Flow on patterned surfaces

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

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

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

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 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°

6. 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)

7. 2a h q -1 Cassie wetting Wenzel wetting q -1 CASSIE / WENZEL CONTACT ANGLES Bico, Marzolin & Quéré Europhys. Lett 47, 220 (1999) Extended Young’s law

8. METASTABILITY OF WETTING ON SH 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

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

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 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 ?

12. 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:

13. 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

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

15. 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…

16. 160 µm 127 µm Pressure drop reduction that would be obtained by suppressing the posts Pressure drop reduction > 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. Non-wetting nano-textured surfaces : MD simulations Cottin-Bizonne & al 2003 Nature Mat 2, 237 1 µm

19.  = {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°

20. 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

21. Cassie-Wenzel transition under applied pressure Cassie state Wenzel state Gibbs energy at applied pressure P Super-hydrophobic state is stable if 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 Pressure (u.L.J.) Volume Wenzel state Cassie state

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 • Large slippage at L/S interface is difficult to obtain • Nanobubbles are unlikely to yield large slippage (and explain data scatter) • For large slippage, 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. 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 No analytical results argument of L. Bocquet L a Posts a<<L

38. 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

39. 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

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

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

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