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					            Liquid flows on surfaces:
                    experimental aspects




Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008
             The Kavli Institute of Theoretical Physics China
  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 )
 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
Brief review of experimental methods


Our experiments with the dynamic-SFA
            Effect of hydrophobicity
            Effect of viscosity


 Measuring the hydroynamic b.c. without flow
                    Velocimetry measurements


                                                   V(z)

                           Particule Imaging Velocimetry
                       Tretheway & Meinhart Phys Fluid 14, L9, (2002)




            V(z)

      Fluorescence recovery                         Fluorescence Double Focus
      in TIR                                        Cross Correlation
    Pit & Leger, PRL 85, 980 (2000)
Schmadtko & Leger, PRL 94 244501 (2005)           O. Vinogradova, PRE 67, 056313 (2003)
                   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
Craig & al, PRL 87, 054504 (2001)                              Israelachvili 1986
Bonnacurso & al, J. Chem. Phys 117, 10311 (2002)               Georges 1994
Vinogradova, Langmuir 19, 1227 (2003)                          Granick PRL 2001
                                                               Mugele PRL 2003
                                                               Cottin-Bizone PRL 2005
• Particle Image Velocimetry (PIV)

Measurement of velocity profile




                      V(z)



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)
                 Effect of tracor-wall interactions
                                       O. Vinogradova, PRE 67 056313 (2003)

  Hydrodynamical lift                                         Colloidal lift
   z                                                    z         +     +
                                                                 +      +
                 d                                                     d
                                                            + + + + + +

Vsphere ≠ Vflow (zcenter)                               electrostatic force:
                                                               Fsphere ~ R exp (-kd)
because of hydrodynamical
sphere-plane interaction                                depletion layer:
                                                                     d ~ 3 k -1
0.75 slower than flow at d/R=0.1                                       ~ 1 µm in 10 -6 M
F. Feuillebois, in Multiphase Science and Technology,
New York, 1989, Vol. 4, pp. 583–798.                         Vsphere > Vslip
          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
                                                            t(ms)
                 P.M.
                                                  fluorescence recovery
                                                  at different shear rates
                   Model for Near Field Laser Velocimetry
Convection //Ox + Diffusion //Oz


No-slip b.c.



               V = gz
                   °



                    z(t)=√ Dmt
     x =g z t
         °



               L




                                        Hexadecane on rough sapphire
                   Model for Near Field Laser Velocimetry



 Partial slip b.c.
                                                        gb
                                                        °


            V = g (z+b)
                °



                     z(t)=√ Dmt
   x = g t (z+b)
       °


                                          Résolution : 100 nm
           L
                                          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




                         Churaev, JCSI 97, 574 (1984)
                         Choi & Breuer, Phys Fluid 15, 2897 (2003)



                                                   Surface Force Apparatus
     Colloidal Probe AFM




                                                        Chan & Horn 1985
Craig & al, PRL 87, 054504 (2001)                       Israelachvili 1986
Bonnacurso & al, J. Chem. Phys 117, 10311 (2002)        Georges 1994
Vinogradova, Langmuir 19, 1227 (2003)                   Granick 2001
                                                        Mugele 2003
                                                        Cottin-Bizone 2005
                                              Tabor et Winterton,
  Princip of SFA measurements                 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
      Princip of colloidal probe measurements
Ducker 1991

                          feedback                                     Y

                                     laser                                   X

         7,5 µm



                                                             Photodetector


                        cantilever   particule   substrate
                                     scanner
                                       xyz
                                      piézo
                                z


 Force is measured directly from cantilever bending
 Probe-surface distance is deduced from piezoelectric drive
       Hydrodynamic force with partial slip b.c.

  R


                                                                D
                                                            f *( )
                                                                b
              D


                                           Reynolds force

Hypothesis:

    Newtonian fluid
    D<<R
    Re<1                          O. Vinogradova Langmuir 11, 2213 (1995)
    rigid surfaces
    b independant of shear rate
      (linear b.c.)
             Shear rate at wall in a drainage flow

Mass conservation                                     R

2pxz U(x) = - p x2 D            z =D+  x2
                                      2R               D       U(x)
                                                                 x

                                               g (x)
                                                               √R D
                                                               D3/2

 Shear rate is not uniform and varies with D
                                                       √ 2RD     x
  AFM/SFA methods are not well adapted for
  investigating shear-rate dependent b.c.
                           Data analysis issues

                                                                  D
                                                              f *( )
                                                                       b


                             Reynolds force

Determination of b:
                                        QuickTime™ et u n
                             décompresseur TIFF (non compressé)
                            sont requis pour visio nner cette image.




      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
                                            1.0

            QuickTime™ et un
 décompresseur TIFF (non compressé)         0.8
sont requis p our vision ner cette image.

                                            0.6


                                            0.4                QuickTime™ et un
                                                   décompresseur TIFF (non compressé)
                                                  sont requis pour visionner cette image.

