Post on 18-Dec-2015
Chapter 01:Flows in micro-fluidic systems
Xiangyu Hu
Technical University of Munich
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
The objectives of micro-fluidic systems
• Micro-Total-Analysis-Systems (TAS)– One system to provide all of th
e 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)
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• …
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-channelCells in a micro-channel.
Typical fluidic components
• Micro-channels and channel-circuit
• Functional structures– Micro-pump and switches
– Mixing and separating devices
Channel-circuit
Typical functional structreElectroosmotic Pumping
Length scales in micro-fluidic systems
Micro-channel
1mm
100m
10m
1m
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
Deviations from continuum hypothesis for micro-fluidics
I: gas microflows
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
Deviations from continuum hypothesis for micro-fluidics
II: simple liquid micro-flows• Slip at wall in nano-scale?
– High shear rate– Hydrophobic surface
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
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
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
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 Rehttp://www.youtube.com/watch?v=gbDscDSUAg4&feature=channel_page
http://www.youtube.com/watch?v=2ghBUcQG1lQ&feature=channel_page
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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
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
U
Ca
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
U
Ca
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Low Capillary number flow
• In micro-fluidics, Ca <<1– Surface force dominant flow
– Wetting effects
Micro-fluidic pin-ball: routing
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
D
LUPe
http://ccl.northwestern.edu/netlogo/models/run.cgi?SolidDiffusion.591.481
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 l
ayer• Long channel• Long trajactory line: Chaotic
mixing (Use of disperseion)
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
Separation in micro-fluidics
• External force used to move the solute
• Separating particle on different mobility– Large mass, small velocity
– Dielectric properties
Separating long DNAs
• Long DNAs– Same mobility
• Mechanism of separation– Weissenberger number: rel
axation time to shear rate or flow time scale
– Longer chain, longer relaxation time
– Longer chain, less diffusion coefficient
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Separating long DNAs (1)
Separating long DNAs (1)
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