Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008
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Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008. Introduction to nano-fluidics. E. CHARLAIX. University of Lyon, France. 1. Flows at a nano-scale: where does classical hydrodynamics stop ?.

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University of lyon france

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

Introduction to nano-fluidics

E. CHARLAIX

University of Lyon, France


University of lyon france

1. Flows at a nano-scale:

where does classical hydrodynamics stop ?

2. Liquid flows on smooth surfaces: the boundary condition

3. Liquid flows on smooth surfaces: experimental aspects

4. Flow on patterned surfaces

5. Effect of boundary hydrodynamics

on other surface transport properties

6. Capillarity at a nano-scale


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Flows at a nano-scale:

Where does classical hydrodynamics stop ?

(and how to describe flow beyond ?)


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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


University of lyon france

500nm

Nanofluidic devices

Microchannels…

…nanochannels

50 nm channels

Wang et al, APL 2002

Miniaturization increases surface to volume ratio:

importance of surface phenomena

Nanochannels are more specifically designed for :

  • manipulation and analysis of biomolecules . with single molecule resolution

  • specific ion transport


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Mesoporous materials

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

catalysis, energy/liquid storage or transfo, …

10nm

Water in mesoporous silica

(B. Lefevre et al, J. Chem. Phys 2004)

Water in nanotubes

Koumoutsakos et al 2003

H. Fang & al Nature Nanotech 2007


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Electrokinetic phenomena

Colloid science, biology, nanofluidic devices…

Electrostatic double layer

3 nm 300 nm

Electric field

electroosmotic flow

Electro-osmosis, streaming potential… are determined by

nano-hydrodynamics at the scale of the Debye length


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Tribology :

Mechanics, biomechanics, MEMS/NEMS friction

Rheology and mechanics

of ultra-thin liquid films

First measurements at a sub-nanometric scale:

Surface Force Apparatus (SFA)

Bowden & Tabor

J. N. Israelachvili

The friction and lubrication of solids

Clarendon press 1958

Intermolecular and surface forces

Academic press 1985


University of lyon france

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


University of lyon france

Surface Force Apparatus (SFA)

Tabor et Winterton, Proc. Royal Soc. London, 1969

Israelachvili, Proc. Nat. Acad. Sci. USA 1972

Ag

D

mica

Ag

Optical resonator


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Franges of equal chromatic order (FECO)

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

Spectrograph

Source of white light

l


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D=28nm

contact

l (nm)

r : reflexion coefficient

n : mica index

a : mica thickness

D : distance between surfaces

l

Distance between surfaces

is obtained within 1 Å


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Force measurement

In a quasi-static regime

(inertia neglected)

Piezoelectric displacement


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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

Horn & Israelachvili, J. Chem Phys 1981


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Electrostatic and hydration force in water films

Horn & al 1989

Chem Phys Lett


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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


University of lyon france

D(t)

L(t)

t

ts

Drainage of confined liquids : Chan & Horn 1985

Run-and-stop experiments

Inertia negligible :

K ∆(t) = Fstatic (D) + Fhydro (D, D)


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2pxz U(x) = - p x2 D

z2

dP

U(x)= -

12h

dx

Lubrication flow in the confined film

  • Hypothesis

Newtonian fluid

z(x)

Quasi-parallel surfaces: dz/dx <<1

u(x,z)

Low Re

( Re ≤ 10-6)

x

Slow time variation: T >> z2/n

No-slip at solid wall

  • Properties

Pressure gradient is // Ox

Velocity profile is parabolic

h: fluid dynamic viscosity

Average velocity at x:

  • Mass conservation

  • Reynolds force (D<<R):


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D(t)

∆(t)

L(t)

t

ts

D > 6nm

6p hR2

D

D(t) -D¥

6p hR2

ln =(t - ts ) + Cte

D

D(t)

KD¥

Drainage of confined liquids : run-and-stop experiments

K (D -D¥) = Fstatic (D) +


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D(t) -D¥

6p hR2

ln =(t - ts ) + Cte

D(t)

KD¥

Chan & Horn 1985 (1)

