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 • • • • • • • 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