Transcript Charlaix2

Nano-hydrodynamics
down to which scale
do macroscopic concepts hold ?
and how to describe flows beyond ?
E. CHARLAIX
University of Lyon, France
INTRODUCTION TO MICROFLUIDICS August 8-26 2005
The Abdus Salam international center for theoretical physics
OUTLINE
Why nano-hydrodynamics ?
Surface Force Apparatus: a fluid 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 ? (90’s)
a controversy resolved
(Becker & Mugele 2003)
Nanofluidic devices
Microchannels…
…nanochannels
Miniaturization increases surface to volume ratio:
500 nm
50 nm channels
Wang et al, APL 2002
importance of surface phenomena
Nanochannels are more specifically designed for :
 manipulation and analysis of biomolecules
.
with single molecule resolution
 ensure specific ion transport
Mesoporous materials
Large specific surface (1000m2 /cm3 ~ pore radius 2nm)
catalysis, energy/liquid storage…
10nm
Water in mesoporous silica
(B. Lefevre et al, J. Chem. Phys 2004)
Water in nanotube
Koumoutsakos et al 2003
Electrokinetic phenomena
Colloid science, biology, nanofluidic devices…
Electric field
Electrostatic double layer
3 nm
300 nm
electroosmotic flow
Electro-osmosis, streaming potential… are determined by
nano-hydrodynamics at the scale of the Debye length
Tribology :
lubrication of solid surfaces
Mechanics, biomechanics, MEMS/NEMS friction
Nano-rheology of
thin liquid films (monomolecular)
Controled studies at the nanoscale:
Surface force apparatus (SFA)
Tabor, Israelaschvili
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 ? (90’s)
a controversy resolved
(Becker & Mugele 2003)
Surface Force Apparatus (SFA)
Tabor et Winterton, Proc. Royal Soc. London, 1969
Israelachvili, Proc. Nat. Acad. Sci. USA 1972
D
Ag
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
Tabor et Winterton, Proc. Royal Soc. London, 1969
Israelachvili, Proc. Nat. Acad. Sci. USA 1972
D=28nm
contact
Distance between surfaces
is obtained within 1 Å
l
l (nm)
r : reflexion coefficient
n : mica index
a : mica thickness
D : distance between surfaces
Force measurement
In a quasi-static regime
(inertia neglected)
Piezoelectric displacement
Piezoelectric calibration
At large D, very low speed
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
The
Chan & Horn, J. Chem Phys 1985
Electrostatic and hydration force in water films
Horn & al
Chem Phys Lett 1989
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 ? (90’s)
a controversy resolved
(Becker & Mugele 2003)
Drainage of confined liquids : Chan & Horn 1985
Run-and-stop experiments
D(t)
L(t)
D
ts
Inertia negligible :
K ∆(t) = Fstatic (D) + Fhydro (D, D)
t
Hydrodynamic force
When D<<R (cylinders radii) and Reynolds number Re < 1
the hydrodynamic force is essentially dominated by the
lubrication flow of liquid drained out of the gap region.
R
D
R
D:Å
µm
R ~ cm
D ~ Å/s
n ~ 10-6 m2/s
Re ≤ 10-9
Re =
DD
n
n : fluid
kinematic viscosity
Velocity in the drainage flow
R
Parabolic approximation
2
x
z=D+
2R
Crossed cylinders are
equivalent to sphere-plane
Mass conservation
2pxz U(x) = - p x2 D
z(x)
D
U(x)
x
U(x)
R D
√ 2D
√ 2RD
~ 10 µm
Lubrication flow in the confined film
Hypothesis
Newtonian fluid
u(x,z)
z(x)
x
Quasi-parallel surfaces: dz/dx <<1
Low Re
Slow time variation: T >> z2/n
Properties
Pressure gradient is // Ox
Velocity profile is parabolic
Average velocity at x:
No-slip at solid wall
2 dP
z
U(x)= 12h dx
h: fluid dynamic viscosity
Pressure profile
R
z(x)
D
U(x)
x
P(x)-P∞
√ 2RD
x
Hydrodynamic force between the surfaces
Reynolds force:
6 p h R2 D
Fhydro = D
D<<R
Drainage of confined liquids : run-and-stop experiments
D(t)
∆(t)
L(t)
D
ts
D < 6nm
6p h R2 D
K ∆(t) = Fstatic (D) D
6p h R2 D
K (D - D) = D
2
D(t)
D
6
p
h
R
 =
ln
(t - ts ) + Cte
D(t)
KD
t
Chan & Horn 1985 (1)
ln D(t) - D
D(t)
=
6p h R2 (t - t ) + Cte
s
KD
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)
Chan & Horn (2)
D ≤ 50nm : drainage too slow
Hypothesis:
fluid layers of thickness Ds
stick onto surfaces
Sticking
layers
6p h R2 D
Fhydro = D - 2Ds
Reynolds
drainage
Excellent agreement
for 5 ≤D≤ 50nm
OMCTS tetradecane hexadecane
Molecular
size
Ds
7,5Å
4Å
4Å
13Å
7Å
7Å
Chan & Horn (3)
D ≤ 5 nm:
drainage occurs by steps
Steps height = molecular size
Including static interaction
(oscillating force) in dynamic
equation yields drainage steps
BUT
Occurrence of steps is NOT predicted
by « sticky » Reynolds + static forces
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
Draining confined liquids with SFA: questions
In very thin films of a few molecular layers macroscopic
picture does not seem to hold anymore
What is the liquid dynamics in those very thin films ?
