Post on 27-Dec-2015
Flow on patterned surfaces
E. CHARLAIXUniversity of Lyon, France
NANOFLUIDICS SUMMER SCHOOL August 20-24 2007THE ABDUS SALAM INTERNATIONAL CENTER FOR THEORETICAL PHYSICS
OUTLINE
1. The bubble mattress
Basics of wetting / Superhydrophobic surfaces
Cassie/Wenzel transition on nanoscale patterns
2. Surfing on an air cushion ?
The flat heterogeneous surface: hydrodynamics predictions Nanoscale patterned surfaces: MD simulations
Nanorheology experiments on carved SH surfaces
CNT’s and the wetted air effect
On non-wetting surfaces,can roughness increase slip ?
Roughness and wetting : a conspiracy ?
Hydrodynamic calculations : roughness decreases slip.
Watanabee et al J.F.M.1999
Rough surface with water-repellent coating
Contact angle 150°
Very large slip effects (200 µm)
Drag reduction in high Re flows
20µm
100µm
Bico, Marzolin & QuéréEurophys. Lett 47, 220 (1999)
Lotus effect
Super-hydrophobic surfaces: surfing on an air-cushion ?
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°
WETTING OF A ROUGH SURFACE
Wenzel law
Young’s law on rough surface:
: contact angle on flat
chemically same surface
1
-1 1
-1
-
Trapped air is favorable if
Liquid must be non-wetting
-1
-1
Wenzel law
composite 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
CASSIE-WENZEL TRANSITION
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Young’s law for Cassie wetting:
-1
-1
Wenzel wetting
Cassie wetting
Cassie-Baxter’s law
METASTABILITY OF WETTING ON MICROPATTERNED 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
METASTABILITY OF CASSIE/WENZEL STATES
-1
prepared in Cassie state
-1
Robust Cassie state requires small scale and deep holes
d
∆P
Transition to Wenzel state at
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
Super-hydrophobic transition at zero pressure
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 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 !
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 REALISATION
127 µm
Ou, Perot & Rothstein Phys Fluids 16, 4635 (2004)
Pre
ssur
e dr
op r
educ
tion
Good agreement with MFD…
… why not just remove the posts ?
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
Effective slippage on the bubble carpet(FEMLAB calculation)
hydrophilicno bubbles
SH surfaces can promote high friction flow
slip planeslip planeno bubble
Take-home message
Low friction flow at L/S interface (large slippage) is difficult to obtain
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
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)
0.28Slip 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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