Liquid flows on surfaces:

1. Liquid flows on surfaces: experimental aspects Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008 The Kavli Institute of Theoretical Physics China

2. Theory for intrinsic b.c. on smooth surfaces : summary (obtained with LJ liquids, some with water) . . • no-slip in wetting systems (except very high shear rate g < 108 s-1 ) • substantial slips in strongly non-wetting systems slip length increases with c.a. slip length decreases with increasing pressure • slip length is moderate (~ 5 nm at q ~ 120° ) • slip length does not depend on fluid viscosity (≠ polymers) • non-linear slip develops at high shear rate (~ 109 s-1 )

3. Some recent experimental results on smooth surfaces slip length (nm) Tretheway et Meinhart (PIV) Non-linear slip Pit et al (FRAP) Churaev et al (perte de charge) 1000 Craig et al(AFM) Bonaccurso et al (AFM) Vinogradova et Yabukov (AFM) Sun et al (AFM) 100 Chan et Horn (SFA) Zhu et Granick (SFA) Baudry et al (SFA) Cottin-Bizonne et al (SFA) 10 MD Simulations 1 0 50 100 150 Contact angle (°) Brenner, Lauga, Stone 2005

4. Brief review of experimental methods Our experiments with the dynamic-SFA Effect of hydrophobicity Effect of viscosity Measuring the hydroynamic b.c. without flow

5. V(z) V(z) Fluorescence recovery in TIR Fluorescence Double Focus Cross Correlation Velocimetry measurements Particule Imaging Velocimetry Tretheway & Meinhart Phys Fluid 14, L9, (2002) Pit & Leger, PRL 85, 980 (2000) Schmadtko & Leger, PRL 94 244501 (2005) O. Vinogradova, PRE 67, 056313 (2003)

6. Dissipation measurements Pressure drop Churaev, JCSI 97, 574 (1984) Choi & Breuer, Phys Fluid 15, 2897 (2003) Surface Force Apparatus Colloidal Probe AFM Chan & Horn 1985 Israelachvili 1986 Georges 1994 Granick PRL 2001 Mugele PRL 2003 Cottin-Bizone PRL 2005 Craig & al, PRL 87, 054504 (2001) Bonnacurso & al, J. Chem. Phys 117, 10311 (2002) Vinogradova, Langmuir 19, 1227 (2003)

7. V(z) • Particle Image Velocimetry (PIV) • Measurement of velocity profile Fluorescent particules High resolution camera Pair of images With Micro-PIV (see S. Wereley) Spatial resolution ~ 50-100nm Use for bc : are velocity of tracor and velocity of flow the same ? Meinardt & al, Experiments in Fluids (1999)

8. Colloidal lift z + + + + d + + + + + + electrostatic force: Fsphere ~ Rexp(-kd) depletion layer: d ~ 3k-1 ~ 1 µm in 10 -6 M Vsphere > Vslip Effect of tracor-wall interactions O. Vinogradova, PRE 67 056313 (2003) Hydrodynamical lift z d Vsphere ≠ Vflow (zcenter) because of hydrodynamical sphere-plane interaction 0.75 slower than flow at d/R=0.1 F. Feuillebois, in Multiphase Science and Technology, New York, 1989, Vol. 4, pp. 583–798.

9. t(ms) fluorescence recovery at different shear rates Using molecules as tracors: Near Field Laser Velocimetry Pit & al Phys Rev Lett 85 980 (2000) Schmadtko & al PRL 94 244501 (2005) evanescent wave (TIR) + photobleaching (FRAP) T. Schmatdko PhD Thesis, 2003 Writing beam v spot L ~ 60 µm Evanescent wave ~ 80 nm Reading beam P.M.

10. ° ° g g x = z t z(t)=√ Dmt Hexadecane on rough sapphire Model for Near Field Laser Velocimetry Convection //Ox + Diffusion //Oz No-slip b.c. V = z L

11. ° ° ° g g g z(t)=√ Dmt Résolution : 100 nm x = t (z+b) Velocity averaged on ~ 1 µm depth Find slip length b~100nm for hexadecane on sapphire (perfect wetting) Needs value of diffusion coefficient Model for Near Field Laser Velocimetry Partial slip b.c. b V = (z+b) L

12. Dissipation measurements Pressure drop Churaev, JCSI 97, 574 (1984) Choi & Breuer, Phys Fluid 15, 2897 (2003) Surface Force Apparatus Colloidal Probe AFM Chan & Horn 1985 Israelachvili 1986 Georges 1994 Granick 2001 Mugele 2003 Cottin-Bizone 2005 Craig & al, PRL 87, 054504 (2001) Bonnacurso & al, J. Chem. Phys 117, 10311 (2002) Vinogradova, Langmuir 19, 1227 (2003)

