University of Lyon, France

Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008

E. CHARLAIX

Introduction to nano-fluidics

1. 1. Flows at a nano-scale: where does classical hydrodynamics stop ?

2. 2. Liquid flows on smooth surfaces: the boundary condition

3. 3. Liquid flows on smooth surfaces: experimental aspects

4. 4. Flow on patterned surfaces

5. 5. Effect of boundary hydrodynamics on other surface transport properties

6. 6. Capillarity at a nano-scale

Flows at a nano-scale:Where does classical hydrodynamics stop ?

(and how to describe flow beyond ?)

OUTLINE

Why nano-hydrodynamics ?

Surface Force Apparatus: a fluid slit controlled at the Angstrom level

First nano-hydrodynamic experiments performed with SFA

Experiments with ultra-thin liquid films

solid or glass transition ?

a controversy resolved

Nanofluidic devices

Miniaturization increases surface to volume ratio:

importance of surface phenomena

manipulation and analysis of biomolecules . with single molecule resolution specific ion transport

50 nm channelsWang et al, APL 2002

500 nm

Nanochannels are more specifically designed for :

Microchannels…

…nanochannels

Large specific surface (1000m2 /cm3 ~ pore radius 2nm)

catalysis, energy/liquid storage or transfo, …

Mesoporous materials

Water in mesoporous silica (B. Lefevre et al, J. Chem. Phys 2004)

Water in nanotubes Koumoutsakos et al 2003H. Fang & al Nature Nanotech 2007

10nm

Electric fieldelectroosmotic flow

Electrostatic double layer3 nm 300 nm

Electrokinetic phenomena

Electro-osmosis, streaming potential… are determined by nano-hydrodynamics at the scale of the Debye length

Colloid science, biology, nanofluidic devices…

Tribology :

Mechanics, biomechanics, MEMS/NEMS friction

Rheology and mechanics of ultra-thin liquid films

Bowden & Tabor

The friction and lubrication of solids Clarendon press 1958

J. N. Israelachvili

Intermolecular and surface forces Academic press 1985

First measurements at a sub-nanometric scale: Surface Force Apparatus (SFA)

OUTLINE

Importance

Surface Force Apparatus : a slit controlled at the Angstrom level

First nano-hydrodynamic experiments performed with SFA:

Experiments with ultra thin liquid films

solid or glass transition ?

a controversy resolved

Tabor et Winterton, Proc. Royal Soc. London, 1969Israelachvili, Proc. Nat. Acad. Sci. USA 1972

Surface Force Apparatus (SFA)

micaAg

Ag

Optical resonator

D

Franges of equal chromatic order (FECO)

Tolanski, Multiple beam Interferometry of surfaces and films, Clarendon Press 1948

Source of white light

Spectrograph

D=28nm

contact

r : reflexion coefficient n : mica indexa : mica thicknessD : distance between surfaces

Distance between surfaces is obtained within 1 Å

(nm)

Force measurement

In a quasi-static regime (inertia neglected)

Piezoelectric displacement

Horn & Israelachvili, J. Chem Phys 1981

The

Oscillating force in organic liquid films

Static force in confined organic liquid films(alkanes, OMCTS…).Oscillations reveal liquid structure in layers parallel to the surfaces

Electrostatic and hydration force in water films

Horn & al 1989Chem Phys Lett

OUTLINE

Importance

Surface Force Apparatus : a slit of thickness controlled at the Angstrom level

First nano-hydrodynamic experiments performed with SFA:

thick liquid films (Chan & Horn 1985)

Experiments with very thin liquid films

solid or glass transition ?

a controversy resolved

K ∆(t) = Fstatic (D) + Fhydro (D, D)

Drainage of confined liquids : Chan & Horn 1985

tts

D(t)

D

L(t)

Run-and-stop experiments

Inertia negligible :

Lubrication flow in the confined film

z(x)

xu(x,z)

Hypothesis

PropertiesPressure gradient is // Ox

Average velocity at x:

Velocity profile is parabolic

Quasi-parallel surfaces: dz/dx <<1 Newtonian fluid

Low Re

Slow time variation: T >> z2/

z2

12dPdx

U(x)= -

fluid dynamic viscosity

No-slip at solid wall

Mass conservation 2xz U(x) = - x2 D

Reynolds force (D<<R):

( Re ≤ 10-6 )

Drainage of confined liquids : run-and-stop experiments

K (D - D) = Fstatic (D) + D6R2

D

tts

D(t)

D

L(t)∆(t)

D > 6nm

D(t) - DD(t) KD

6R2

ln = (t - ts ) + Cte

Chan & Horn 1985 (1)

D(t) - DD(t) KD

6R2

ln = (t - ts ) + Cte

D > 50 nm : excellent agreementwith macroscpic hydrodynamics

Various values of D: determination of fluid viscosity excellent agreement with bulk value

Chan et Horn, J. Chem. Phys. 83 (10) 5311 (1985)

Chan & Horn (2)

D ≤ 50nm : drainage too slow

Reynolds drainage

Sticking layers

Hypothesis: fluid layers of thickness Ds

stick onto surfaces

D - 2Ds

D6R2

Fhydro = -

Excellent agreement for 5 ≤D≤ 50nm

OMCTS tetradecane hexadecane

Molecular size

Ds

7,5Å

13Å

4Å

7Å

4Å

7Å

Chan & Horn (3)

