Introduction of Micro- /Nano-fluidic Flow Surface Tension 6/1/2015 1 J. L. Lin Assistant Professor...
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![Page 1: Introduction of Micro- /Nano-fluidic Flow Surface Tension 6/1/2015 1 J. L. Lin Assistant Professor Department of Mechanical and Automation Engineering.](https://reader030.fdocuments.in/reader030/viewer/2022012916/56649d235503460f949fa34e/html5/thumbnails/1.jpg)
Introduction of Micro-/Nano-fluidic Flow
Surface Tension
04/21/23 1
J. L. Lin
Assistant Professor
Department of Mechanical and Automation Engineering
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Outline
04/21/23 2
• Surface tension concept and origin
• Surface tension induced pressure, Laplace law,
minimal surfaces, meniscus on a fiber
• Influence of gravity, capillary length, capillary rise
• Contact angle, Young’s law
• Spreading parameter
• Zismann equation
• Contact angle measurements, contact angle hysteresis
• Surface roughness, Wenzel and Cassie-Baxter equations
• Superhydrophobic surfaces
• Electrowetting, electrically tunable surfaces
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Surface tension
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Liquid Jet
4
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Liquid Jet
jet speed 10 km/s
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Liquid Jet
6
caseexplosiveliner
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Liquid Jet
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Surface tension
229
-123
22 m
mJ20~
)m101(2
K300KJ104.1~
2~
2~
a
kT
a
U
UU/2
a
A
E
l
dx
dxlFdxdE 2
m
N
m
J2
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Surface tensionLiquid T [°C] [mN/m]
Acetone 20 23.7
Diethyl ether 20 17.0
Ethanol 20 22.27
Glycerol 20 63
n-Hexane 20 18.4
Isopropanol 20 21.7
Mercury 15 487
Methanol 20 22.6
n-Octane 20 21.8
Water 0 75.64
Water 25 71.97
Water 50 67.91
Water 100 58.85
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Laplace Equation
21
11
RRp
1R
2R
Δp for water drops of different radii
Droplet radius 1 mm 0.1 mm 1 μm 10 nmΔp (atm) 0.0014 0.0144 1.436 143.61
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Zero curvature surface
z
x
b
bz
z
21
b
xbz cosh
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Capillary length, capillary rise
gc
gRh
cos2
h
2R
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Contact angle
solid
liquid
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Youngs' Equation
Vapor-Liquid
Liquid-SolidVapor-Solidcos
Contact angle is determined by the interfacial tensions :
solid
liquid
dx SLSV
LV
cosdxdxdxdE LVSVSL
0dx
dEEquilibrium
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Spreading parameter
)( LVSLSV S
0S
0S
- total wetting
- partial wetting
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Zismann equation
Zisman plot of alkanes on a planar CVD coated wafer
0.5
0.6
0.7
0.8
0.9
1
18 20 22 24 26 28 30
Surface Tension (mN/m)
Co
sin
e o
f C
on
tact
An
gle
Hexane
Octane
Decane
Undecane
Dodecane
Tetradecane
Hexadecane
Trendline
c
cos 1 - const ( - c ) (Fox & Zismann (1950))
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Contact angle measurements
Camera 1(control)
Camera 2 (measurement)
Sample
Experimental setup
depositionsystem
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Contact angle hysteresis
no stick-slip
a
ra
advancing
receding
stick-slip
- hysteresisr
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Wenzel Equation
Vapor-Liquid
Liquid-SolidVapor-Solidcos
Contact angle is determined by the interfacial tensions :
dx SLSV
LV
cosdxdxdxdE LVSVSL
0dx
dEEquilibrium
solid
liquid
cosdxwdxwdxdE LVSVSL
0coscos w
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Composite surfaces
liquid
solid
Vapor-Liquid
*Liquid-SolidVapor-Solid
*
cos
Vapor-LiquidLiquid-Solid*
Liquid-Solid 1 ff
A 1
A 2
21 / AAf
0
1)1(coscos 0 f
Vapor-Liquid
Liquid-SoidVapor-Solid0cos
3 m
Vapor-VaporVapor-Solid*
Vapor-Solid 1 ff
0=
Cassie & Baxter (1944)
Cassie – Baxter equation
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Superhydrophobic surfaces
Solvent evaporationinduced i-PP gel
Porous isotactic polypropylene (i-PP)Fractal alkylketene dimer (AKD)
AKD solidified from melt
0 = 109°
0 = 174°
fractal
0 = 160°
porous
flat
H.Y. Erbil, A.L. Demirel,Y. Avcy, O. Mert (2003)
S. Shibuichi, T. Onda, N. Satoh, K. Tsujii (1996)
5 m
0 = 104°
flat
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Superhydrophobic surfaces
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Superhydrophobic surfacesTopography hierarchy in lotus leaves
A. Large-scale SEM image of the lotus leaf. Every epidermal cell forms a papilla and has a dense layer of epicuticular waxes superimposed on it. B. Magnified image on a single papilla of A.
