Flow on patterned surfaces E CHARLAIX University of

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 ü Basics of wetting / Superhydrophobic surfaces ü Cassie/Wenzel transition on nanoscale patterns 2. Surfing on an air cushion ? ü The flat heterogeneous surface: hydrodynamics predictions ü Nanoscale patterned surfaces: MD simulations ü Nanorheology experiments on carved SH surfaces ü CNT’s and the wetted air effect

Roughness and wetting : a conspiracy ? Hydrodynamic calculations : roughness decreases slip. On non-wetting surfaces, can roughness increase slip ?

n 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 20µm

Super-hydrophobic surfaces: surfing on an air-cushion ? Lotus effect Bico, Marzolin & Quéré Europhys. Lett 47, 220 (1999)

BASICS OF WETTING g. SL : solid-liquid surface tension g. SV : solid-liquid surface tension g. LV partially wetting liquid : < 90° g. SV g. SL non wetting liquid : > 90° equilibrium contact angle : Young Dupré relation g. SV - g. SL = g. LV cos perfect wetting liquid : =0°

WETTING OF A ROUGH SURFACE Young’s law on rough surface: Wenzel law o : contact angle on flat chemically same surface 1 -1

2 a WETTING OF A PATTERNED SURFACE h Bico, Marzolin & Quéré Europhys. Lett 47, 220 (1999) Trapped air is favorable if -1 composite wetting Wenzel law Liquid must be non-wetting -1

2 a CASSIE-WENZEL TRANSITION h Young’s law for Cassie wetting: Bico, Marzolin & Quéré Europhys. Lett 47, 220 (1999) -1 Cassie wetting Cassie-Baxter’s law Wenzel wetting -1

METASTABILITY OF WETTING ON MICROPATTERNED SURFACES Lafuma & Quéré 2003 Nature Mat. 2, 457 Cassie state Compression of a water drop between two identical microtextured hydrophobic surfaces. The contact angle is measured as a function of the imposed pressure. Wenzel state

Lafuma & Quéré 2003 Nature Mat. 2, 457 Contact angle after separating the plates Cassie state Wenzel state Maximum pressure applied

METASTABILITY OF CASSIE/WENZEL STATES ∆P prepared in Cassie state d Transition to Wenzel state at -1 Robust Cassie state requires small scale and deep holes -1

Non-wetting nano-textured surfaces : MD simulations Cottin-Bizonne & al 2003 Nature Mat 2, 237 1 µm

Lennard-Jones fluid = {liquid, solid}, e : energy scale : molecular diameter c b : wetting control parameter Non-wetting situation : c. Ls = 0, 5 : o =140° N : nb of molecule in the cell

Wetting state as a function of applied pressure Pressure (u. L. J. ) C b = 0. 5 = 140° N is constant Volume Imbibated (Wenzel) state Super-hydrophobic (Cassie) state

Cassie-Wenzel transition under applied pressure Cassie state Wenzel state Gibbs energy at applied pressure P Super-hydrophobic state is stable if Super-hydrophobic transition at zero pressure For a given material and texture shape, super-hydrophobic state is favored if scale is small

Pressure (u. L. J. ) Wetting state as a function of applied pressure Volume Wenzel state Cassie state

Flow on surface with non-uniform local bc y x Local slip length : b(x, y) (Independant of shear rate) b=∞ : (favorable) approximation for gaz surface What is the apparent bc far from the surface ?

Effective slip on a patterned surface: macroscopic calculation Couette flow L Local slip length : b(x, y) Bulk flow : Stokes equations Apparent slip: Shear applied at z = Decay of flow corrugations

Stripes of perfect slip and no-slip h. b. c. Effective slip length flow · Stripes parallel to shear (Philip 1972) analytical calculation Bad news ! The length scale for slip is the texture scale Even with parallel stripes of perfect slip, effective slip is weak: B// = L for z = 0. 98

flow · Stripes perpendicular to the shear (Stone and Lauga 2003) · 2 D pattern: semi-analytical calculation (Barentin et al EPJE 2004)

AN EXPERIMENTAL REALISATION Hydrophobic silicon microposts 127 µm Pressure drop reduction Ou, Perot & Rothstein Phys Fluids 16, 4635 (2004) 21 µm Slip length 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 Roughness increases slip - on the super-hydrophobic surface : slip = 57

Influence of pressure on the boundary slip d Pcap = -2 glv cos d Slip length (u. L. J. ) Barentin et al EPJ E 2005 150 Superhydrophobic state 100 50 Imbibated state 0 0 1 P/Pcap 2 3 The boundary condition depends highly on pressure. Low friction flow is obtained under a critical pressure, which is the pressure for Cassie-Wenzel transition

Comparison of MD slip length with a macroscopic calculation on a flat surface with a periodic pattern of h. b. c. More dissipation than macroscopic calculation because of the meniscus

Flow on patterned surface : experiment square lattice of holes in silicon obtained by photolithography fraction area of holes: 1 -F = 68 ± 6 % L = 1. 4 µm holes Ø : 1. 2 µm ± 5% bare silicon hydrophilic OTS-coated silicon superhydrophobic L = 1. 4 µm B =50 +/-20 nm Wenzel wetting Calculation of BC: effective slip plane B =170 +/-30 nm Cassie wetting Qa=148° Qr =139°

Nanorheology on patterned surface: SFA experiments Hydrophobic (silanized) Cassie Hydrophilic Wenzel 1/G"(w) Bapp = 100 +/- 30 nm 0 D(nm) 1200 Bapp = 20 +/- 30 nm

Elastic response on Super. Hydrophobic surfaces Elasticity G’(w) SH surface Hydrophilic surface Force response on SH surface shows non-zero elastic response. Signature of trapped bubbles in holes.

Flow on a compressible surface Newtonian incompressible fluid Lubrication approximation Local surface compliance viscous damping K : stiffness per unit surface [N/m 3] d elastic response

Flow on a compressible surface no-slip on sphere partial slip on plane d Non-contact measurement of surface elasticity K

Surface stiffness of a bubble carpet L=1, 4 µm a=0, 65 µm a Experimental value meniscus gaz L

Effective slippage on the bubble carpet (FEMLAB calculation) slip plane no bubble hydrophilic no bubbles SH surfaces can promote high friction flow slip plane

Take-home message q Low friction flow at L/S interface (large slippage) is difficult to obtain q Tailoring of surfaces is crucial !!! Eg: for pattern L=1µm, want to obtain b=10µm requires Fs = 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 No analytical results L a Posts a<<L argument of L. Bocquet

Flow on a « dotted » surface: hydrodynamic model L a Posts a<<L ØThe flow is perturbed over the dots only, in a region of order of their size Ø Friction occurs only on the solid surface better than stripes Numerical resolution of Stoke’s equation: ~1/p

SLIPPAGE ON A NANOTUBE FOREST q Nanostructured surfaces C. Journet, J. M. Benoit, S. Purcell, LPMCN PECVD, growth under electric field 1 µm q Superhydrophobic (thiol functionnalization) = 163° (no hysteresis) C. Journet, Moulinet, Ybert, Purcell, Bocquet, Eur. Phys. Lett, 2005

thiol in gaz phase thiol in liquid phase before after Bundling due to capillary adhesion

L=1. 5 µm L=3. 2 µm L=6 µm Stiction is used to vary the pattern size of CNT’s forest

CNT forest is embeded in microchanel Pressure driven flow PIV measurement b (µm) Cassie state Slip length increases with the pattern period L 0. 28 Wenzel state