flow on patterned surfaces nanoscale interfacial phenomena in complex fluids - may 19 - june 20 2008...

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


2a

h

WETTING OF A PATTERNED SURFACE

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.






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






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)




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…



Pre

ssur

e dr

op r

educ

tion

Pressure drop reductionthat would be obtainedby suppressing the posts

127 µm 160 µm

> 50%

OUTLINE






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






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

La

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.

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



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)

0.28 ~1/πSlip 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 nanoscale interfacial phenomena in complex fluids - may 19 - june 20 2008...

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