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 ineficient. 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 eficiency 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 eficiency

Chaos can improve the mixing eficiency

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. K. Hosokawa, T. Fujii and I. Endo, Droplet-based nano/picoliter mixer using hydrophobic microcapillary vent, presented at IEEE MEMS Workshop, Orlando, Florida, 1999. A. A. Deshmukh, D. Liepmann and A. P. Pisano, Characterization of a micro-mixing, pumping, and valving system presented at 11th International Conference on Solid-State Sensors and Actuators, Munich, Germany, 2001. Ultrasonic or piezoelectric actuation R. M. Moroney, R. M. White and R. T. Howe, Ultrasonically induced microtransport, presented at IEEE MEMS Workshop, Nara, Japan, 1991. Z. Yang, H. Goto, M. Matsumoto and R. Maeda, Ultrasonic micromixer for microfluidic systems, presented at 13th Annual International Conference on Micro Electro Mechanical Systems, Miyazaki, Japan, 2000. X. Zhu and E. S. Kim, Microfluidic motion generation with acoustic waves, Sens. Actuators A: Physical, 1998, 66(1–3), 355 Electrokinetic (EK) pressure Y.-K. Lee, J. Deval, P. Tabeling and C.-M. Ho, Chaotic mixing in electrokinetically and pressure driven micro flow, presented at IEEE MEMS Workshop, Interlaken, Switzerland, 2001 Active Mixer

Chang Liu et. al in Lab on Chip Volume 4, 2004 Active Mixer

An alternative approach is to increase the interfacial area between two or more luids. At the molecular level, the volume mixed at a given time t is V~A (Dt)1/2 where A is the contact area between the luids being mixed D is the diffusion constant. Mixing time is reduced when the area A increases.

Active Mixer Active Mixer Magnetic Bead Mixer

Seung Hwan Lee, Danny van Noort, Ji Youn Lee, Byoung-Tak Zhang and Tai Hyun Park in Lab on Chip Volume 9, (2009)

Magnetic Bead Mixer

Seung Hwan Lee, Danny van Noort, Ji Youn Lee, Byoung-Tak Zhang and Tai Hyun Park in Lab on Chip Volume 9, (2009)

Add an Electric Field Droplet Recombination

Big drops Oil: 100 mL/h Water: 50 mL/h

Small drops Oil: 100 mL/h Water: 10 mL/h

Close-up Oil: 60 mL/h Water: 20 mL/h UnchargedCharged droplets droplets Dielectrophoretic recombination

Ahn, Agresti, Marquez, Weitz, APL, 2006