Flow on patterned surfaces
Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008
The Kavli Institute of Theoretical Physics China
On non-wetting surfaces,can roughness increase slip ?
Roughness and wetting : a conspiracy ?
Hydrodynamic calculations : roughness decreases slip.
Bico, Marzolin & QuéréEurophys. Lett 47, 220 (1999)
Lotus effect
Super-hydrophobic surfaces
OUTLINE
Basics of wetting / Superhydrophobic surfaces
Surfing on an air cushion ? Hydrodynamics predictions
Flow on nanopatterned surfaces : MD simulations
The sticky bubbles mattress
How to design highly slippery surfaces
BASICS OF WETTING
SL : solid-liquid surface tension
SV : solid-liquid surface tension
LV : solid-liquid surface tension
SL
LVSV
equilibrium contact angle :Young Dupré relation
SV - SL = LV cos
non wetting liquid : > 90°
partially wetting liquid : < 90°
perfect wetting liquid : =0°
Trapped air is favorable if
Liquid must be non-wetting
Bico, Marzolin & QuéréEurophys. Lett 47, 220 (1999)
2a
h
WETTING OF A PATTERNED SURFACE
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Bico, Marzolin & QuéréEurophys. Lett 47, 220 (1999)
2a
h
Extended Young’s law
-1
-1
Wenzel wetting
Cassie wetting
CASSIE / WENZEL CONTACT ANGLES
METASTABILITY OF WETTING ON SH SURFACES
Compression of a water drop between two identical microtextured hydrophobic surfaces. The contact angle is measured as a function of the imposed pressure.
Lafuma & Quéré 2003 Nature Mat. 2, 457
Cassie state
Wenzel state
Contact angle afterseparating the plates
Maximum pressure applied
Cassie state
Wenzel state
Lafuma & Quéré 2003 Nature Mat. 2, 457
OUTLINE
Basics of wetting / Superhydrophobic surfaces
Surfing on an air cushion ? Hydrodynamics predictions
Flow on nanopatterned surfaces : MD simulations
The sticky bubbles mattress
How to design highly slippery surfaces
Flow on surface with non-uniform local bc
Local slip length : b(x,y)
x
y
What is the apparent bc far from the surface ?
(Independant of shear rate)
b=∞ : (favorable) approximation for gaz surface
Effective slip on a patterned surface: macroscopic calculation
Bulk flow : Stokes equations
Shear applied at z =
Apparent slip:
Couette flow
Decay of flow corrugations
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Local slip length : b(x,y)
L
Stripes of perfect slip and no-slip h.b.c.
flow
analytical calculation
Effective slip length
Stripes parallel to shear (Philip 1972)
The length scale for slip is the texture scale
Even with parallel stripes of perfect slip, effective slip is weak:B// = L for = 0.98
Bad news !
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Stripes perpendicular to the shear (Stone and Lauga 2003)
flow
2D pattern: semi-analytical calculation (Barentin et al EPJE 2004)
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Hydrophobic silicon microposts
21 µm
Slip length
AN EXPERIMENTAL REALISATIONOu, Perot & Rothstein Phys Fluids 16, 4635 (2004)
Pre
ssur
e dr
op r
educ
tion
Good agreement with MFD…
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Pre
ssur
e dr
op r
educ
tion
Pressure drop reductionthat would be obtainedby suppressing the posts
127 µm 160 µm
> 50%
OUTLINE
Basics of wetting / Superhydrophobic surfaces
Surfing on an air cushion ? Hydrodynamics predictions
Flow on nanopatterned surfaces : MD simulations
The sticky bubbles mattress
How to design highly slippery surfaces
1 µm
Non-wetting nano-textured surfaces : MD simulations
Cottin-Bizonne & al 2003 Nature Mat 2, 237
Lennard-Jones fluid
Non-wetting situation : cLs = 0,5 : =140°
N : nb of molecule in the cell
= {liquid,solid}, : energy scale : molecular diameter
c : wetting control parameter
Wetting state as a function of applied pressure
Super-hydrophobic (Cassie) stateImbibated (Wenzel) state
Pre
ssu
re (
u.L.
J.)
Volume
C= 0.5 = 140°
N is constant
Cassie state Wenzel state
Gibbs energy at applied pressure P
Super-hydrophobic state is stable if
Cassie-Wenzel transition under applied pressure
For a given material and texture shape, super-hydrophobic state is favored if scale is small
Wetting state as a function of applied pressure
Cassie stateWenzel state
Pre
ssu
re (
u.L.
