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## 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 • 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**Roughness and wetting : a conspiracy ?**Hydrodynamic calculations : roughness decreases slip. On non-wetting surfaces, can roughness increase slip ?**Watanabee et al J.F.M.1999**Rough surface with water-repellent coating Contact angle 150° 100µm Very large slip effects (200 µm) Drag reduction in high Re flows 20µm**Super-hydrophobic surfaces: surfing on an air-cushion ?**Lotus effect Bico, Marzolin & Quéré Europhys. Lett 47, 220 (1999)**BASICS OF WETTING**gSL : solid-liquid surface tension gSV : solid-liquid surface tension partially wetting liquid : q < 90° gLV: solid-liquid surface tension gLV gSV gSL non wetting liquid : q > 90° equilibrium contact angle : Young Dupré relation gSV - gSL =gLV cos q perfect wetting liquid : q =0°**1**- -1 1 -1 WETTING OF A ROUGH SURFACE Young’s law on rough surface: q Wenzel law qo : contact angle on flat chemically same surface**2a**h Trapped air is favorable if Liquid must be non-wetting WETTING OF A PATTERNED SURFACE Bico, Marzolin & Quéré Europhys. Lett 47, 220 (1999) -1 composite wetting Wenzel law -1**2a**h q -1 Cassie wetting Wenzel wetting -1 CASSIE-WENZEL TRANSITION Bico, Marzolin & Quéré Europhys. Lett 47, 220 (1999) Young’s law for Cassie wetting: Cassie-Baxter’s law**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**∆P**d Transition to Wenzel state at METASTABILITY OF CASSIE/WENZEL STATES q prepared in Cassie state -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** = {liquid,solid},**• : energy scale : molecular diameter • cab : wetting control parameter Lennard-Jones fluid N : nb of molecule in the cell Non-wetting situation : cLs = 0,5 : qo =140°**Wetting state as a function of applied pressure**Cab = 0.5 q = 140° N is constant Pressure (u.L.J.) 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**Wetting state as a function of applied pressure**Pressure (u.L.J.) 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 ?**Shear applied at z =**Effective slip on a patterned surface: macroscopic calculation Couette flow L Local slip length : b(x,y) Decay of flow corrugations Bulk flow : Stokes equations Apparent slip:**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) • 2D pattern: semi-analytical calculation (Barentin et al EPJE 2004)**127 µm**AN EXPERIMENTAL REALISATION Ou, Perot & Rothstein Phys Fluids 16, 4635 (2004) 21 µm Pressure drop reduction Slip length Hydrophobic silicon microposts 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 s - on the imbibated rough surface : slip = 2 s Roughness decreases slip**Flow on the nano-textured surface : Cassie state**- on the smooth surface : slip = 24 s - on the super-hydrophobic surface : slip = 57 s Roughness increases slip**d**Pcap= -2glv cos q d Influence of pressure on the boundary slip Barentin et al EPJ E 2005 150 100 50 0 Superhydrophobic state Slip length (u.L.J.) Imbibated state 0 1 2 3 P/Pcap 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 Calculation of BC: L = 1.4 µm effective slip plane B =50 +/-20 nm B =170 +/-30 nm Qa=148° Qr =139° Wenzel wetting Cassie wetting**1/G"(w)**Bapp 0 D(nm) 1200 Nanorheology on patterned surface: SFA experiments Hydrophobic (silanized) Cassie Hydrophilic Wenzel Bapp = 100 +/- 30 nm Bapp = 20 +/- 30 nm**Elastic response on SuperHydrophobic surfaces**Elasticity G’(w) SH surface Hydrophilic surface Force response on SH surface shows non-zero elastic response. Signature of trapped bubbles in holes.**viscous damping**elastic response Flow on a compressible surface Newtonian incompressible fluid Lubrication approximation Local surface compliance K : stiffness per unit surface [N/m3] d**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 slip plane hydrophilic no bubbles SH surfaces can promote high friction flow**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 Fs = 0.1% (solid/liquid area) corresponds to c.a. q ~ 178° (using Cassie relation) meniscii should be (nearly) flat**Some hope….**flow on a « dotted » surface: hydrodynamic model No analytical results argument of L. Bocquet L a Posts a<<L**Flow on a « dotted » surface: hydrodynamic model**L a Posts a<<L • The flow is perturbed over the dots only, in a region of order of their size • Friction occurs only on the solid surface better than stripes Numerical resolution of Stoke’s equation: a~1/p**SLIPPAGE ON A NANOTUBE FOREST**• Nanostructured surfaces C. Journet, J.M. Benoit, S. Purcell, LPMCN PECVD, growth under electric field 1 µm • Superhydrophobic (thiol functionnalization) q= 163° (no hysteresis) C. Journet, Moulinet, Ybert, Purcell, Bocquet, Eur. Phys. Lett, 2005**before**after thiol in gaz phase thiol in liquid phase 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 0.28 Slip length increases with the pattern period L Wenzel state