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Flow on patterned surfaces Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008 The Kavli Institute of Theoretical Physics China

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

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Bico, Marzolin & Quéré Europhys. Lett 47, 220 (1999) Lotus effect Super-hydrophobic surfaces

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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

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

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

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Bico, Marzolin & Quéré Europhys. Lett 47, 220 (1999) 2a h Extended Young’s law Wenzel wetting Cassie wetting CASSIE / WENZEL CONTACT ANGLES

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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

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

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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

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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

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

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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 !

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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 Ou, Perot & Rothstein Phys Fluids 16, 4635 (2004) Pressure drop reduction Good agreement with MFD…

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Pressure drop reduction that would be obtained by suppressing the posts 127 µm 160 µm > 50%

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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

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

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

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Wetting state as a function of applied pressure Super-hydrophobic (Cassie) stateImbibated (Wenzel) state Pressure (u.L.J.) Volume C = 0.5 = 140° N is constant

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Cassie stateWenzel 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

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

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Flow on nano-textured SH surfaces : MD simulation

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Flow on nano-textured surface : Wenzel state - on the smooth surface : slip = 22 - on the imbibated rough surface : slip = 2 Roughness decreases slip

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Flow on the nano-textured surface : Cassie state - on the smooth surface : slip = 24 - on the super-hydrophobic surface : slip = 57 Roughness increases slip

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P cap = -2 lv 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/P cap Slip length (u.L.J.) 150 100 50 0 Superhydrophobic state Imbibated state Barentin et al EPJ E 2005 d

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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

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fraction area of holes: 1- = 68 ± 6 % Flow on patterned surface : experiment square lattice of holes in silicon obtained 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 wettingCassie wetting

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B app = 20 +/- 30 nm B app 12000 D(nm) 1/G"( ) B app = 100 +/- 30 nm Hydrophilic Wenzel Hydrophobic (silanized) Cassie Nanorheology on patterned surface: SFA experiments

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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.

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

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

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

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

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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)

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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

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

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Flow on a « dotted » surface: hydrodynamic model Posts a<

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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 before after

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Stiction is used to vary the pattern size of CNT’s forest L=1.5 µm L=3.2 µmL=6 µm

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b (µm) 0.28 ~1/π Slip length increases with the pattern period L CNT forest is embeded in microchanel Pressure driven flow PIV measurement Wenzel state Cassie state

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