                                            0.2


                                            0.0
                                                  20              40               60       80   100

                                                                     D(nm)

                 calculated
                  b(nm)




                                                                         10           D(nm)            100
Brief review of experimental methods


Our experiments with the dynamic-SFA
            Effect of hydrophobicity
            Effect of viscosity


 Measuring the hydroynamic b.c. without flow
                 Dynamic Surface Force Apparatus
       F. Restagno, J. Crassous, E. Charlaix, C.Cottin-Bizonne, Rev.Sci. Inst. 2002




                                  k=7000N/m
            Interferometric                               Capacitive
            force sensor                                  displacement sensor
                                                         Capacitor
                                                         plates
                                                                    :
                                                         Excitation Micrometer
                                                             0.05 nm < hac < 5 nm
                                                            w/2p : [ 5 Hz ; 100 Hz ]
Nomarski
interferometer           Mirors                          Resolution :
                                                       Piezoelectric elements
                                                              Displacement Force
                        Coil
                               Magnet Plane              Static       0.1 nm    600 nN

                                                         Dynamic       5 pm     40 nN
   Dynamic force response to an
oscillatory motion of small amplitude




          stiffness       damping
                              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)
         Newtonian liquid with no-slip b.c.


R ~ mm                         Hypothesis :
          D(t)
                           The confined liquid remains newtonian
                           Surfaces are perfectly rigid
  D µm      nm
                           No-slip boundary condition

           F(t)


  No stiffness

  The viscous damping is
 given by the Reynolds force
           Simple liquid on a wetting surface
N-dodecane
Molecular Ø : 4,5 Å
                                            • Quasi-static force
Molecular length : 12 Å

Smooth surface: float pyrex
Roughness : 3 Å r.m.s.
Perfectly wetted by dodecane (q = 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)
         Partial slip b.c.: data analysis
R


                                                                       D
                                                                   f *( )
            D                                                            b




 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.
Water on smooth hydrophilic and hydrophobic surfaces

 Smooth float pyrex:              OTS silanized pyrex : 0,7nm r.m.s.
  0,3nm r.m.s.                       octadecyltricholorosilane




                Contact angle
           Float pyrex   OTS pyrex
   Water        0°         110°
   Dodecane     0°         30°
      Water confined between plain and OTS-coated pyrex
                                                  Environment : clean room

                                                                 Experiment
                                                                 Theory
  Water on bare pyrex :
  no-slip                                silanized plane
                                        bare pyrex sphere
                                          b = 17±3 nm
 Water on silanized pyrex :
 partial slip
 one single slip length
 b = 17±3 nm


                                                    bare pyrex plane
Linear b.c. up to                                  and sphere : b≤ 3nm
.shear rate ~ 5.103 s-1


                                                     D (nm)
C. Cottin-Bizonne et al, PRL 94, 056102 (2005)
                 Intrinsic slip length : properties




 well-defined   unique slip length for 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 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
                       DPPC monolayer age in water.


200 nm                          200 nm                        200 nm




                       200 nm                       200 nm                    200 nm

            after 1h                     after 7h
                                                                       after 1 day

         roughness : 0,7 nm r.m.s                            roughness : 2,2 nm r.m.s
                     ~ 3 nm pk-pk                                        6,5 nm pk-pk
                                                           b=10 nm
                                                       b= 10nm
G’’-1(w) nm/µN




                                                                         b= 0
                                                                        b= 0

                 0       10     20        30   40     0                         100
                                     D (nm)                     D(nm)

                     water on DPPC bilayer :             water fresh DDPC monolayer
                                                    water on aon a DPPC monolayer :
                     no-slip within 3 nm                  hours day hydratation
                                                    (1-2after 1 in water)
                                                         No-slip
                                                    slip length b=10±3nm




      B. Cross et al, EPL 73, 390 (2006)
                        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
                           0°     30°           90°     110° Contact
                                                              angle

   Pyrex / water ; dodecane ; glycerol
   Silicon / dodecane
   Dense DPPC bilayers / water
Mechanism for slip : the gaz layer ?




                  Neutron reflectivity study of
 h1        d      OTS-coated quarz/water interface
 h2               D. Doshi, E. Watkins, J. Israelachvili,
                  J. Majewski PNAS (102) 9458, 2005

                  d = 0.5 nm



                        b = 25 nm
   Boundary slip of water-glycerol mixtures
       as a function of viscosity
                                 C. Cottin-Bizonne et al, Langmuir 24,1165 (2008)

                   20           OTS-pyrex
Slip length (nm)


                   15

                   10

                   5                 Pyrex
                   0
                        0.001             0.01
                            viscosity (Pa.s)
                 Intrinsic slip length : properties




 well-defined   unique slip length for 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.
Brief review of experimental methods


Our experiments with the dynamic-SFA
            Effect of hydrophobicity
            Effect of viscosity


 Measuring the hydroynamic b.c. without flow
                 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.
No-slip b.c.
Perfect slip b.c.
L. Joly, C. Ybert, L. Bocquet,
Phys Rev Lett 2005




                                 Fluorescence
                                 correlation
                                 spectroscopy


  Measure:
     confinement :
     diffusion time :
            Diffusion of confined colloids measured by
            Fluorescence Correlation Spectroscopy


                      OTS-coated pyrex
                      b=20nm
                                            b=100nm
Dmeasured
Dno-slip

                                    Float pyrex


                             Rough pyrex
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
 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
             Are very large differences in measured slip lengths
                         due to some surface problems ?




                                                               QuickTime™ et u n
                                                    décompresseur TIFF (non compressé)
                                                   sont requis pour visio nner cette image.




 Ishida, Langmuir 16, 6377 (2000)         Lou & al,, J. Vac. Sci. Tech B, 2573 (2000)
Nanobubbles on OTS-coated silicon               Nanobubbles in water on mica

				
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