Contents. Microfluidics - Jens Ducrée Physics: Fluid Dynamics 1

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1 Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors 12.Analytical Chips 13.Particle-Laden Fluids a. Measurement Techniques b. Fundamentals of Biotechnology c. High-Throughput Screening Microfluidics - Jens Ducrée Physics: Fluid Dynamics 1

2 3. Physics of Microfluidic Systems 3.1. Navier-Stokes Equations 3.2. Laminar and Turbulent Flow 3.3. Fluid Dynamics 3.4. Fluidic Networks 3.5. Energy Transport 3.6. Interfacial Surface Tension 3.7. Electrokinetics Microfluidics - Jens Ducrée Physics: Fluid Dynamics 2

3 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction 3.3. Fluid Dynamics Microfluidics - Jens Ducrée Physics: Fluid Dynamics 3

4 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction 3.3. Fluid Dynamics Microfluidics - Jens Ducrée Physics: Fluid Dynamics 4

5 Pressure measurement Static Dynamic Bernoulli equation Total pressure Also stagnation pressure Preserved in flow Dynamic pressure ~v 2 Static pressure Dynamic Pressure - Measured by manometer moving with flow Microfluidics - Jens Ducrée Physics: Fluid Dynamics 5

6 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction 3.3. Fluid Dynamics Microfluidics - Jens Ducrée Physics: Fluid Dynamics 6

7 Cavitation Formation of bubbles at regions of high velocities Related to dynamic pressure Vapor pressure p vap Static pressure p < p vap Vaporization of liquid Energy Work against bending pressure Stored energy E = A Release of E - Local hot-spots - Chemical reactions - Corrosion - Emission of light Possible detrimental to functionality of device Microfluidics - Jens Ducrée Physics: Fluid Dynamics 7

8 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction 3.3. Fluid Dynamics Microfluidics - Jens Ducrée Physics: Fluid Dynamics 8

9 Coanda Effect Deflection of jets at curved surfaces Discovered by Thomas Young in 1800 Rediscovered by Coanda in 1910 Understood in 1930 In turbulent jets up to moderate Reynolds numbers Curvature and angle not too sharp Microfluidics - Jens Ducrée Physics: Fluid Dynamics 9

10 Coanda Effect Explanation Velocities of turbulently moving particles far greater than jet speed Underpressure Nearby gas sucked into stream Space between adjacent wall and jet evacuated Jet tends to stick to wall Application Flow switches Fluidic amplifiers Microfluidics - Jens Ducrée Physics: Fluid Dynamics 10

11 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction 3.3. Fluid Dynamics Microfluidics - Jens Ducrée Physics: Fluid Dynamics 11

12 Drag Coefficient Drag F Body in fluid stream at velocity v Unconfined medium Characteristic area (cross-section) A d Fluid density Drag coefficient Shape of body Surface roughness Reynolds number Re Microfluidics - Jens Ducrée Physics: Fluid Dynamics 12

13 Drag Coefficient Large v C d const. F ~ v 2 Low Re C d ~ 1 / v F ~ v Examples: Microfluidics - Jens Ducrée Physics: Fluid Dynamics 13

14 Stokes Drag Force on sphere in fluid stream Approximation by Stokes Radius r 0 Relative speed v Viscosity Laminar flow Flow undisturbed at sufficient distance v = 0 on surface of sphere more detailed calculation Microfluidics - Jens Ducrée Physics: Fluid Dynamics 14

15 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction 3.3. Fluid Dynamics Microfluidics - Jens Ducrée Physics: Fluid Dynamics 15

16 Interplay Oscillating external pressure Finite compressibility of fluid Longitudinal modes only Pressure Waves - No restoring force upon shear stress Density oscillations Harmonic actuation Angular frequency Stamp amplitude 0 Sound particle velocity v Phase velocity Microfluidics - Jens Ducrée Physics: Fluid Dynamics 16

17 Pressure Waves Wave Equation Using Laplacian compare Relation Newton Microfluidics - Jens Ducrée Physics: Fluid Dynamics 17

18 Pressure Waves Typical values Typical wave length c = 1000 m / s = 1 khz = c / = 1 m Microfluidics - Jens Ducrée Physics: Fluid Dynamics 18

19 Pressure Waves Characteristic numbers Strouhal number Mach number Intensity Radiation pressure Microfluidics - Jens Ducrée Physics: Fluid Dynamics 19

20 Energy dissipation Inner friction of fluid Heating of fluid Damping of Pressure Waves Friction term in wave equation Planar wave Microfluidics - Jens Ducrée Physics: Fluid Dynamics 20

21 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction 3.3. Fluid Dynamics Microfluidics - Jens Ducrée Physics: Fluid Dynamics 21

22 Flow through Constriction Outflow Pressurized chamber Nozzle Flow velocities v 1 and v 2 inside and outside chamber Flow rate I m Function of pressure ratio p 2 / p 1 Shape of constriction Microfluidics - Jens Ducrée Physics: Fluid Dynamics 22

23 Flow through Constriction Bendemann formula Flow rate Conservation of mass Isenotropic conditions v 1 << v 2 Outlet function Dimensionless Microfluidics - Jens Ducrée Physics: Fluid Dynamics 23

24 Laval Pressure Ratio Outlet function Maximum value Obtained at critical Laval ratio - Propagation of pressure signal limited by speed of sound Microfluidics - Jens Ducrée Physics: Fluid Dynamics 24

25 Outflow of Compressible Gases Additional correction factors Velocity factor 1 - Outlet shape - Velocity Contraction number 2 - Outlet shape Microfluidics - Jens Ducrée Physics: Fluid Dynamics 25

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