Chapter 01: Flows in micro-fluidic systems

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

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

3. The objectives of micro-fluidic systems • Micro-Total-Analysis-Systems (mTAS) • 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 Injection of a droplet into a micro-channel. • Simple fluids • liquids and gases • Complex fluids • immersed structures, surfactants, polymers, DNA … Cells in a micro-channel. Polymer flow in a micro-channel

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

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

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 DNA molecule stretched by flow • Detailed modeling can not use continuum model • Nano-Scale Polymer molecules in a channel flow Nanowires deformed under shearing

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.591.481

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)

25. 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