Introduction to nano-fluidics

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University of Lyon, France

Nanoscale Interfacial Phenomena in Complex Fluids
-

May 19
-

June 20 2008

E. CHARLAIX


Introduction to nano
-
fluidics


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

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 channels

Wang et al, APL 2002

500

nm

Nanochannels are more specifically designed for :

Microchannels…

…nanochannels

Large specific surface
(1000m
2

/cm
3

~ pore radius 2nm)

catalys
is
,

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 2003

H. Fang & al Nature Nanotech 2007

10nm

Electric field

electroosmotic flow

Electrostatic double layer

3 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, 1969

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

Surface Force Apparatus (SFA)

mica

Ag

Ag

Optical resonator

D

Franges of equal chromatic order (FECO)

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

l

Source of white light

Spectrograph

D=28nm

contact

r : reflexion coefficient

n : mica index

a : mica thickness

D : distance between surfaces

Distance between surfaces

is obtained within 1 Å

l

l
(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 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

K ∆(t) = F
static
(D) + F
hydro

(D, D)

Drainage of confined liquids : Chan & Horn 1985

t

t
s

D(t)

D


L(t)

Run
-
and
-
stop experiments

Inertia negligible :

Lubrication flow in the confined film

z(x)

x

u(x,z)


Hypothesis


Properties

Pressure 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 >> z
2
/
n

z
2

12
h

d
P

d
x

U(x)=
-

h
:
fluid dynamic viscosity

No
-
slip at solid wall


Mass conservation

2
p
xz
U(x)

=
-

p
x
2
D



Reynolds force (D<<R):

( Re ≤ 10
-
6

)

Drainage of confined liquids : run
-
and
-
stop experiments

K
(D
-

D

) = F
static
(D) +

D

6
p h

R
2

D

t

t
s

D(t)

D


L(t)

∆(t)

D > 6nm

D(t)
-

D


D(t)

KD


6
p h

R
2

ln
=

(t
-

t
s
)

+ Cte

Chan & Horn 1985 (1)

D(t)
-

D


D(t)

KD


6
p h

R
2

ln
=

(t
-

t
s
)

+ Cte

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

Reynolds
drainage

Sticking
layers

Hypothesis:

fluid layers of thickness D
s
stick onto surfaces

D
-

2D
s

D

6
p h

R
2

F
hydro

=
-

Excellent agreement


for 5 ≤D≤ 50nm

OMCTS tetradecane hexadecane

Molecular
size

D
s

7,5Å

13Å









Chan & Horn (3)

D ≤ 5 nm:

drainage occurs by steps

Steps height = molecular size


BUT


Occurrence of steps is NOT predicted

by «

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

Shearing ultra
-
thin films (1)

McGuiggan &Israelachvili,

J. Chem Phys 1990

Flattened mica surfaces

Strain
gauges

Velocity

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

very high viscosities, long relaxation times


Frictional force

‘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)

h
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

High precision device

with both normal and shear force

Confinement
-
induced

solid
-
liquid transition at n=6 layers

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 molecule

Ø 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

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 layers

transition

N
-
1

layers

No flow

Average velocity V(x)

x

P=Cte

Hypothesis :

transition region moves at velocity r(t)


Lubrication flow

in the N
-
layers region


Constant pressure P
o

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

x
o

:
maximum extend

of the layered region

A
o

=
p
x
o

2

maximum area of the layered region

A

=
p
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 3

3 2

2 1

2 1

A
o

measured

P
o

= Load / A
o

One ajustable parameter for each curve : µ

P
o

determined from load

PT model describes very well the dynamics of a monolayer expulsion

with 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+dx

x

F

i+1

i

i
-
1

i

F

Hydrodynamic limit:



Solving discrete layers flow model

m

i,i
±
1
=
m

ll

m

1,0

=
m

N,N+1
=
m

ls

solid
-
liquid friction



Solve for 1D flow : mass conservation

liquid
-
liquid friction

1≤ i ≤N

Velocity of transition

region, measured

N+1 equations give V
i

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



Assume two different friction coefficients

N

Discrete model describes very well the thickness variations of µ

h

d
2

=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