D > 50 nm : excellent agreement

with macroscpic hydrodynamics

Various values of D¥ :

determination of fluid viscosity h

excellent agreement with bulk value

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


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Hypothesis:

fluid layers of thickness Ds stick onto surfaces

6p hR2

D

Fhydro = -

Excellent agreement

for 5 ≤D≤ 50nm

D - 2Ds

Reynolds drainage

OMCTS tetradecane hexadecane

Molecular size

7,5Å

Ds

13Å

Chan & Horn (2)

D ≤ 50nm : drainage too slow

Sticking layers


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Including static force in dynamic equation yields drainage steps

BUT

Occurrence of steps is NOT predicted

by « sticky » Reynolds + static forces

Chan & Horn (3)

D ≤ 5 nm:

drainage occurs by steps

Steps height = molecular size


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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


University of lyon france

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


University of lyon france

Velocity

Shearing ultra-thin films (1)

McGuiggan &Israelachvili,

J. Chem Phys 1990

Strain gauges

Frictional force

Solid or liquid behaviour depending on V, V/D, history

very high viscosities, long relaxation times

Flattened mica surfaces

‘Continuous’ solid-liquid transition


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Shearing ultra-thin films (2)

Granick, Science 1991

hbulk= 0.01 poise

Shear force thickness

area velocity

Dodecane D=2,7nm

Giant increase of viscosity under

confinement

Shear-thinning behaviour

OMCTS D=2,7 nm

Confinement-induced

liquid-glass transition


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Shearing ultra-thin films (3)

Klein et Kumacheva,

J. Chem. Phys. 1998

High precision device

with both normal and shear force

tangential motion

confined organic liquid

Shear force response

Confinement-induced

solid-liquid transition at n=6 layers

times


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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:

Liquid-glass transition ?

Liquid-solid transition ?

How can one describe flows ?


University of lyon france

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


University of lyon france

Langmuir 99


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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)

They seem to be removed by water

Methods to cleave mica without particules have been designed

(Franz & Salmeron 98, recleaved mica).


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Drainage of ultra-thin films

Becker & Mugele

Phys. Rev. Lett 2003

Direct imaging with SFA

recleaved mica

(particle free)

OMCTS molecule

Ø 9-10 Å

Monochromatic light


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Layering transitions

F. Mugele & T. Becker PRL 2003

Drainage occurs by steps

corresponding to layering transitions

2 layers 3 layers

Each step is the expulsion of a single monolayer

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


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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.


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Persson & Tossati model for the dynamics of the layer expulsion

No flow

Average velocity V(x)

P=Cte

x

N -1

layers

r(t)

N layers

transition

transition region moves at velocity r(t)

Hypothesis :

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

  • Lubrication flow in the N-layers region

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

Hydrodynamic limit:


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  • Mass conservation :

d : layer thickness

Nd : flowing film thickness

  • + lubrication

xo : maximum extend

of the layered region

  • Constant pressure in the non-flowing region :

Ao = p xo2maximum area of the layered region

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


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4 3

3 2

2 1

2 1

PT model:

Ao measured

Po determined from load

Po = Load / Ao

One ajustable parameter for each curve : µ

PT model describes very well the dynamics of a monolayer expulsion

with an ad hoc friction coefficient µ depending on the flowing film thickness


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N

Comparison with macroscopic hydrodynamics

Macroscopic hydrodynamic:

(with no-slip at wall)

N

Ad hoc friction model meets hydrodynamic friction at large N

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

Effective friction is larger than predicted by hydrodynamic.


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i -1

i

i+1

i

Discrete layers flow model

N-1

P=Cte

N

transition

Force balance on one layer of thickness d and length dx

F

x

x+dx

F

Hydrodynamic limit:


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Solving discrete layers flow model

1≤ i ≤N

  • Assume two different friction coefficients

mi,i±1 = m ll

liquid-liquid friction

m1,0 = mN,N+1 = m ls

solid-liquid friction

  • Solve for 1D flow : mass conservation

Velocity of transition

region, measured

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

  • Adjust m ll and m ls so that

Ad hoc friction coefficient

of the PT model


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h

d2

N

=0.3

Discrete model describes very well the thickness variations of µ


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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 intrinsicfriction 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


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