V06 Diffusion WS 23.pdf

V06 V06 Diffusion and Micromixer Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 1 Contents V06 Contents V06 6.1 Brownian Motion 6.2 Diffusion 6.2.1 1. Fick Law 6.2.2 2. Fick Law 6.2.3 Diffusion Profil...

V06 V06 Diffusion and Micromixer Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 1 Contents V06 Contents V06 6.1 Brownian Motion 6.2 Diffusion 6.2.1 1. Fick Law 6.2.2 2. Fick Law 6.2.3 Diffusion Profile of a Concentration Front 6.2.4 Diffusivity / Diffusion Coefficient 6.3 Passive Diffusive Micromixers 6.3.1 Concept 6.3.2 Layering Techniques 6.3.3 Mixing in Droplets 6.4 Micromixers at High Reynolds Numbers Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 2 Learning Targets V06 V06 Learning Targets V06  Diffusion effects in laminar flow  Methods for reducing diffusion lengths at different Reynolds number regimes  Diffusive mixing in droplets Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 3 V06 6.1 Brownian Motion Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 4 V06 5 www.nndb.com 6.1 Brownian Motion Brownian Motion (1827)* http://www.britannica.com Robert Brown (1773 - 1858) https://www.youtube.com/watch?v=6VdMp46ZIL8  Arbitrary non-directional jitter movement of suspended particles / molecules ….  Resulting from kicks of single molecules of surrounding medium (gas, liquid) * First description by Jan Ingenhousz 1784 Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 Jan Ingenhousz (1730 - 1799) 6.1 Brownian Motion V06 6 www.emis.de Brownian Motion  Thermal agitation  Einstein 1905 https://upload.wikimedia.org/  Smoluchowski 1906  Langevin 1907 x  Paul Langevin (1872 - 1946) k BT t 3  r    Albert Einstein (1897 – 1955) cyfronet.krakow.pl  Theoretical prediction by Brownian motion is the origin of diffusion x … Distance from origin kB...Boltzmann constant η … Viscosity of fluid T … Absolute temperature r … Radius of particle t … Time Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 Marian Smóluchowski (1872 -1917) 6.1 Brownian Motion V06 Note k BT x  t 3  r     Boltzmann constant kB can easily be calculated by macroscopically determinable variables  This allows direct experimental determination of and therefore other variables, e.g.  Avogadro constant  Size  Number  Mass of tiny particles / molecules Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 7 6.2 Diffusion V06 6.2 Diffusion Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 8 6.2 Diffusion V06 9 Diffusion  Transport process  Spontaneous spreading of particles / molecules etc.  From regions of high concentration to regions of low concentration  Driven by gradient of concentration (inhomogeneity)  Process driven by entropy www.en.wikipedia.org  Refers to the net migration owing to random thermal fluctuations → Entropy is increasing → Ends up in homogeneous Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 particle distribution 6.2 Diffusion V06 Diffusion in Microfluidics  Is carried along with the fluid flow  Moves with the fluid  Does not affect the fluid flow Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 10 6.3.2 Layering Techniques 6.2 Diffusion V06 Transport Diffusion Advection Transport due to Transport due to concentration gradient bulk motion* of a fluid Convection Combination of diffusion and advection * Bulk flow is often the movement of fluid down a channel driven by a pressure gradient Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 11 6.2 Diffusion V06 12 Diffusion Macro world Micro world  Low Reynolds numbers  Mixing through inertial forces  No turbulences and vortices  Shaking  Steering  Laminar flow, no inertial forces Turbulences + Vortices  Active mixing  Mixing by diffusion !!! www.einslive.de  Passive mixing Flow direction www.syrris.com/Flow-Basics.aspx Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.2.1 1. Fick‘s Law of Diffusion V06 13 1. Fick‘s Law c jx   D  x de.academic.ru Fick‘s Laws of Diffusion for one direction  Gradient of concentration drives net mass flow  No dependency of time Adolf Eugen Fick (1829 – 1901)  Highest transport at highest gradient  The net effect is a flux in the direction opposite to the local gradient  System goes for homogeneity  Fick’s law is a macroscopic representation of a summed effect of random motion of species owing to thermal fluctuations j … Particle flux density: amount of particles diffusing across a