Nano-meniscii E. CHARLAIX Université de Lyon, France NANOFLUIDICS SUMMER SCHOOL August 20-24 2007 THE ABDUS SALAM INTERNATIONAL CENTER FOR THEORETICAL

Nano-meniscii

E. CHARLAIXUniversité de Lyon, France

NANOFLUIDICS SUMMER SCHOOL August 20-24 2007THE ABDUS SALAM INTERNATIONAL CENTER FOR THEORETICAL PHYSICS

OUTLINE

Capillarity at a nanoscale : orders of magnitude

Some experiments involving nano-meniscii

Intrusion-extrusion of water in mesoporous media

Measuring capillary forces with SFA experiments

Micro-Nanofluidic devices

Micro-heat pipes

evaporation-condensationprocesses in thin liquid films

Two-phase flow in nano-channels

Tas & al, Appl. Phys Lett 2004

Biological & environmental processes

Sap in trees

Transport of solute in underground

Stability of soils

Material science

Humidity-induceed creep in composite materials

Frost heave

Cracks propagation in glass

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

1. NEGATIVE PRESSURES

Jurin’s law

r

2R

h

Sap in trees….

Capillary rise

liquid r

lv: l-v surface tensionr: radius of mean curvature

Laplace law of capillarity

For water: r = 1µm Pcap ~ 1 atm

If r<< R : the capillary force is

R

Israelachvili, Molecular and Surface Forces, 1985

vanishing amount of liquid gives macroscopic force

r

Two spheres in contact: a wetting liquid ( < 90°) forms a liquid bridge

2. HUGE CAPILLARY FORCES

Nanomeniscus can sustain a Ø 2mm steal bead !

The Kelvin’s radius

is the mean radius of curvature for L/V equilibrium across a curved interface

RH = PV / PSAT < 100%D

3. CAPILLARY CONDENSATION

Vapor reservoir

Condensed state favored if if

rKDc

RH 50% 80% 99%

rK 1.5nm 4.5nm 100nm

4. NUCLEATION

See recent work of E. Herbert, F. Caupin, S. Balibar if

Some experiments involving nano-meniscii

Bowden et TaborThe friction and lubrication of solids

Clarendon press 1958

Surface Force Apparatus

J. IsraelachviliIntermolecular and surface forces

Academic press 1985

First measurement of capillary forceswith nano-meniscii

See also Christenson & al

PONT LIQUIDE MICROSCOPIQUE hr ~ 4 - 50 nmρ ∼ μmPV

Surface Force Apparatusin vapor atmosphere

J.L. Loubet, ECL Lyon

Crassous et al, Europhys Letter 1994

heptane vapor metal surfaces

D

F

D (nm)0 50

F (

µN

)

4π LVR rK = 24 nmQuickTime™ et un

décompresseur TIFF (non compressé)sont requis pour visionner cette image.

Classical capillarity

R

Radius of curvature of nanomeniscus is derived from F(D) curve

Strong negative pressure in the liquid bridge

Pv

0 20 D (nm) 60 80 100

rK 3.6 52 nm

Maximum adhesion force does not change much with LB size

-0.34

-0.32

-0.30

-0.28

-0.26

-0.24

-0.22

-0.20

F/R (N/m)

100500

h (A)0 5 10 D (nm)

rK

Maximum adhesion increases slightly with increasing curvature

D (nm)0 50

F (

µN

)

Capillary force with van der Waals wetting films

R

4π LVR

3e

ASLV Hamaker constant

30

25

20

Fmax/4π

( / )R mN m

0.60.50.40.30.20.10.0

r-2/3 (nm-2/3)rK



Wetting effects are important with nano-scale meniscii

Dc

Dc

0 20 D (nm) 60 80 100

Wetting-drying of hydrophobic mesoporous media



Micelle-templated silicas

Lefevre & al, J. Chem. Phys. 2004

CTAB + TMB Octadecyltriammonium bromide

Trimethylbenzene

Covalent grafting of silanen-octyl-dimethylchlorosilane

Pore radius from 1.3nm to 5.6 nm

Intrusion-extrusion pressure





Rp = 1.3nm

Rp = 1.5nm

Rp = 2.3nm

Rp = 5.6 nm



intrusion

drying

log


sont requis pour visionner cette image.Pliq



liquidRp

cos a = 120.3°

advancing angle

Classical capillarity

does not work for extrusion

Laplace law for intrusion pressure

Very good agreeement with classical capillarity up to Rp=1.3 nm

Temperature dependance of pressure cycle



Pintrusion as T : LV(T) accounts for shift

Pextrusion as T

Nucleation model for water extrusion





Annular bump







Wall bubble

Excess free energy for the vapor nucleus at liquid pressure PL= PV +∆p


sont requis pour visionner cette image.QuickTime™ et un






V/R3 QuickTime™ et undécompresseur TIFF (non compressé)


QuickTime™ et undécompresseur TIFF (non compressé)sont requis pour visionner cette image.

QuickTime™ et undécompresseur TIFF (non compressé)sont requis pour visionner cette image.

bump

bubble

The bubble is more favorable



Number of critical vapor nucleus per unit time and length of pore



Pore empties whenQuickTime™ et un


QuickTime™ et undécompresseur TIFF (non compressé)sont requis pour visionner cette image., microscopic length and time




∆c = 135 kBT∆c = 142 kBT

∆c = 190 kBT

Activation barrier accounts for: strong variation of extrusion pressure with pore size threshold pore size for extrusion temperature dependance of extrusion pressure

But: classical capillarity model gives much too high energy barrier



Number of critical vapor nucleus per unit time and length of pore



Pore empties whenQuickTime™ et un


QuickTime™ et undécompresseur TIFF (non compressé)sont requis pour visionner cette image., microscopic length and time




L ~1 µm

t exp ~ s

Classical capillarity accounts well for pressure drop across nano-meniscus

It does not work well for estimating energy barrier of LV nucleation

Heterogeneous nucleation ? (wetting defects in nanopores)

Three-phase line tension effects ?

(line tension of 10 -11 N decreases ∆c by 400%)

See recent work of S. Balibar & al on homogeneous nucleation in water


sont requis pour visionner cette image.∆c = 35 kBT

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Nano-meniscii E. CHARLAIX Université de Lyon, France NANOFLUIDICS SUMMER SCHOOL August 20-24 2007 THE ABDUS SALAM INTERNATIONAL CENTER FOR THEORETICAL