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Flow on patterned surfaces E. CHARLAIX University of Lyon, France NANOFLUIDICS SUMMER SCHOOL August 20-24 2007 THE ABDUS SALAM INTERNATIONAL CENTER FOR THEORETICAL PHYSICS

Flow on patterned surfaces

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Flow on patterned surfaces. E. CHARLAIX. University of Lyon, France. NANOFLUIDICS SUMMER SCHOOL August 20-24 2007. THE ABDUS SALAM INTERNATIONAL CENTER FOR THEORETICAL PHYSICS. OUTLINE. 1. The bubble mattress. Basics of wetting / Superhydrophobic surfaces. - PowerPoint PPT Presentation

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Page 1: Flow on patterned surfaces

Flow on patterned surfaces

E. CHARLAIXUniversity of Lyon, France

NANOFLUIDICS SUMMER SCHOOL August 20-24 2007THE ABDUS SALAM INTERNATIONAL CENTER FOR THEORETICAL PHYSICS

Page 2: Flow on patterned surfaces

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

Page 3: Flow on patterned surfaces

On non-wetting surfaces,can roughness increase slip ?

Roughness and wetting : a conspiracy ?

Hydrodynamic calculations : roughness decreases slip.

Page 4: Flow on patterned surfaces

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

Page 5: Flow on patterned surfaces

Bico, Marzolin & QuéréEurophys. Lett 47, 220 (1999)

Lotus effect

Super-hydrophobic surfaces: surfing on an air-cushion ?

Page 6: Flow on patterned 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°

Page 7: Flow on patterned surfaces

WETTING OF A ROUGH SURFACE

Wenzel law

Young’s law on rough surface:

: contact angle on flat

chemically same surface

1

-1 1

-1

-

Page 8: Flow on patterned surfaces

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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Page 9: Flow on patterned surfaces

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

Page 10: Flow on patterned surfaces

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

Page 11: Flow on patterned surfaces

Contact angle afterseparating the plates

Maximum pressure applied

Cassie state

Wenzel state

Lafuma & Quéré 2003 Nature Mat. 2, 457

Page 12: Flow on patterned surfaces

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

Page 13: Flow on patterned surfaces

1 µm

Non-wetting nano-textured surfaces : MD simulations

Cottin-Bizonne & al 2003 Nature Mat 2, 237

Page 14: Flow on patterned surfaces

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

Page 15: Flow on patterned surfaces

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

Page 16: Flow on patterned surfaces

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

Page 17: Flow on patterned surfaces

Wetting state as a function of applied pressure

Cassie stateWenzel state

Pre

ssu

re (

u.L.

J.)

Volume

Page 18: Flow on patterned 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

Page 19: Flow on patterned surfaces

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

Page 20: Flow on patterned surfaces

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 !

Page 21: Flow on patterned surfaces

Stripes perpendicular to the shear (Stone and Lauga 2003)

flow

2D pattern: semi-analytical calculation (Barentin et al EPJE 2004)

Page 22: Flow on patterned surfaces

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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 ?

Page 23: Flow on patterned surfaces

Flow on nano-textured SH surfaces : MD simulation

Page 24: Flow on patterned surfaces

Flow on nano-textured surface : Wenzel state

- on the smooth surface : slip = 22 - on the imbibated rough surface : slip = 2

Roughness decreases slip

Page 25: Flow on patterned surfaces

Flow on the nano-textured surface : Cassie state

- on the smooth surface : slip = 24 - on the super-hydrophobic surface : slip = 57 Roughness increases slip

Page 26: Flow on patterned surfaces

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

Page 27: Flow on patterned surfaces

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

Page 28: Flow on patterned surfaces

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

Page 29: Flow on patterned surfaces

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

Page 30: Flow on patterned surfaces

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.

Page 31: Flow on patterned surfaces

Local surface compliance

Flow on a compressible surface

Newtonian incompressible fluid

Lubrication approximation

K : stiffness per unit surface [N/m3]

elastic response

viscous damping

Page 32: Flow on patterned surfaces

no-slip on spherepartial slip on plane

Flow on a compressible surface

Non-contact measurement of surface elasticity K

Page 33: Flow on patterned surfaces

L

a

Surface stiffness of a bubble carpet

L=1,4 µma=0,65 µm

Experimentalvalue

gazmeniscus

Page 34: Flow on patterned surfaces

Effective slippage on the bubble carpet(FEMLAB calculation)

hydrophilicno bubbles

SH surfaces can promote high friction flow

slip planeslip planeno bubble

Page 35: Flow on patterned surfaces

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

Page 36: Flow on patterned surfaces

Some hope….flow on a « dotted » surface: hydrodynamic model

La

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No analytical results

argument of L. Bocquet

Page 37: Flow on patterned surfaces

Flow on a « dotted » surface: hydrodynamic model

Posts a<<L QuickTime™ et undécompresseur TIFF (non compressé)sont requis pour visionner cette image.

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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:

better than stripes QuickTime™ et un

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La

Page 38: Flow on patterned surfaces

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

Page 39: Flow on patterned surfaces

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thiol in gaz phase thiol in liquid phase

Bundling due to capillary adhesion

beforeafter

Page 40: Flow on patterned surfaces

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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

Page 41: Flow on patterned surfaces

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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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