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

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

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 < 108 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 (~ 109 s-1 )

.

(obtained with LJ liquids, some with water)

1

10

100

1000

slip length (nm)

150100500

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 hydrophobicityEffect of viscosity

Velocimetry measurements

V(z)

Particule Imaging Velocimetry

V(z)

Fluorescence recoveryin TIR

Fluorescence Double Focus Cross Correlation

O. Vinogradova, PRE 67, 056313 (2003)Pit & Leger, PRL 85, 980 (2000)

Schmadtko & Leger, PRL 94 244501 (2005)

Tretheway & Meinhart Phys Fluid 14, L9, (2002)

Dissipation measurementsPressure drop

Colloidal Probe AFM

Surface Force Apparatus

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

Craig & al, PRL 87, 054504 (2001) Bonnacurso & al, J. Chem. Phys 117, 10311 (2002) Vinogradova, Langmuir 19, 1227 (2003)

Chan & Horn 1985 Israelachvili 1986 Georges 1994Granick PRL 2001Mugele PRL 2003Cottin-Bizone PRL 2005

• Particle Image Velocimetry (PIV)

Measurement of velocity profile

V(z)

Spatial resolution ~ 50-100nm

Fluorescent particules High resolution cameraPair 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 67 056313 (2003)

z

Vsphere ≠ Vflow (zcenter)

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 10 -6 M

Colloidal lift

z

d+

+

+

+

+ + + +

+

+

electrostatic force:

depletion layer:

Fsphere ~ R exp (-d)

d ~ 3 -1

Vsphere > Vslip

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 85 980 (2000)

fluorescence recoveryat different shear rates

t(ms)

T. Schmatdko PhD Thesis, 2003

Schmadtko & al PRL 94 244501 (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)=√ Dmt

z(t)=√ Dmt

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 measurementsPressure drop

Colloidal Probe AFM

Surface Force Apparatus

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

Craig & al, PRL 87, 054504 (2001) Bonnacurso & al, J. Chem. Phys 117, 10311 (2002) Vinogradova, Langmuir 19, 1227 (2003)

Chan & Horn 1985 Israelachvili 1986 Georges 1994Granick 2001Mugele 2003Cottin-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

substratecantilever 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 *( ) Db

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+ x2

2R

Mass conservation

2xz U(x) = - x2 D

R

x

D

(x)

U(x)

√ 2RD

D√RD3/2

AFM/SFA methods are not well adapted for investigating shear-rate dependent b.c.

xShear rate is not uniform and varies with D

f *( ) Db

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

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Determination of b:

10 100

calculated b(nm)

1.0

0.8

0.6

0.4

0.2

0.0

10080604020

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D(nm)

D(nm)

Brief review of experimental methods

Measuring the hydroynamic b.c. without flow

Our experiments with the dynamic-SFA

Effect of hydrophobicityEffect of viscosity

Dynamic Surface Force Apparatus

Interferometric force sensor

Capacitive displacement sensor

Nomarskiinterferometer Mirors

MagnetCoil

Plane

Piezoelectric elements

Capacitor plates

Micrometer

F. Restagno, J. Crassous, E. Charlaix, C.Cottin-Bizonne, Rev.Sci. Inst. 2002

k=7000N/m

Excitation : 0.05 nm < hac < 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

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)

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)

0 10 20 30

0 10 20 30

• Inverse of visc. damping

No-slip : b ≤ 2nm

Bulk hydro. OK for D ≥ 4nm

• Quasi-static force

Simple liquid on a wetting surface

N-dodecaneMolecular Ø : 4,5 ÅMolecular length : 12 Å

Smooth surface: float pyrexRoughness : 3 Å r.m.s.Perfectly wetted by dodecane ( = 0°)

Inverse of G’’() 0 as D 0

f *( ) Db

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.

SiSiSiOOSiSiSiOOO(CH2)-18(CH2)-18

Smooth float pyrex: 0,3nm r.m.s.

OTS silanized pyrex : 0,7nm r.m.s.

Water

Dodecane

Float pyrex OTS pyrex

0°

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)

TheoryExperiment

Environment : clean room

Water on bare pyrex :no-slip

b = 17±3 nm

silanized planebare pyrex sphere

Linear b.c. up to .shear rate ~ 5.103 s-1

Water on silanized pyrex :partial slip one single slip lengthb = 17±3 nm

C. Cottin-Bizonne et al, PRL 94, 056102 (2005)

Intrinsic slip length : properties

slip length does not depend on shear rate (< 5. 103 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

200 nm

200 nm

roughness : 0,7 nm r.m.s ~ 3 nm pk-pk

200 nm

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 hydratationNo-slip

D(nm)

water on DPPC bilayer :no-slip within 3 nm

D (nm)

G’’-1

()

nm

/µN

0 10 20 30 40

water on a fresh DDPC monolayer :(1-2 hours in water)slip length b=10±3nm

b= 0

b=10 nm

0 100

B. Cross et al, EPL 73, 390 (2006)

Intrinsic slip length : summary

b (nm)

10

20

< 2Contact angle

30° 90° 110°

DPPC monolayer/water (fresh)

OTS-pyrex / water

0°

OTS-pyrex/dodecane

Pyrex / water ; dodecane ; glycerolSilicon / dodecaneDense DPPC bilayers / water

C. Cottin-Bizonne et al, Langmuir 1165 (2008)

Mechanism for slip : the gaz layer ?

1

2

D. Doshi, E. Watkins, J. Israelachvili, J. Majewski PNAS (102) 9458, 2005

= 0.5 nm

b = 25 nm

Neutron reflectivity study ofOTS-coated quarz/water interface

0.001 0.01

viscosity (Pa.s)

20

15

10

5

0

Slip

len

gth

(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 (< 5. 103 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 hydrophobicityEffect of viscosity

Measuring slippage without flow….

Einstein 1905

L. Joly, C. Ybert, L. Bocquet, Phys Rev Lett 2005

e

F

mobilityDiffusion 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 byFluorescence Correlation Spectroscopy

Float pyrex

OTS-coated pyrexb=20nm

Rough pyrex

b=100nmDmeasured

Dno-slip

Brief review of experimental methods

Measuring the hydroynamic b.c. without flow

Our experiments with the dynamic-SFA

Effect of hydrophobicityEffect of viscosity

Summary

1

10

100

1000

slip length (nm)

150100500

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 ?

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Lou & al,, J. Vac. Sci. Tech B, 2573 (2000)

Nanobubbles in water on mica