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Flow on patterned surfaces

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.

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Flow on patterned surfaces

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  1. 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

  2. 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

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

  4. 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

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

  6. 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°

  7. 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

  8. 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

  9. 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

  10. 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

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

  12. ∆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

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

  14.  = {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°

  15. 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

  16. 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

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

  18. 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 ?

  19. 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:

  20. 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

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

  22. 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 ?

  23. Flow on nano-textured SH surfaces : MD simulation

  24. 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

  25. 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

  26. 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

  27. 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 

  28. 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

  29. 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

  30. 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.

  31. 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

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

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

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

  35. 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

  36. Some hope…. flow on a « dotted » surface: hydrodynamic model No analytical results argument of L. Bocquet L a Posts a<<L

  37. 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

  38. 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

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

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

  41. 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

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