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

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

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

Trapped air is favorable if

Liquid must be non-wetting

Wenzel law

composite wetting

WETTING OF A PATTERNED SURFACE

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

CASSIE-WENZEL TRANSITION

Young’s law for Cassie wetting:

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

prepared in Cassie state

Robust Cassie state requires small scale and deep holes

Transition to Wenzel state at

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

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

Volume

Flow on surface with non-uniform local bc

Local slip length : b(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

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

Local slip length : b(x,y)

Stripes of perfect slip and no-slip h.b.c.

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)

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

Hydrophobic silicon microposts

21 µm

Slip length

AN EXPERIMENTAL REALISATION

127 µm

Ou, Perot & Rothstein Phys Fluids 16, 4635 (2004)

Good agreement with MFD…

… why not just remove the posts ?

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

.) 150

Superhydrophobic state

Imbibated state

Barentin et al EPJ E 2005

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

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

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

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

Posts a<<LQuickTime™ et un

décompresseur TIFF (non compressé)sont requis pour visionner cette image.

No analytical results

argument of L. Bocquet

Flow on a « dotted » surface: hydrodynamic model

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

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

décompresseur TIFF (non compressé)sont requis pour visionner cette image.

SLIPPAGE ON A NANOTUBE FOREST

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

thiol in gaz phase thiol in liquid phase

Bundling due to capillary adhesion

beforeafter

Stiction is used to vary the pattern size of CNT’s forest

L=1.5 µm

L=3.2 µm L=6 µm

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

Flow on patterned surfaces

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