How can one describe flows ?
Drainage of thin water films
Water confined between silica surfaces:
Horn & al Chem Phys Lett 162 404, 1989
Static force has no oscillations
(no smectic layering) but shows
electrostatic effects
Drainage of thin water films
Water confined between silica surfaces:
Horn & al Chem Phys Lett 162 404, 1989
Static force has no oscillations
(no smectic layering)
Macroscopic hydrodynamics
holds down to molecular size
with bulk value of viscosity
and no-slip boundary condition
(no sticking layer)
Results for water confined
between mica surfaces are
similar
Israelachvili JCSI1985
Why do ultra-thin films of organic liquids
behave differently from water ?
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 ? (90’s)
a controversy resolved
(Becker & Mugele 2003)
Shearing ultra-thin films (1)
Loaded mica surface flatten
and form a film of area A and
constant thickness D measured by
FECO fringes
McGuiggan et Israelachvili,
J. Chem Phys 1990
Shearign ultra-thin films (1)
« stop-and-go » experiments
McGuiggan et Israelachvili,
J. Chem Phys 1990
V
Solid or liquid behaviour
depending on V, V/D, history…
very high viscosities
long relaxation times
‘continuous’ solid-liquid transition
Shearing ultra-thin films (2)
Shear force
Granick, Science 1991
velocity
Dodecane D=2,7nm
area
thickness
Giant increase of viscosity
under shear
OMCTS D=2,7 nm
Shear-thinning behaviour
Glass transition induced by confinement
hbulk = 0,01 poise
Shearing ultra thin films (3)
High precision device
with both normal and shear force
Sensitive in shear up to 6 molecular layers
Klein et Kumacheva,
J. Chem. Phys. 1996
Shearing ultra thin films (3)
Imposed tangential motion
Klein et Kumacheva,
J. Chem. Phys. 1996
OMCTS, cyclohexane
Force response
Abrupt and reproducible
Solid-liquid transition at
n=7
n=6 couches
only induced by confinement
independant of normal pressure
times
Shearing ultra thin films (3)
Creep viscosity of solid film
Klein et Kumacheva,
J. Chem. Phys. 1996
Shearing ultra-thin flims has open a research area with
controversial effects
Same fluids, same technique,different results
Increase of viscocisites of ORDER OF MAGNITUDE
Shear-thinning, Memory effects, slow relaxation times
Glass transition (out of equilibrium)
Well defined liquid-solid transition under a critical
confinment
 When D << R (cylinders radii) crossed cylinders geometry is
equivalent to a sphere of radius R at distance D from a plane
R
R
D
 When D<<R and Reynolds < 1, the hydrodynamic force is essentially
dominated by the lubrication flow of liquid drained out of the gap region.
This is the Reynolds force
2
6
p
h
R
Fhydro =
D
D
D
h : fluid kinematic viscosity
Lubrication flow in the confined film
Hypothesis
u(x,z)
z(x)
x
Newtonian fluid
Small angle: dz/dx <<1
Low Re
Slow time variation: T >> z2/n
No-slip at solid wall
Lubrication flow in the confined film
Properties
u(x,z)
z(x)
Stokes flow:
x
Pressure gradient is // Ox
Velocity profile is parabolic
Average velocity at x:
2 dP
z
U(x)= 12h dx
h: fluid dynamic viscosity
The hydrodynamic force between two crossed cylinders of radii R
is the same as between a sphere of radius R and a plane
R
R
D
This is the Reynolds force
h : fluid dynamic viscosity
2
6
p
h
R
Fhydro =
D
D
D<<R
Drainage de liquides confinés (2) : méthode dynamique
Israelachvili, J. Coll. Inter. Sci. 1985
D(t) = D +A cos (w t+f)
Amortissement
visqueux
y(t) = y+Ao cos wt
mx¨ +K(x-xo) + Ka D = Fs(D)
x = y+D
Pour w << wo =√K/m
Hydrodynamique macroscopique :
a=
R2
6ph
KD
f=
(
∂Fs
∂D D
)
Drainage de liquides confinés (2)
Israelachvili, J. Coll. Inter. Sci. 1985
Tétradécane confiné entre des surfaces de mica
Force statique
Inverse de l’amortissement a
Détermination indépendante de la viscosité et de la condition limite
Pas de couche immobile à 3Å près
Drainage de liquides confinés (2)
Israelachvili, J. Coll. Inter. Sci. 1985
Eau+NaCl confiné entre des lames de mica
TB accord avec l’hydrodynamique macroscopique
Pas de couche immobile à la paroi
Drainage de liquides confinés (1)
Chan et Horn,
J. Chem. Phys. 1985
Drainage de films fins de liquides non-polaires : importance de l’humidité