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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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 ?

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


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


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


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


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


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


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


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


Franges of equal chromatic order (FECO)

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

Spectrograph

Source of white light

l


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


Force measurement

In a quasi-static regime

(inertia neglected)

Piezoelectric displacement


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


Electrostatic and hydration force in water films

Horn & al 1989

Chem 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


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)


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):


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) +


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)


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


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


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


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


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


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


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 ?


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)

They seem to be removed by water

Methods to cleave mica without particules have been designed

(Franz & Salmeron 98, recleaved mica).


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


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


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

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:


  • 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


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


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.


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:


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


h

d2

N

=0.3

Discrete model describes very well the thickness variations of µ


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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