Chapter 01:
Flows in micro-fluidic systems
Xiangyu Hu
Technical University of Munich
What is a micro-fluidic system?
Micro-channels
Nano-tubes
• A system manipulating fluids in channels having cross section
dimension on less than 100 micro-meters
– Smallest micro-channel: Nano-tube
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)
Micro-fluidics is Interdisciplinary
•
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•
•
•
•
•
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
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
Typical fluidic components
Channel-circuit
• Micro-channels and channelcircuit
• Functional structures
– Micro-pump and switches
– Mixing and separating devices
Typical functional structre
Electroosmotic Pumping
Length scales in micro-fluidic systems
1mm
Typical size of a chip
100mm
Extended lenght of DNA
Micro-channel
10mm
Microstructure and micro-drops
Cellular scale
1mm
100nm
Colloid and polymer molecular size
10nm
Radius of Gyration of DNA
Deviations from continuum hypothesis for
micro-fluidics
I: gas microflows
Deviations from continuum hypothesis for microfluidics
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 microfluidics
II: simple liquid micro-flows
•
Slip at wall in nano-scale?
– High shear rate
– Hydrophobic surface
Deviations from continuum hypothesis for microfluidics
III: micro-flows with complex fluids
• Detailed modeling can not use
continuum model
DNA molecule stretched by flow
– Nano-Scale
Polymer molecules in a
channel flow
Nanowires deformed under shearing
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
u
1
 u  u   p  2u
t

• 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
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
mU
Ca 

• What is surface tension?
– Stretch force along the material interface
Low Capillary number flow
• Capillary number (Ca) is the ratio between viscous force
to surface force
mU
Ca 

• Scaling between viscous force and surface force in NS
equation
– Length scale L
– Velocity scale U
u
1
1
2
 u  u   p  u  n   S  S
t


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
LU
Pe 
D
• 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
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)
Chaotic Mixing
• Stretching and folding the
mixing layer by localized flows
• Different approaches
– Geometric structure
– Surface tension effects
– Electrohydrodynamicallydriven
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:
relaxation time to shear
rate or flow time scale
Wi  
– Longer chain, longer
relaxation time
– Longer chain, less diffusion
coefficient
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