Introduction of Micro/Nano-fluidic Flow
J. L. Lin
Assistant Professor
Department of Mechanical and
Automation Engineering
3/22/2016
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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
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Course outline
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
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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
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Course objectives
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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
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Grade
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Cumulative score:
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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
When a shear stress is applied:
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Fluids continuously deform
•
Solids deform or bend
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Velocity field
Eulerian velocity field
y
y

V (r , t )

V ( r , t  t )
x
material derivative
x

DB
B

 (V  ) B
Dt
t
Lagrangian velocity field
y
y

V (r (t  t ), t  t )
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
V (r (t ), t )
x
x
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Stress Field
y
x
A F
z
dFi    ij dA j   ij dA j
j
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couette flow
Viscosity
du
~
dy
du
 
dy
viscosity
- Newtonian
 du 
 du  du
  f      
 dy 
 dy  dy
apparent
viscosity
- 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
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Viscosity
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 [m2·s−1].
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Dynamic viscosity
viscosity 
[Pa s]
[cP]
Viscosity 
[cP]
honey
2,000–10,000
molasses
5,000–10,000
0.306
molten glass
10,000–1,000,000
5.44 × 10−4
0.544
chocolate syrup
10,000–25,000
water
1.00 × 10−3
1.000
molten chocolate
45,000–130,000
ethanol
1.074 × 10−3
1.074
ketchup
50,000–100,000
mercury
1.526 × 10−3
1.526
peanut butter
~250,000
nitrobenzene
1.863 × 10−3
1.863
shortening
~250,000
propanol
1.945 × 10−3
1.945
ethylene glycol
1.61 × 10−2
16.1
viscosity 
sulfuric acid
2.42 × 10−2
24.2
hydrogen
8.4 × 10−3
olive oil
.081
81
air
17.4 × 10−3
glycerol
.934
934
xenon
2.12 × 10-2
corn syrup
1.3806
1380.6
liquid nitrogen
1.58 × 10−4
0.158
acetone
3.06 × 10−4
methanol
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[cP]
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Non-Newtonian: Power law fluids
ln
du
dy
k
= flow consistency index
n = flow behavior index
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Power law fluids
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Conservation of mass
“Continuity Equation”
“Del” Operator
Rectangular Coordinate System
Conservation of mass
Incompressible Fluid:
Rectangular Coordinate System
Momentum equation
Newtonian Fluid: Navier-Stokes Equations



DV

  g  p   V
Dt



 V
DV
 (V  ) V 
Dt
t
- material derivative
- Del operator
2
2
2



  2      2  2  2
x
y
z
- Laplacian operator
Navier-Stokes Equations
Rectangular Coordinate System
Momentum equation
Special Case:   0 (ideal fluid; inviscid)
- Euler’s equation



 V
DV
 (V  ) V 
Dt
t
- Material derivative
- Del operator
Momentum equation
Special Case: Re << 1, stationary flow


 V 

 

DV

  (V  ) V 
   g  p   V
Dt
t 

~
 ~
~ V 
~

~
~
~

Re (V  ) V  ~    g  p   V
r  L0 r

t


~

 V0 L0
Re 



0   g  p   V
V  V0 V
L0 ~
t
t
V0
p
 V0 ~
p
L0
- Low Reynolds number flow
(creeping flow, Stokes flow)