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
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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