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

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

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

4. 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

5. 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°

6. 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

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

8. 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

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

10. 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

11. 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

12. 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

13. 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 !

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

15. 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…

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

17. 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

18. 1 µm Non-wetting nano-textured surfaces : MD simulations Cottin-Bizonne & al 2003 Nature Mat 2, 237

19. 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

20. 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

21. 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

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

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

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

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

26. 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

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. 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

29. 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

30. 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.

31. 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 

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

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

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

35. 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)

36. 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

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

38. Flow on a « dotted » surface: hydrodynamic model 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 Numerical resolution of Stoke’s equation:  better than stripes L a

39. 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

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

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

42. 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