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

Wi

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