J.)
Volume
Flow on nano-textured SH surfaces : MD simulation
Flow on nano-textured surface : Wenzel state
- on the smooth surface : slip = 22 - on the imbibated rough surface : slip = 2
Roughness decreases slip
Flow on the nano-textured surface : Cassie state
- on the smooth surface : slip = 24 - on the super-hydrophobic surface : slip = 57 Roughness increases slip
Pcap = -2lv cos d
Influence of pressure on the boundary slip
The boundary condition depends highly on pressure.
Low friction flow is obtained under a critical pressure, which is the pressure for Cassie-Wenzel transition
0 1 2 3
P/Pcap
Slip
len
gth
(u.
L.J
.) 150
100
50
0
Superhydrophobic state
Imbibated state
Barentin et al EPJ E 2005
d
Comparison of MD slip length with a macroscopic calculation
on a flat surface with a periodic pattern of h.b.c.
More dissipation thanmacroscopic calculationbecause of the meniscus
fraction area of holes: 1- = 68 ± 6 %
Flow on patterned surface : experiment
square lattice of holes in siliconobtained by photolithography
L = 1.4 µm
bare silicon hydrophilic
Calculation of BC:
B =50 +/-20 nm effective slip plane B =170 +/-30 nm
OTS-coated silicon superhydrophobic
a=148°
r =139°
L = 1.4 µm
holes Ø : 1.2 µm ± 5%
Wenzel wetting Cassie wetting
Bapp = 20 +/- 30 nm
Bapp
12000 D(nm)
1/G"()
Bapp = 100 +/- 30 nm
Hydrophilic Wenzel
Hydrophobic (silanized) Cassie
Nanorheology on patterned surface: SFA experiments
Elastic response on SuperHydrophobic surfaces
Elasticity G’()
Hydrophilic surface
SH surface
Force response on SH surface shows non-zero elastic response.
Signature of trapped bubbles in holes.
Local surface compliance
Flow on a compressible surface
Newtonian incompressible fluid
Lubrication approximation
K : stiffness per unit surface [N/m3]
elastic response
viscous damping
no-slip on spherepartial slip on plane
Flow on a compressible surface
Non-contact measurement of surface elasticity K
L
a
Surface stiffness of a bubble carpet
L=1,4 µma=0,65 µm
Experimentalvalue
gazmeniscus
Effective slippage on the bubble carpet(FEMLAB calculation)
hydrophilicno bubbles
SH surfaces can promote high friction flow
slip planeslip planeno bubble
Take-home message
Large slippage at L/S interface is difficult to obtain
For large slippage, tailoring of surfaces is crucial !!!
Eg: for pattern L=1µm, want to obtain b=10µm
requires s = 0.1% (solid/liquid area)
corresponds to c.a. ~ 178° (using Cassie relation)
meniscii should be (nearly) flat
Nanobubbles are unlikely to yield large slippage (and explain data scatter)
OUTLINE
Basics of wetting / Superhydrophobic surfaces
Surfing on an air cushion ? Hydrodynamics predictions
Flow on nanopatterned surfaces : MD simulations
The sticky bubbles mattress
How to design highly slippery surfaces
Some hope….flow on a « dotted » surface: hydrodynamic model
La
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No analytical results
argument of L. Bocquet
Flow on a « dotted » surface: hydrodynamic model
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The flow is perturbed over the dots only, in a region of order of their size
Friction occurs only on the solid surface
Numerical resolution of Stoke’s equation:
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La
SLIPPAGE ON A NANOTUBE FOREST
1 µm
C. Journet, J.M. Benoit, S. Purcell, LPMCN
Nanostructured surfaces
PECVD, growth under electric field
Superhydrophobic (thiol functionnalization)
= 163° (no hysteresis)
C. Journet, Moulinet, Ybert, Purcell, Bocquet, Eur. Phys. Lett, 2005
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thiol in gaz phase thiol in liquid phase
Bundling due to capillary adhesion
beforeafter
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Stiction is used to vary the pattern size of CNT’s forest
L=1.5 µm
L=3.2 µm L=6 µm
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b (µm)
0.28 ~1/πSlip length increases with the pattern period L
CNT forest is embeded in microchanelPressure driven flow
PIV measurement
Wenzel state
Cassie state
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