D ≤ 5 nm: drainage occurs by steps

Steps height = molecular size

BUT

Occurrence of steps is NOT predictedby « sticky » Reynolds + static forces

Including static force in dynamic equation yields drainage steps

Draining confined liquids with SFA: conclusion

Efficient method to study flows at a nanoscale

Excellent agreement with macroscopic hydrodynamics down to ~ 5 nm (6-7 molecular size thick film)

« Immobile » layer at solid surface, about 1 molecular size

Israelachvili JCSI1985 : water on mica

George et al JCP 1994 : alcanes on metal

Becker & Mugele PRL 2003 : D<5nm

In very thin films of a few molecular layers macroscopic picture does not seem to hold anymore

OUTLINE

Importance

Surface Force Apparatus : a slit of thickness controlled at the Angstrom level

First nano-hydrodynamic experiments performed with SFA :

Experiments with ultra thin liquid films

solid or glass transition ?

a controversy resolved

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Shearing ultra-thin films (1)McGuiggan &Israelachvili, J. Chem Phys 1990

Flattened mica surfaces

Strain gauges

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Velocity

Solid or liquid behaviour depending on V, V/D, historyvery high viscosities, long relaxation times

F

rict

ion

al f

orc

e

‘Continuous’ solid-liquid transition

Granick, Science 1991

Shear force thickness

area velocity

Dodecane D=2,7nm

OMCTS D=2,7 nm

Shear-thinning behaviour

Shearing ultra-thin films (2)

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bulk = 0.01 poise

Giant increase of viscosity under confinement

Confinement-induced liquid-glass transition

Shearing ultra-thin films (3) Klein et Kumacheva, J. Chem. Phys. 1998

tangential motion

times

Shear force response

confined organic liquid

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High precision devicewith both normal and shear force

Confinement-induced solid-liquid transition at n=6 layers

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Flow in ultra-thin liquid films: questions

In very thin films of a few molecular layers macroscopic hydrodynamics does not seem to hold anymore

What is the liquid dynamics:

How can one describe flows ?

Liquid-solid transition ?

Liquid-glass transition ?

OUTLINE

Importance

Surface Force Apparatus : a slit of thickness controlled at the Angstrom level

First nano-hydrodynamic experiments performed with SFA :

Experiments with ultra thin liquid films

solid or glass transition ?

a controversy resolved

Langmuir 99

Nano- particules are present on mica surfaces when cut with platinum hot-wire

They affect significantly properties of ultra-thin sheared films (Zhu & Granick 2003, Heuberger 2003, Mugele & Salmeron)

Methods to cleave mica without particules have been designed(Franz & Salmeron 98, recleaved mica).

They seem to be removed by water

Drainage of ultra-thin films

Monochromatic light

OMCTS moleculeØ 9-10 Å

recleaved mica(particle free)

Direct imaging with SFA

Becker & Mugele Phys. Rev. Lett 2003

Drainage occurs by steps corresponding to layering transitions

Layering transitions

F. Mugele & T. Becker PRL 2003

The heigth between each steps is the size of a OMCTS molecule

Each step is the expulsion of a single monolayer

2 layers 3 layers

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http://pcf.tnw.utwente.nl/people/pcf_fm.doc/

The growth of the N-1 layers region gives information on the flow in the N-layers film.

Persson & Tossati model for the dynamics of the layer expulsion

N layerstransition

N -1layers

No flowAverage velocity V(x)

x

P=Cte

Hypothesis :transition region moves at velocity r(t)

Lubrication flow in the N-layers region

Constant pressure Po in the non-flowing N-1 layers region

(Assumes some linear friction law for the flow in the thin film)

Hydrodynamic limit:

r(t)

+ lubrication

xo : maximum extend of the layered region

Ao = xo 2 maximum area of the layered region

A = r 2 actual area of the N-1 layers region

Constant pressure in the non-flowing region :

Mass conservation :

d : layer thickness

Nd : flowing film thickness

4 33 2

2 1

2 1

Ao measured

Po = Load / Ao

One ajustable parameter for each curve : µ

Po determined from load

PT model describes very well the dynamics of a monolayer expulsionwith an ad hoc friction coefficient µ depending on the flowing film thickness

PT model:

N

Macroscopic hydrodynamic:(with no-slip at wall)

Comparison with macroscopic hydrodynamics

N

Effective friction is larger than predicted by hydrodynamic.

For N≤5 layers, discrepancies with macroscopic hydrodynamic occur.

Ad hoc friction model meets hydrodynamic friction at large N

P=Cte

N-1

N

Discrete layers flow model

transition

Force balance on one layer of thickness d and length dx

x+dxx

F

i+1 i

i -1 i

F

Hydrodynamic limit:

Solving discrete layers flow model

i,i±1 = ll

1,0 = N,N+1 = lssolid-liquid friction

Solve for 1D flow : mass conservation

liquid-liquid friction

1≤ i ≤N

Velocity of transitionregion, measured

N+1 equations give Vi and dP/dx as a function of ll and ls

Adjust ll and ls so that

Ad hoc friction coefficientof the PT model

Assume two different friction coefficients

N

Discrete model describes very well the thickness variations of µ

d2

=0.3

Results of Becker & Mugele 2003

Flow in ultra-thin films is very well described by a lubrication flow with . ad-hoc friction coefficient depending on the film thickness.

For N≤5 layers the friction coefficient is slightly larger than predicted by . macroscopic hydrodynamics with no-slip b.c.

The dependence of the ad-hoc friction with the film thickness is well . accounted by 2 intrinsic friction coefficients, one for liquid-liquid friction . and one for liquid-solid friction

Liquid-liquid friction is close to the value of hydrodynamic limit

Liquid-solid friction is about 20 times larger than liquid-liquid friction