Introduction of Micro-/Nano-fluidic Flow

Surface Tension

04/21/23 1

J. L. Lin

Assistant Professor

Department of Mechanical and Automation Engineering

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

Surface tension

Liquid Jet

4

Liquid Jet

jet speed 10 km/s

Liquid Jet

6

caseexplosiveliner

Liquid Jet

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

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

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

Zero curvature surface

z

x

b

bz

z

21

b

xbz cosh

Capillary length, capillary rise

gc

gRh

cos2

h

2R

Contact angle

solid

liquid

Youngs' Equation

Vapor-Liquid

Liquid-SolidVapor-Solidcos

Contact angle is determined by the interfacial tensions :

solid

liquid

dx SLSV

LV

cosdxdxdxdE LVSVSL

0dx

dEEquilibrium

Spreading parameter

)( LVSLSV S

0S

0S

- total wetting

- partial wetting

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))

Contact angle measurements

Camera 1(control)

Camera 2 (measurement)

Sample

Experimental setup

depositionsystem

Contact angle hysteresis

no stick-slip

a

ra

advancing

receding

stick-slip

- hysteresisr

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

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

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

Superhydrophobic surfaces

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)

Superhydrophobic surfacesExamples

Superhydrophobic surfacesSelf-cleaning surfaces

Superhydrophobic surfacesExamples

Nanostructured surface of the superhydrophobic wings of cicada (Cicada orni).

Superhydrophobic surfacesExamples

Nanostructured surface of the superhydrophobic legs of the water strider (Gerris remigis).

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

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

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

Electrowetting

Substrate: ITO / 250 nm SiNx / 1 m Cytop

0 V – 60 V – 0 V

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

Tunable superhydrophobic surfaces

10 m

Rolling ball

Sticky droplet

superhydrophobicslip boundary

hydrophilicno slip

liquid

solid

superhydrophobic

hydrophilic

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

Rolling ball Sticky droplet

Tunable superhydrophobic surfaces

Electrowetting induced transitions

molten salt*, = 62 mN/m*1-ethyl-3-methyl-1 H-imidazolium tetrafluoroborate

3 m

pitch 4 m

Tunable superhydrophobic surfaces

180°

90°

cos

V 2 [V2]

pitch 1.05 m

pitch 4 m

Tunable superhydrophobic surfaces