Fluid Dynamics

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Measurement Techniques b. Fundamentals of. Biotechnology c. High- Throughput Screening. Microfluidics - Jens Ducrée. Physics: Fluid Dynamics. 1 ...
Contents

1. Introduction

9. Liquid Handling

2. Fluids

10.Microarrays

3. Physics of Microfluidic Systems

11.Microreactors 12.Analytical Chips

4. Microfabrication Technologies Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

13.Particle-Laden Fluids

5. Flow Control

a. Measurement Techniques

6. Micropumps 7. Sensors

b. Fundamentals of Biotechnology

8. Ink-Jet Technology

c. High-Throughput Screening

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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

Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

3.6. Interfacial Surface Tension 3.7. Electrokinetics

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3.3. Fluid Dynamics 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

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3.3. Fluid Dynamics 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

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3.3.1. Dynamic Pressure  Pressure measurement  Static  Dynamic

 Bernoulli equation     

Total pressure Also stagnation pressure Preserved in flow Dynamic pressure ~v 2 Static pressure

Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

- Measured by manometer moving with flow

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3.3. Fluid Dynamics 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

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3.3.2. Cavitation  Formation of bubbles at regions of high velocities    

Related to dynamic pressure Vapor pressure pvap Static pressure p < pvap Vaporization of liquid

 Energy  Work against bending pressure  Stored energy E = A  Release of E -

Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

Local hot-spots Chemical reactions Corrosion Emission of light

 Possible detrimental to functionality of device

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3.3. Fluid Dynamics 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

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3.3.3. 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 Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

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3.3.3. 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 Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

 Application  Flow switches  Fluidic amplifiers

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3.3. Fluid Dynamics 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

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3.3.4. Drag Coefficient

 Drag F    

Body in fluid stream at velocity v Unconfined medium Characteristic area (cross-section) Ad Fluid density  Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

 Drag coefficient  Shape of body  Surface roughness  Reynolds number Re

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3.3.4. Drag Coefficient

 Large v  Cd  const.  F~v2

Examples: Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

 Low Re  Cd ~ 1 / v  F~v

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3.3.4. Stokes Drag

 Force on sphere in fluid stream       

Approximation by Stokes Radius r0 Relative speed v Viscosity  Laminar flow Flow undisturbed at sufficient distance v = 0 on surface of sphere Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

more detailed calculation

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3.3. Fluid Dynamics 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

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3.3.5. Pressure Waves  Interplay  Oscillating external pressure  Finite compressibility  of fluid  Longitudinal modes only - No restoring force upon shear stress

 Density oscillations    

Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

Harmonic actuation Angular frequency  Stamp amplitude 0 Sound particle velocity v

 Phase velocity

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3.3.5. Pressure Waves – Wave Equation

 Using

Laplacian compare Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

 Relation

Newton

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3.3.5. Pressure Waves  Typical values

Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

 Typical wave length  c = 1000 m / s   = 1 kHz   = c /  = 1 m

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3.3.5. Pressure Waves •

Characteristic numbers • Strouhal number

• Mach number

Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

 Intensity

 Radiation pressure

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3.3.5. Damping of Pressure Waves  Energy dissipation  Inner friction of fluid  Heating of fluid

 Friction term in wave equation

Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

 Planar wave

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3.3. Fluid Dynamics 1. Dynamic Pressure 2. Cavitation 3. Coanda Effect 4. Hydrodynamic Forces 5. Pressure Waves 6. Flow through Constriction Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

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3.3.6. Flow through Constriction

 Outflow

Pr isbexa ispel: Ausar beitun gspha Au tsarbei ungde rStand ard-Ze el

 Pressurized chamber  Nozzle  Flow velocities v1 and v2 inside and outside chamber

 Flow rate Im  Function of pressure ratio p‘2 / p‘1  Shape of constriction

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3.3.6. Flow through Constriction  Bendemann formula    

Flow rate Conservation of mass Isenotropic conditions v1