surface per unit area per time D.. Diffusion coefficient, diffusivity [m2/s] c … Particle concentration Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.2.2 2. Fick‘s Law of Diffusion V06 14 Combination of 1. Fick‘s Law with Conservation of Mass c j  D  x j … Particle flux density D.. Diffusion coefficient c … Particle concentration 2. Fick‘s Law j c  t x Minus sign Concentration decreases when more particles flow out than in c  2c  D 2 t x For one dimension c  D  2 c t For three dimensions Temporal change of concentration in correlation to spatial variation of concentration. Description of non-static (dynamic) diffusion processes Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.2.3 Diffusion of a Concentration Front V06 Diffusion of a Concentration Front c  2c  D 2 t x x0 In one direction x Initial conditions c  c0 c( x  0, t  0)  c0 c0 c( x  0, t  0)  0 Walls are placed at infinity Steady state - without flow - 1  c( x, t )  c0  1  erf 2  Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23  x    2 Dt   15 6.2.3 Diffusion of a Concentration Front V06 1  c( x, t )  c0  1  erf 2  x0 t=1s    c0 t = 0.1 s D = 1∙10-11 m2/s t = 100 s t=∞ Steady state - without flow - * Error function erf ( x)  2  * t = 10 s c / c0 c  cstart  x   2 Dt x u  e du 2 Distance from interface [µm] 0 Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 16 6.2.3 Diffusion of a Concentration Front V06 17 In Presence of Steady-State Fluid Flow When the channels are shallow relative to their width (w >> h, slit-type channels)  Diffusion is 1-dimensional  Diffusion transverse to the flow direction, averaged over the depth, is described by the error function  Due to flow, the distribution of particles varies with y/v = t (the time since the fluid entered the channel) B.J. Kirby: Micro- and Nanoscale Fluid Mechanics, ISBN 978-0-521-11903-0 Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 6.2.4 Diffusivity / Diffusion Coefficient Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 18 6.2.5 Diffusivity / Diffusion Coefficient V06 19 Stokes-Einstein Equation (1905)  Diffusion of a spherical particle  In low viscous fluid Diffusion coefficient Diffusivity D www.nnbd.com  Low Reynolds number Re kBT 6   r  High diffusion for  High temperatures  Low viscous fluids George Gabriel Stokes (1819 – 1903)  Small particles / molecules *derived by Einstein in his Ph.D thesis A. Einstein, A.: Annalen der Physik 322 (8) 549-560 (1905), doi:10.1002/andp.19053220806 Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.2.5 Diffusivity / Diffusion Coefficient V06 Diffusivity / Diffusion Coefficient Particle Size Diffusion coefficient D* [µm2/s] [nm] Solved ion 0.1 2*103 Small protein 5 40 Virus 100 2 Bacterium 1000 0.2 Human Cell 10000 0.02 * in water at room temperature T.M. Squires et al.: Rev. Mod. Phys. 17 977-1026 (2005) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 20 6.2.5 Diffusivity / Diffusion Coefficient V06 Diffusion Coefficient Depends on Temperature kBT D 6   r https://www.youtube.com/watch?v=STLAJH7_zkY Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 21 V06 6.3 Passive Diffusive Micromixers 6.3.1 Concept Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 22 6.3.1 Concept of Passive Diffusive Micromixers Diffusion Time tD of Particle Time needed for a particle to diffuse the length lD Diffusion Length V06 lD2 tD  2D lD  2 D  t Length over which diffusion has occurred Favorable for microfluidics Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 23 From slides 7 and 19 6.3.1 Concept of Passive Diffusive Micromixers V06 Y-mixer Fluid A Fluid B Mixing by Diffusion in Laminar Flow  Is determined by device geometry  lD is small in µF  Only passive structures needed   lD  w 2 lD2 tD  cadf 2D Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 lD lchannel w 24 6.3.1 Concept of Passive Diffusive Micromixers Mixing by Diffusion in Laminar Flow Diffusive mixing is easy in microfluidics → ID is small, defined by half of the channel width lD2 tD  2D ID Y.