Nano-meniscii E. CHARLAIX Université de Lyon, France NANOFLUIDICS SUMMER SCHOOL August THE 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-condensation processes 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

1. NEGATIVE PRESSURES Jurin’s law  r 2R h Sap in trees…. Capillary rise liquidr  lv : l-v surface tension r: radius of mean curvature Laplace law of capillarity For water: r = 1µm P cap ~ 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 R H = P V / P SAT < 100% D 3. CAPILLARY CONDENSATION Vapor reservoir Condensed state favored if if rKrK DcDc R H 50% 80% 99% r K 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 Tabor The friction and lubrication of solids Clarendon press 1958 Surface Force Apparatus J. Israelachvili Intermolecular and surface forces Academic press 1985 First measurement of capillary forces with nano-meniscii See also Christenson & al

Surface Force Apparatus in vapor atmosphere J.L. Loubet, ECL Lyon Crassous et al, Europhys Letter 1994 heptane vapor metal surfaces D F

D (nm)050 F (µN) 4π  LV R r K = 24 nm Classical capillarity R Radius of curvature of nanomeniscus is derived from F(D) curve Strong negative pressure in the liquid bridge

PvPv 0 20 D (nm) r K nm Maximum adhesion force does not change much with LB size

D (nm) rKrK Maximum adhesion increases slightly with increasing curvature

D (nm)050 F (µN) Capillary force with van der Waals wetting films R 4π  LV R 3e A SLV Hamaker constant

rKrK Wetting effects are important with nano-scale meniscii DcDc

DcDc 0 20 D (nm)

Wetting-drying of hydrophobic mesoporous media Micelle-templated silicas Lefevre & al, J. Chem. Phys CTAB + TMB Octadecyl triammonium bromide Trimethyl benzene Covalent grafting of silane n-octyl-dimethylchlorosilane Pore radius from 1.3nm to 5.6 nm

Intrusion-extrusion pressure R p = 1.3nm R p = 1.5nm R p = 2.3nm R p = 5.6 nm

intrusion drying log

P liq liquid RpRp 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 R p =1.3 nm

Temperature dependance of pressure cycle P intrusion as T :  LV (T) accounts for shift P extrusion as T

Nucleation model for water extrusion Annular bump Wall bubble

Excess free energy for the vapor nucleus at liquid pressure P L = P V +∆p V/R 3 bump bubble The bubble is more favorable

Number of critical vapor nucleus per unit time and length of pore Pore empties when, microscopic length and time Nucleation model for water extrusion

∆  c = 135 k B T ∆  c = 142 k B T ∆  c = 190 k B T 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 when, microscopic length and time Nucleation model for water extrusion 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 N decreases ∆  c by 400%) See recent work of S. Balibar & al on homogeneous nucleation in water

∆  c = 35 k B T

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