1. Flow on patterned surfaces
Diapo 19 Reynolds force : rajouer ref Brenner
E. CHARLAIX
University of Lyon, France
NANOFLUIDICS SUMMER SCHOOL August
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. Rough surface with water-repellent coating
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. gSL : solid-liquid surface tension
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. WETTING OF A ROUGH SURFACE
Young’s law on rough surface: q
Wenzel law
qo : contact angle on flat chemically same surface 1 -1 -

8. WETTING OF A PATTERNED SURFACEh
WETTING OF A PATTERNED SURFACE
Bico, Marzolin & Quéré
Europhys. Lett 47, 220 (1999)
Trapped air is favorable if -1
composite wetting
Wenzel law
Liquid must be non-wetting -1

9. CASSIE-WENZEL TRANSITIONh
CASSIE-WENZEL TRANSITION
Bico, Marzolin & Quéré
Europhys. Lett 47, 220 (1999) -1
Wenzel wetting
Cassie wetting q
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. Maximum pressure applied
Lafuma & Quéré 2003 Nature Mat. 2, 457
Contact angle after
separating the plates
Cassie state
Wenzel state
Maximum pressure applied

12. METASTABILITY OF CASSIE/WENZEL STATESd ∆P
Transition to Wenzel state at 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. Lennard-Jones fluid  = {liquid,solid}, : energy scale
 : molecular diameter
cab : wetting control parameter
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 = q = 140°
N is constant
Pressure (u.L.J.)
Volume
Imbibated (Wenzel) state
Super-hydrophobic (Cassie) state

16. Gibbs energy at applied pressure P
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 bcy 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. Effective slip on a patterned surface: macroscopic calculation
Couette flow L
Shear applied at z =
Local slip length : b(x,y)
Bulk flow : Stokes equations
Decay of flow corrugations
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. AN EXPERIMENTAL REALISATION
Ou, Perot & Rothstein Phys Fluids 16, 4635 (2004)
21 µm
Pressure drop reduction
Slip length
Hydrophobic silicon microposts
127 µm
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. Influence of pressure on the boundary slip
Barentin et al EPJ E 2005
150
100 50 d
Superhydrophobic state
Slip length (u.L.J.)
Pcap =
-2glv cos q d
Imbibated state
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
B =50 +/-20 nm
effective slip plane
B =170 +/-30 nm
Qa=148°
Qr =139°
Wenzel wetting
Cassie wetting

29. Nanorheology on patterned surface: SFA experiments
Hydrophobic (silanized)
Cassie
Hydrophilic
Wenzel
Bapp
1200
D(nm)
1/G"(w)
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. Flow on a compressible surface
Newtonian incompressible fluid
Lubrication approximation
elastic response
viscous damping
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. SH surfaces can promote high friction flow
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. flow on a « dotted » surface: hydrodynamic model
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
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. thiol in gaz phase
thiol in liquid phase
before
after
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