1. Chapter 01: Flows in micro-fluidic systems Xiangyu Hu Technical University of Munich

2. What is a micro-fluidic system? A system manipulating fluids in channels having cross section dimension on less than 100 micro-meters –Smallest micro-channel: Nano-tube Micro-channels Nano-tubes

3. The objectives of micro-fluidic systems Micro-Total-Analysis-Systems (  TAS) –One system to provide all of the possible required analyses for a given type problem –All processing steps are performed on the chip –No user interaction required except for initialization –Portable bedside systems possible Lab-on-a-chip Micro-fluidics in nature –Aveoli (Lung bubbles)

4. Micro-fluidics is Interdisciplinary Micro-Fabrication Chemistry Biology Mechanics Control Systems Micro-Scale Physics and Thermal/Fluidic Transport Numerical Modeling –Simulation of micro-flows Material Science …

5. The fluids in micro-fluidic system Simple fluids –liquids and gases Complex fluids –immersed structures, surfactants, polymers, DNA … Injection of a droplet into a micro-channel. Polymer flow in a micro-channel Cells in a micro-channel.

6. Typical fluidic components Micro-channels and channel- circuit Functional structures –Micro-pump and switches –Mixing and separating devices Channel-circuit Typical functional structre Electroosmotic Pumping

7. Length scales in micro-fluidic systems Micro-channel 1mm 100  m 10  m 1m1m 100nm 10nm Cellular scale Radius of Gyration of DNA Microstructure and micro-drops Extended lenght of DNA Typical size of a chip Colloid and polymer molecular size

8. Deviations from continuum hypothesis for micro-fluidics I: gas microflows

9. Deviations from continuum hypothesis for micro- fluidics II: simple liquid micro-flows How small should a volume of fluid be so that we can assign it mean properties? –Nano-meter scale At what scales will the statistical fluctuations be significant? –Nano-meter scales

10. Deviations from continuum hypothesis for micro- fluidics II: simple liquid micro-flows Slip at wall in nano-scale? –High shear rate –Hydrophobic surface

11. Deviations from continuum hypothesis for micro- fluidics III: micro-flows with complex fluids Detailed modeling can not use continuum model –Nano-Scale DNA molecule stretched by flow Nanowires deformed under shearing Polymer molecules in a channel flow

12. Conclusion on continuum hypothesis for micro-fluidics Dependent on length scales –Nano-meter scales: NO –Micro-meter scales: Yes, but NO for Gas Influence on numerical method –Nano-meter scales: non- continuum Micro- and meso-copic methods –Micro-meter scales: continuum Macroscopic methods –Micro-meter scales for gas: non- continuum Micro- and meso-copic methods –Nano- to micro-meter scales Multi-scale modeling

13. Other flow features for micro-fluidics Low Reynolds number flow –Large viscous force Low Capillary number flow –Large surface force High Peclet number flow –Disperse and diffusion –Slow diffusion effects Special transport mechanism –Mixing: chaotic mixing –Separation: particle, polymer and DNA

14. Low Reynolds number flow (Stokes flow) Reynolds number (Re) is the ratio between inertial force to viscous force Scaling between intertial force and viscous force in NS equation –Length scale L –Velocity scale U Flow classification based on Re http://www.youtube.com/watch?v=gbDscDSUAg4&feature=channel_page http://www.youtube.com/watch?v=2ghBUcQG1lQ&feature=channel_page

15. Low Reynolds number flow (Stokes flow) In micro-fluidics, Re<1 –Laminar flow –the viscous force dominant the inertial force –Inertial irrelevance Purcell 1977 http://www.youtube.com/user/Swimmers1

16. Low Capillary number flow Capillary number (Ca) is the ratio between viscous force to surface force What is surface tension? –Stretch force along the material interface

17. Low Capillary number flow Capillary number (Ca) is the ratio between viscous force to surface force Scaling between viscous force and surface force in NS equation –Length scale L –Velocity scale U

18. Low Capillary number flow In micro-fluidics, Ca <<1 –Surface force dominant flow –Wetting effects Micro-fluidic pin-ball: routing

19. High Peclet number flow Peclet number (Pe) is the ratio advection rate of a flow to its diffusion rate Advection, diffusion and dispersion –Advection : transport that is due to flow –Diffusion: results from movement of particles along concentration gradients –Dispersion: transport that describes local mixing, which results in locally varying fluid flow velocity http://ccl.northwestern.edu/netlogo/models/run.cgi?SolidDiffusion.591.481ccl.northwestern.edu/netlogo/models/run.cgi?SolidDiffusion.591.481

20. High Peclet number flow In most of the liquid flow, also in micro-fluidics, Pe >>1 Strategy for faster mixing –increase the length of mixing layer Long channel Long trajactory line: Chaotic mixing (Use of disperseion)

21. Chaotic Mixing Stretching and folding the mixing layer by localized flows Different approaches –Geometric structure –Surface tension effects –Electrohydrodynamically- driven Micro-fluidics crystallization system. Electrohydrodynamically-driven microfluidic mixing

22. Separation in micro-fluidics External force used to move the solute Separating particle on different mobility –Large mass, small velocity –Dielectric properties

23. Separating long DNAs Long DNAs –Same mobility Mechanism of separation –Weissenberger number: relaxation time to shear rate or flow time scale –Longer chain, longer relaxation time –Longer chain, less diffusion coefficient

24. Separating long DNAs (1)

26. Numerical Modeling Challenges Multi Physical Phenomenon –Thermal, Fluidic, Mechanical, Biological, Chemical, Electrical Multi-scale –Continuum and atomistic modeling may coexist Multi-phase –Gas, liquid Complex fluids –Particle, nano-structures, polymer, DNA Complex geometry