Chapter 01: Flows in micro-fluidic systems

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Chapter 01Flows in micro-fluidic systems

• Xiangyu Hu
• Technical University of Munich

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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

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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)

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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

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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
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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
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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
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Deviations from continuum hypothesis for
micro-fluidics I gas microflows
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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

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Deviations from continuum hypothesis for
micro-fluidics II simple liquid micro-flows

• Slip at wall in nano-scale?
• High shear rate
• Hydrophobic surface

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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
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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

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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

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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?vgbDscDSUAg4feature
channel_page
http//www.youtube.com/watch?v2ghBUcQG1lQfeature
channel_page
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Low Reynolds number flow (Stokes flow)

• In micro-fluidics, Relt1
• Laminar flow
• the viscous force dominant the inertial force
• Inertial irrelevance

Purcell 1977
http//www.youtube.com/user/Swimmers1
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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

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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

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Low Capillary number flow

• In micro-fluidics, Ca ltlt1
• Surface force dominant flow
• Wetting effects

Micro-fluidic pin-ball routing
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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
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High Peclet number flow

• In most of the liquid flow, also in
  micro-fluidics, Pe gtgt1
• Strategy for faster mixing
• increase the length of mixing layer
• Long channel
• Long trajactory line Chaotic mixing (Use of
  disperseion)

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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
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Separation in micro-fluidics

• External force used to move the solute
• Separating particle on different mobility
• Large mass, small velocity
• Dielectric properties

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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

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Separating long DNAs (1)
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Separating long DNAs (1)
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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