Introduction of Micro-/Nano-fluidic Flow

J. L. Lin

Assistant Professor

Department of Mechanical and Automation Engineering

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Outline

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• Defenition of a fluid, fluid particle

• Viscosity

• Continuity equation

• Navier – Stokes equation

• Reynolds number

• Stokes (creeping) flow

Course outline

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Unit I Physics of Microfluidics  • Physics at micrometer scale, scaling laws, understanding implications of miniaturization• Hydrodynamics at micrometer and nanometer scale• Surface tension, wetting and capillarity• Diffusion and mixing• Electrodynamics at micrometer scale• Thermal transfer at micrometer scale Unit II Fabrication Methods of Microfluidics •Clean room micro-fabrication process Unit III Applications of Microfluidics • Basic components of microfluidic devices, fluidic control and micro “plumbing”• Lab-on-a-chip and TAS, their application to cell, protein, and DNA analysis• Optofluidics, Power microfluidics• Emerging applications of microfluidics

Course objectives

• Introduction and a broad overview of the basic laws and applications of micro and nano fluidics

• Hands-on experience in modern microfabrication techniques, design and operation of microfluidic devices

• The ability to work effectively with the original publications in the area of microfluidics.

• The ability to effectively present literature data in the area of microfluidics.

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Textbooks

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• Introduction to Microfluidics, Patrick Tabeling and Suelin Chen

Oxford University Press, 2006

• Theoretical Microfluidics, Henrik Bruus, Oxford University Press, 2007

• Fundamentals And Applications of Microfluidics

Nam-Trung Nguyen, Steven T. Wereley, Artech House Publishers, 2006

• Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves

Pierre-Gilles de Gennes, Francoise Brochard-Wyart , David Quere, Springer, 2003

• Microfluidic Lab-on-a-Chip for Chemical and Biological Analysis and Discovery

Paul C.H. Li, CRC, 2005

• Fundamentals of BioMEMS and Medical Microdevices

Steven S. Saliterman, SPIE, 2006

Grade

• Cumulative score: Attendance 20% Homeworks 30% Final Report 20% Oral Presentation 30%

• Each student will have an opportunity to present a 15-minute talk based on original publication(s) in the field of micro/nano fluidics. List of recommended topics and papers will be provided.

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Definition of a fluid

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When a shear stress is applied:• Fluids continuously deform• Solids deform or bend

Velocity field

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y

x),( ttrV

y

x

),( trV

y

x)),(( ttttrV

y

x

)),(( ttrV

Lagrangian velocity field

Eulerian velocity field

BVt

B

Dt

DB)(

material derivative

j

jiji dAdF

Stress Field

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FAxy

z

jijdA

Viscosity

10

dy

du

dy

du

dy

duf

dy

du - Newtonian

- non-Newtonian

Newtonian Fluids Most of the common fluids (water, air, oil, etc.) “Linear” fluids

Non-Newtonian Fluids Special fluids (e.g., most biological fluids, toothpaste, some paints, etc.) “Non-linear” fluids

dy

du~

viscosity

apparent

viscosity

couette flow

Viscosity

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The SI physical unit of dynamic viscosity m is the pascal-second (Pa·s), which is identical to 1 kg·m−1·s−1.

The cgs physical unit for dynamic viscosity m is the poise (P) 1 P = 1 g·cm−1·s−1

It is more commonly expressed as centipoise (cP). The centipoise is commonly used because water has a viscosity of 1.0020 cP @ 20 C

The relation between poise and pascal-seconds is: 1 cP = 0.001 Pa·s = 1 mPa·s

In many situations, we are concerned with the ratio of the viscous force to the inertial force, the latter characterized by the fluid density ρ. This ratio is characterized by the kinematic viscosity, defined as follows:

where μ is the dynamic viscosity, and ρ is the density.

Kinematic viscosity n has SI units [mm22·s·s−1−1].

Dynamic viscosity

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viscosity [Pa s] [cP]

liquid nitrogen 1.58 × 10−4 0.158

acetone 3.06 × 10−4 0.306

methanol 5.44 × 10−4 0.544

water 1.00 × 10−3 1.000

ethanol 1.074 × 10−3 1.074

mercury 1.526 × 10−3 1.526

nitrobenzene 1.863 × 10−3 1.863

propanol 1.945 × 10−3 1.945

ethylene glycol 1.61 × 10−2 16.1

sulfuric acid 2.42 × 10−2 24.2

olive oil .081 81

glycerol .934 934

corn syrup 1.3806 1380.6

Viscosity [cP]

honey 2,000–10,000

molasses 5,000–10,000

molten glass 10,000–1,000,000

chocolate syrup 10,000–25,000

molten chocolate 45,000–130,000

ketchup 50,000–100,000

peanut butter ~250,000

shortening ~250,000

viscosity [cP]

hydrogen 8.4 × 10−3

air 17.4 × 10−3

xenon 2.12 × 10-2

Non-Newtonian: Power law fluids

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k = flow consistency indexn = flow behavior index

dy

duln

Power law fluids

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Conservation of mass

Rectangular Coordinate System

“Continuity Equation”

“Del” Operator

Conservation of mass

Rectangular Coordinate System

Incompressible Fluid:

Momentum equation

Newtonian Fluid: Navier-Stokes Equations

t

VVV

Dt

VD

)(

VpgDt

VD

2

2

2

2

2

22

zyx

- material derivative

- Del operator

- Laplacian operator

Navier-Stokes Equations

Rectangular Coordinate System

Momentum equation

Special Case: 0 (ideal fluid; inviscid)

- Euler’s equation

t

VVV

Dt

VD

)( - Material derivative

- Del operator

Momentum equation

Special Case: Re << 1, stationary flow

- Low Reynolds number flow (creeping flow, Stokes flow)Vpg

0

Vpgt

VVV

Dt

VD

)(

00Re

LV

Vpgt

VVV

~~~~

~~

)~

(Re

rLr~

0

VVV~

0

tV

Lt ~

0

0

pL

Vp ~

0

0