-K Suh et al.: Micromachines 1 82-111 (2010) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 25 6.3.1 Concept of Passive Diffusive Micromixers V06 How long must the channel be for complete diffusive mixing? Fluid A Time of residence tr for particle in channel Time of residence tr  Fluid B lchannel vmean tr  t D Diffusion time lD lchannel 2 D lchannel l  vmean 2  D l min channel vmean 2   lD 2D Minimum channel length of channel for complete mixing Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 26 6.3.1 Concept of Passive Diffusive Micromixers V06 Example: Protein min lchannel  vmean 2  lD 2D  Diffusion coefficient D = 40 µm2/s  Half channel width lD = 100 µm  Mean flow velocity vmean = 100 µm/s min lchannel  1.25 cm t r  t D  125 s Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 27 6.3.1 Concept of Passive Diffusive Micromixers 1 vmean    lD  lD 2 D Péclet number Pe  28 www.wikipedia.de l min channel V06 vmean  lD D Jean Claude Eugène Péclet (1793 – 1857) Péclet number  Dimensionless characteristic number  Describes mass transport  Relation of advection flow (particle transport in flow) and diffusive transport  High Péclet number: Transport determined by advection  Low Péclet number: Transport determined by diffusion Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.3.1 Concept of Passive Diffusive Micromixers Application V06 H-filter for Particle Separation Solute Influenced by  Particle size kBT D 6   r l min channel 1 vmean 2   lD 2 D  Particle shape  Diffusion constant  Viscosity  Temperature  Mean flow velocity S.J. Trietsch et al.: Chemometrics and Intelligent Laboratory Systems 108 (1) 64-75 (2011) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 29 6.3.1 Concept of Passive Diffusive Micromixers V06 Solute vmean Pe   lD D H-filter works when  Pe small for small particles  High diffusion  Pe high for large particles  Low diffusion S.J. Trietsch et al.: Chemometrics and Intelligent Laboratory Systems 108 (1) 64-75 (2011) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 30 6.3.1 Concept of Passive Diffusive Micromixers V06 Fluid A min l kanal vmean 2   lD 2D 31 Fluid B Minimum channel length for complete diffusive mixing When the diffusivity D is too small the channel length will be too long to be integrated in a chip format How can the channel length be shortened? Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 lD lchannel V06 6.3.2 Layering Techniques Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 32 6.3.2 Layering Techniques V06 Shortening of Channel Length by Layering Technique lD  Reduced diffusion length l*D  l *D lD n  Reduced minimum channel length l min channel vmean *2 vmean lD2   lD   2 2D 2D n Minimum channel length can be reduced by layering ! Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 33 6.3.2 Layering Techniques Passive Mixing by Interdigitated Lamella P. Löb et al.: Chem. Eng. J. 101 75-85 (2004) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 34 6.3.2 Layering Techniques Split-And-Recombine (SAR) S.W. Lee et al.: J. Micromech. Microeng. 16 1067-1072 (2006) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 35 6.3.2 Layering Techniques V06 36 Split-And-Recombine (SAR) Split N.-T. Nguyen et al.: J. Micromech. Microeng. 15 R1-R6 (2005) Shift Recombine http://www.youtube.com/watch?v=z9E5kwcMoHE Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.3.2 Layering Techniques V06 Split-And-Recombine (SAR) Re  3.89 vm  50 D.S. Kim et al.: Lab on a Chip 5 739-747 (2005) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 l min 37 6.3.2 Layering Techniques V06 Split-And-Recombine (SAR) A. El Hasni, …., U. Schnakenberg: Microfluidics and Nanofluidics 21 41 (9pp) (2017) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 38 6.3.2 Layering Techniques V06 39 F-Bar SAR Structures were Fabricated Using by Lamination of Dry Film SU-8 Resist Lamination of six layers SU-8 Glass S. Abada et al.: J Micromech. Microengineering, 27 (5), 055018 (2017) A. El Hasni, …, U. Schnakenberg: Microfluid Nanofluid 21 41 (2017) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.3.2 Layering Techniques V06 Dean Mixer Dean number 40 dh De  Re r  De low  No vortices  De high  Fast flow in the middle will be pushed to the outer channel wall by centrifugal De >> 1 forces  Appearance of Dean vortices A. Sundarsan: http://repository.tamu.edu/bitstream/handle/1969.1/4686/etd-tamu-2006C-CHEN-Sudarsan.pdf?sequence=1 Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.3.2 Layering Techniques V06 41 Dean Mixer De  1 De  10 Low fluid velocities High fluid velocities Centrifugal forces not high enough Centrifugal forces transport fluid from to influence laminar flow channel’s inside to outside and visa versa A. Sundarsan: