuation methods Heat convection J. W. Choi and C. H. Ahn, An active micro mixer using electrohydrodynamic (EHD), convection presented at Solid-State Sensors and Actuator Workshop, Hilton Head Island, South Carolina, 2000. Differential pressure M. Volpert, C. D. Meinhart, I. Mezic and M. Dahelh, An actively controlled micromixer, presented at MEMS, ASME IMECE, Nashville, Tennessee, 1999. J. Voldman, M. L. Gary and M. A. Schimdt, An integrated liquid mixer/valve, Microelectromech. Syst., 2000, 9, 295–302.
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