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Liquid flows on surfaces:

Liquid flows on surfaces:

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Liquid flows on surfaces:

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  1. Liquid flows on surfaces: experimental aspects E. CHARLAIX University of Lyon, France NANOFLUIDICS SUMMER SCHOOL August 20-24 2007 THE ABDUS SALAM INTERNATIONAL CENTER FOR THEORETICAL PHYSICS

  2. Intrinsic b.c. on smooth surfaces : conclusion . • at moderate shear rate (g < 108 s-1 ) essentially no slip in wetting systems • substantial slips occurs in strongly non-wetting systems slip length increases with c.a. slip length depends strongly on pressure • slip length amplitude is moderate (~ 5 nm at q ~ 120° ) • slip length is not expected to depend on fluid viscosity (≠ polymers) • non-linear slip develops above a high critical shear rate (~ 109 s-1 ) Thomson-Troian Nature 1997

  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. 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)

  5. 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)

  6. 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)

  7. 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.

  8. 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.

  9. ° ° 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

  10. ° ° ° 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

  11. 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)

  12. 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

  13. 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

  14. 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)

  15. 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 adapted for investigating shear-rate dependent b.c.

  16. 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

  17. 10 100 D(nm) calculated b(nm) D(nm) AFM experiments: Honig & Ducker, Phys Rev Lett 98, 028305 2007

  18. 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

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

  20. Viscous damping with partial slip: Specificity of the method Two separate sensors with Å resolution : no piezoelectric calibration required More rigid than usual SFA (no glue) or AFM (no torsion allowed) In and out-of-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 of excitation at fixed D No background viscous force that cannot be substracted

  21. 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

  22. 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)

  23. f *( ) D D O. Vinogradova : b Langmuir 11, 2213 (1995) Viscous damping with a partial slip h.b.c. R At large distance (D>>b) :

  24. 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.

  25. Best fit with constant slip length Contamination • Quasi-static force • Inverse of damping D (nm)

  26. 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°

  27. 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)

  28. 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)

  29. Intrinsic slip length : summary 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 • slippage increases with c.a.

  30. 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

  31. Boundary slip of water-glycerol mixtures as a function of viscosity 20 15 10 5 0 OTS-pyrex Slip length (nm) Pyrex 0.001 0.01 viscosity (Pa.s)

  32. 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.

  33. 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

  34. Nanobubbles ? Ishida Langmuir 16, 6377 (2000) Nanobubbles on OTS-coated silicon water

  35. 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.

  36. No-slip b.c.

  37. Perfect slip b.c.

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

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