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

Theory for intrinsic b.c. on smooth surfaces : summary  substantial slips in strongly non-wetting systems slip length increases with c.a. slip length decreases with increasing pressure  no-slip in wetting systems (except very high shear rate  < 10 8 s -1 )  slip length is moderate (~ 5 nm at  ).  slip length does not depend on fluid viscosity (≠ polymers)  non-linear slip develops at high shear rate (~ 10 9 s -1 ). (obtained with LJ liquids, some with water)

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

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

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

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

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

Effect of tracor-wall interactions Hydrodynamical lift O. Vinogradova, PRE (2003) z V sphere ≠ V flow (z center ) because of hydrodynamical sphere-plane interaction F. Feuillebois, in Multiphase Science and Technology, New York, 1989, Vol. 4, pp. 583–798. d 0.75 slower than flow at d/R=0.1 ~ 1 µm in M Colloidal lift z d electrostatic force: depletion layer: F sphere ~ R exp (-  d) d ~ 3   -1 V sphere > V slip

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

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

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

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

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

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

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

Shear rate at wall in a drainage flow z =D+ x2x2 2R  Mass conservation 2  xz U(x) = -  x 2 D R x D  (x) U(x) √ 2RD D √R D 3/2 AFM/SFA methods are not well adapted for investigating shear-rate dependent b.c. x Shear rate is not uniform and varies with D

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

calculated b(nm) D(nm)

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

Dynamic Surface Force Apparatus Interferometric force sensor Capacitive displacement sensor Nomarski interferometer Mirors Magnet Coil Plane Piezoelectric elements Capacitor plates Micrometer F. Restagno, J. Crassous, E. Charlaix, C.Cottin-Bizonne, Rev.Sci. Inst k=7000N/m Excitation : 0.05 nm < h ac < 5 nm  : [ 5 Hz ; 100 Hz ] Resolution : Displacement Force Static 0.1 nm 600 nN Dynamic 5 pm 40 nN

Dynamic force response to an oscillatory motion of small amplitude stiffnessdamping

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)

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

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

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

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

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

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

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

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

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

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

Mechanism for slip : the gaz layer ? 11 22  D. Doshi, E. Watkins, J. Israelachvili, J. Majewski PNAS (102) 9458, 2005  = 0.5 nm b = 25 nm Neutron reflectivity study of OTS-coated quarz/water interface

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

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

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

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

No-slip b.c.

Perfect slip b.c.

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

Diffusion of confined colloids measured by Fluorescence Correlation Spectroscopy Float pyrex OTS-coated pyrex b=20nm Rough pyrex b=100nm D measured D no-slip

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

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

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