http://repository.tamu.edu/bitstream/handle/1969.1/4686/etd-tamu-2006C-CHEN-Sudarsan.pdf?sequence=1 Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.3.2 Layering Techniques http://www.youtube.com/watch?v=LNeUqNVS5VE Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 42 6.3.2 Layering Techniques V06 43 Dean Mixer De    Re dh r A. P. Sundarsan et al. : PNAS 103 (19) 7228-7233 (2006) dh …. Hydraulic diameter of channel R ….. Flow path radius of curvature Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.3.2 Layering Techniques V06 44 Staggered Herringbone Mixer (SHM) viskoser Fluss A. D. Stroock et al.: Science 295 647-651 (2002) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 Re < 10 6.3.2 Layering Techniques A. D. Stroock et al.: Science 295 647-651 (2002) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 45 Re < 10 6.3.2 Layering Techniques V06 Staggered Herringbone Mixer (SHM)  Asymmetry of rolls change periodically  Efficiency depending on  Asymmetry of grating structure  Geometry of gratings  Number of gratings per unit → determines the rotation angle ∆Φ A. D. Stroock et al.: Science 295 647-651 (2002) Re < 10 Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 46 6.3.2 Layering Techniques V06 47 Staggered Herringbone Mixer (SHM)  Asymmetry of rolls change periodically  Efficiency depending on  Asymmetry of grating structure  Geometry of gratings  Number of gratings per unit → determines the rotation angle ∆Φ Unfortunately, this video is not available on youtube anymore Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 6.3.3 Mixing in Droplets Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 48 6.3.3 Mixing in Droplets V06 Mixing in Droplets (Introduction to Droplets → V08 Droplets) Water Droplet Oil H. Song et al.: Angew. Chem. Int. Ed. 42 (7) 767-772 (2003) M. R. Bringer et al.: Phil. Trans. R. Soc. Lond. A 362 1087-1104 (2004) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 49 6.3.3 Mixing in Droplets V06 50 Chaotic Advection in Droplet  Fluid is in relative motion with regard to channel walls  Walls induce vortices in droplets  Straight Channel Geometry  Symmetric vortices  Droplet will be mixed symmetrically  Curved Channel Geometry  Different relative fluid velocities at top and bottom wall result in asymmetric vortices in the droplet when the radii of curvature are different M. R. Bringer et al.: Phil. Trans. R. Soc. Lond. A 362 1087-1104 (2004) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 6.3.3 Mixing in Droplets http://www.youtube.com/watch?v=E7e237QVQfo Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 51 6.3.3 Mixing in Droplets V06 52 In sharp turn  Only one vortex occurs  Reorientation of droplet In straight part  Stretching and folding M. R. Bringer et al.: Phil. Trans. R. Soc. Lond. A 362 1087-1104 (2004) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 U  vm  53 mm / s V06 6.4 Micromixers at High Reynolds Numbers Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 53 6.4 Micromixers at High Reynolds Numbers V06 Advection  Transport due to bulk motion* of a fluid  Transport along the streamlines in laminar flow Chaotic Advection  Enforce turbulences and vortices by distinct channel geometries  Designs of channel geometries depends on Re Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 54 6.4 Micromixers at High Reynolds Numbers V. Mengeaud et al: Anal. Chem. 74 4279-5286 (2002) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 55 Re > 100 6.4 Micromixers at High Reynolds Numbers V06 56 10 < Re < 100 N.-T. Nguyen et al.: J. Micromech. Microeng. 15 R1-R6 (2005) Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 Conclusion Conclusion V06 V06 57 Diffusion is an important property in microfluidics  Surface-to-volume ratio significantly higher than in macrofluidics  Fast diffusive mixing possible Passive Diffusive Micromixers  No external forces needed (no shaking or steering)  Mixing time and channel length can be shortened by layering techniques Active Micromixers  Need externally applied energy/forces  Examples will be presented in next lectures Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 V06 One Minute Paper 1. What was the most important topic you understood? 2. What was the topic you didn‘t catch? Lecture „Microfluidic Systemes- Bio-MEMS“ - Diffusion Prof. Dr.-Ing. Uwe Schnakenberg | Institute of Materials in Electrical Engineering 1 | WS 23 58