13. Princip of SFA measurements Tabor et Winterton, Proc. Royal Soc. London, 1969 D is measured with FECO fringes (Å resolution, low band-pass) In a quasi-static regime (inertia neglected) Distance is measured accurately, Force is deduced from piezoelectric drive

14. feedback Y laser X Photodetector 7,5 µm cantilever particule substrate scanner xyz piézo z Princip of colloidal probe measurements Ducker 1991 Force is measured directly from cantilever bending Probe-surface distance is deduced from piezoelectric drive

15. D D f *( ) b Hydrodynamic force with partial slip b.c. R Reynolds force Hypothesis: • Newtonian fluid • D<<R • Re<1 • rigid surfaces • b independant of shear rate (linear b.c.) O. Vinogradova Langmuir 11, 2213 (1995)

16. z =D+ x2 2R 2pxz U(x) = - p x2 D √R D √ 2RD D3/2 Shear rate at wall in a drainage flow R • Mass conservation D U(x) x g (x) Shear rate is not uniform and varies with D x AFM/SFA methods are not well adapted for investigating shear-rate dependent b.c.

17. D f *( ) b Data analysis issues Reynolds force Determination of b: f* varies between 0.25 and 1 and has a log dependence in D/b requires precise measurement of F over a large range in D accurate knowledge of D, R, h

18. 10 100 D(nm) calculated b(nm) D(nm)

19. Brief review of experimental methods Our experiments with the dynamic-SFA Effect of hydrophobicity Effect of viscosity Measuring the hydroynamic b.c. without flow

20. Capacitive displacement sensor Excitation : 0.05 nm < hac < 5 nm w/2p : [ 5 Hz ; 100 Hz ] Resolution : Displacement Force Static 0.1 nm 600 nN Dynamic 5 pm40 nN Dynamic Surface Force Apparatus F. Restagno, J. Crassous, E. Charlaix, C.Cottin-Bizonne, Rev.Sci. Inst. 2002 k=7000N/m Interferometric force sensor Capacitor plates Micrometer Nomarski interferometer Mirors Piezoelectric elements Coil Magnet Plane

22. Dynamic force response to an oscillatory motion of small amplitude stiffness damping

23. Specificities Two separate sensors with Å resolution : no piezoelectric calibration required More rigid than usual SFA (no glue) or AFM (no torsion allowed) Phase measurement allows to check for unwanted elastic deformations (and associated error on distance) Easy check for linearity of the b.c. with shear rate: change amplitude or frequency at fixed D Background viscous force easy to measure (≠ AFM cantilever)

24. R ~ mm D(t) D µm nm F(t) Newtonian liquid with no-slip b.c. Hypothesis : • The confined liquid remains newtonian • Surfaces are perfectly rigid • No-slip boundary condition • No stiffness • The viscous damping is given by the Reynolds force

25. Simple liquid on a wetting surface N-dodecane Molecular Ø : 4,5 Å Molecular length : 12 Å • Quasi-static force Smooth surface: float pyrex Roughness : 3 Å r.m.s. Perfectly wetted by dodecane ( = 0°) 0 10 20 30 • Inverse of visc. damping • Bulk hydro. OK for D ≥ 4nm • No-slip : b ≤ 2nm 0 10 20 30 D(nm)

26. R f *( ) D D b Partial slip b.c.: data analysis • At large distance (D>>b) : Inverse of G’’(w) is a straight line intersecting x-axis at D = -b Determination of b without injecting values of h, R… Error on D is not amplified • At short distance (D≤b) : f* 1/4 Inverse of G’’(w) 0 as D 0 Check of D=0 position.

27. Water on smooth hydrophilic and hydrophobic surfaces • OTS silanized pyrex : 0,7nm r.m.s. • Smooth float pyrex: 0,3nm r.m.s. octadecyltricholorosilane Contact angle Float pyrex OTS pyrex Water Dodecane 0° 0° 110° 30°

28. silanized plane bare pyrex sphere b =17±3 nm Water on silanized pyrex : partial slip one single slip length b = 17±3 nm Linear b.c. up to .shear rate ~ 5.103 s-1 Experiment Theory Water confined between plain and OTS-coated pyrex Environment : clean room Water on bare pyrex : no-slip bare pyrex plane and sphere : b≤ 3nm D (nm) C. Cottin-Bizonne et al, PRL 94, 056102 (2005)