Micro- and nanostructures on the lotus leaf (Nelumbo nucifera)
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Superhydrophobic surfacesExamples
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Superhydrophobic surfacesSelf-cleaning surfaces
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Superhydrophobic surfacesExamples
Nanostructured surface of the superhydrophobic wings of cicada (Cicada orni).
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Superhydrophobic surfacesExamples
Nanostructured surface of the superhydrophobic legs of the water strider (Gerris remigis).
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Electrowetting
m1d
m1.0 d
m5.0 d
2
L
0
2)0(cos)(cos V
dVV r
conducting liquid
V L
conductive electrodedielectric film
r
d
Example: Water droplet on Cytop® surface
1.2rmN/m72L
112)0( V
[º]
]V[V
dxd
VdxdxdxdE o
LVSVSL
2
cos2
0dx
dEEquilibrium
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Electrowetting Equation
Vapor-Liquid
Liquid-SolidVapor-Solidcos
Contact angle is determined by the interfacial tensions :
dx SLSV
LV
cosdxdxdxdE LVSVSL
0dx
dEEquilibrium
solid
liquid
dxd
VdxdxdxdE o
LVSVSL
2
cos2
2
L
0
2)0(cos)(cos V
dVV r
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Electrowetting
Substrate: Si / 60 nm SiO2 / 20 nm CF1.55 (CVD)Liquid:1-ethyl-3-methyl-1 H-imidazolium tetrafluoroborate
0 V – 80 V – 0 V
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Electrowetting
Substrate: ITO / 250 nm SiNx / 1 m Cytop
0 V – 60 V – 0 V
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Lubrication principle
Possible sources of hysteresis and stick-slip
– mechanical roughness– compositional
inhomogeneity– chemical contamination
= 1 = 2 = 3
1cosLF
SLSF
jiijjiij 2
LF
S
10 20 30 40 50 60 70 80
100
120
140
160
180
mN/m16F
mN/m20F
[mN/m]S
][
SLSFLF
SF
L
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Tunable superhydrophobic surfaces
10 m
Rolling ball
Sticky droplet
superhydrophobicslip boundary
hydrophilicno slip
liquid
solid
superhydrophobic
hydrophilic
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f2 >> f1
cos ~ f
strongly nonlinear effectcontact angle controlcontact angle hysteresis control
V = 0
V 0
liquid
solid
0
liquid
solid
f1
f2
conductor
isolator
low-energycoating
Tunable superhydrophobic surfaces
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Rolling ball Sticky droplet
Tunable superhydrophobic surfaces
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Electrowetting induced transitions
molten salt*, = 62 mN/m*1-ethyl-3-methyl-1 H-imidazolium tetrafluoroborate
3 m
pitch 4 m
Tunable superhydrophobic surfaces
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180°
90°
cos
V 2 [V2]
pitch 1.05 m
pitch 4 m
Tunable superhydrophobic surfaces