29. Intrinsic slip length : properties • well-defined unique slip lengthfor flow sizes D varying on 2 decades • slip length does not depend on shear rate (< 5. 103 s-1 ) slip length depends only on S/L interface • slippage has moderate amplitude (~ tens of mol. size)

30. Water flow on phospholipid monolayers and bilayers Phospholipid bilayers are model for biological cell membrane Monolayers are hydrophobic (q =95°) Bilayers are (highly) hydrophilic DPPC molecule DPPC Langmuir-Blodgett deposition on float pyrex Water on DPPC monolayer

31. DPPC monolayer age in water. 200 nm 200 nm 200 nm 200 nm 200 nm 200 nm after 7h after 1h after 1 day roughness : 0,7 nm r.m.s ~ 3 nm pk-pk roughness : 2,2 nm r.m.s 6,5 nm pk-pk

32. b= 10nm b=10 nm b= 0 water on a fresh DDPC monolayer : (1-2 hours in water) slip length b=10±3nm water on a DPPC monolayer after 1 day hydratation No-slip b= 0 G’’-1(w) nm/µN 0 10 20 30 40 0 100 D(nm) D (nm) water on DPPC bilayer : no-slip within 3 nm B. Cross et al, EPL 73, 390 (2006)

33. Intrinsic slip length : summary C. Cottin-Bizonne et al, Langmuir 1165 (2008) b (nm) 20 OTS-pyrex / water 10 DPPC monolayer/water (fresh) OTS-pyrex/ dodecane < 2 110° 90° 0° 30° Contact angle Pyrex / water ; dodecane ; glycerol Silicon / dodecane Dense DPPC bilayers / water

34. h1 d h2 Mechanism for slip : the gaz layer ? Neutron reflectivity study of OTS-coated quarz/water interface D. Doshi, E. Watkins, J. Israelachvili, J. Majewski PNAS (102) 9458, 2005 d = 0.5 nm b = 25 nm

35. Boundary slip of water-glycerol mixtures as a function of viscosity C. Cottin-Bizonne et al, Langmuir 24,1165 (2008) 20 15 10 5 0 OTS-pyrex Slip length (nm) Pyrex 0.001 0.01 viscosity (Pa.s)

36. Intrinsic slip length : properties • well-defined unique slip lengthfor flow sizes D varying on 2 decades • slip length does not depend on shear rate (< 5. 103 s-1 ) slip length depends only on S/L interface • slippage has moderate amplitude (~ tens of mol. size) • water: slippage increases with c.a. • water-glycerol solutions: slippage does not depend on viscosity.

37. Brief review of experimental methods Our experiments with the dynamic-SFA Effect of hydrophobicity Effect of viscosity Measuring the hydroynamic b.c. without flow

38. Measuring slippage without flow…. L. Joly, C. Ybert, L. Bocquet, Phys Rev Lett 2005 Einstein 1905 Diffusion of a colloidal particle mobility F e Measuring tangential diffusion as a function of wall distance gives information on the flow boundary condition.

39. No-slip b.c.

40. Perfect slip b.c.

41. L. Joly, C. Ybert, L. Bocquet, Phys Rev Lett 2005 Fluorescence correlation spectroscopy • Measure: • confinement : • diffusion time :

42. Dmeasured Dno-slip Diffusion of confined colloids measured by Fluorescence Correlation Spectroscopy OTS-coated pyrex b=20nm b=100nm Float pyrex Rough pyrex

43. Brief review of experimental methods Our experiments with the dynamic-SFA Effect of hydrophobicity Effect of viscosity Measuring the hydroynamic b.c. without flow Summary

44. Some recent experimental results on smooth surfaces slip length (nm) Tretheway et Meinhart (PIV) Non-linear slip Pit et al (FRAP) Churaev et al (perte de charge) 1000 Craig et al(AFM) Bonaccurso et al (AFM) Vinogradova et Yabukov (AFM) Sun et al (AFM) 100 Chan et Horn (SFA) Zhu et Granick (SFA) Baudry et al (SFA) Cottin-Bizonne et al (SFA) 10 MD Simulations 1 0 50 100 150 Contact angle (°) Brenner, Lauga, Stone 2005

45. Are very large differences in measured slip lengths due to some surface problems ? Lou & al,, J. Vac. Sci. Tech B, 2573 (2000) Ishida, Langmuir 16, 6377 (2000) Nanobubbles on OTS-coated silicon Nanobubbles in water on mica