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Nano-meniscii

Nano-meniscii. E. CHARLAIX. Université de Lyon, France. NANOFLUIDICS SUMMER SCHOOL August 20-24 2007. THE ABDUS SALAM INTERNATIONAL CENTER FOR THEORETICAL PHYSICS. OUTLINE. Capillarity at a nanoscale : orders of magnitude. Some experiments involving nano-meniscii.

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Nano-meniscii

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

  2. OUTLINE Capillarity at a nanoscale : orders of magnitude Some experiments involving nano-meniscii Measuring capillary forces with SFA experiments Intrusion-extrusion of water in mesoporous media

  3. Micro-Nanofluidic devices Two-phase flow in nano-channels Micro-heat pipes Tas & al, Appl. Phys Lett 2004 evaporation-condensation processes in thin liquid films

  4. Biological & environmental processes Sap in trees Transport of solute in underground Stability of soils

  5. Material science Humidity-induceed creep in composite materials Frost heave Cracks propagation in glass

  6. 2R r q h liquid r For water: r = 1µm Pcap ~ 1 atm 1. NEGATIVE PRESSURES Laplace law of capillarity glv: l-v surface tension r: radius of mean curvature Capillary rise Jurin’s law Sap in trees….

  7. 2. HUGE CAPILLARY FORCES R • Two spheres in contact: a wetting liquid (q < 90°) forms a liquid bridge r q If r<< R : the capillary force is • vanishing amount of liquid gives macroscopic force Nanomeniscus can sustain a Ø 2mm steal bead ! Israelachvili, Molecular and Surface Forces, 1985

  8. rK Dc RH 50% 80% 99% rK1.5nm 4.5nm 100nm 3. CAPILLARY CONDENSATION Vapor reservoir RH= PV / PSAT < 100% D Condensed state favored if if The Kelvin’s radius is the mean radius of curvature for L/V equilibrium across a curved interface

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

  10. Some experiments involving nano-meniscii

  11. First measurement of capillary forces with nano-meniscii Surface Force Apparatus Bowden et Tabor The friction and lubrication of solids Clarendon press 1958 J. Israelachvili Intermolecular and surface forces Academic press 1985 See also Christenson & al

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

  13. 0 D (nm) 50 R F (µN) Classical capillarity rK = 24 nm 4π gLVR Radius of curvature of nanomeniscus is derived from F(D) curve Strong negative pressure in the liquid bridge

  14. Pv rK 3.6 52 nm 0 20 D (nm) 60 80 100 Maximum adhesion force does not change much with LB size

  15. rK 0 5 10 D (nm) Maximum adhesion increases slightly with increasing curvature

  16. 4π gLVR 3e 0 D (nm) 50 Capillary force with van der Waals wetting films R ASLV Hamaker constant F (µN)

  17. Dc rK Wetting effects are important with nano-scale meniscii

  18. Dc 0 20 D (nm) 60 80 100

  19. Wetting-drying of hydrophobic mesoporous media Lefevre & al, J. Chem. Phys. 2004 Micelle-templated silicas Covalent grafting of silane n-octyl-dimethylchlorosilane CTAB + TMB Octadecyl triammonium bromide Trimethyl benzene Pore radius from 1.3nm to 5.6 nm

  20. Intrusion-extrusion pressure Rp = 1.3nm Rp = 1.5nm Rp = 5.6 nm Rp = 2.3nm

  21. intrusion drying log

  22. Rp liquid Pliq Laplace law for intrusion pressure Classical capillarity cos qa = 120.3° advancing angle • Very good agreeement with classical capillarity up to Rp=1.3 nm • does not work for extrusion

  23. Temperature dependance of pressure cycle Pintrusion as T : gLV(T) accounts for shift Pextrusion as T

  24. Nucleation model for water extrusion Annular bump Wall bubble

  25. Excess free energy for the vapor nucleus at liquid pressure PL= PV +∆p bump bubble V/R3 The bubble is more favorable

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

  27. ∆Wc = 190 kBT ∆Wc = 135 kBT ∆Wc = 142 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

  28. Nucleation model for water extrusion Number of critical vapor nucleus per unit time and length of pore microscopic length and time , Pore empties when L ~1 µm t exp ~ s

  29. 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 ∆Wc by 400%) See recent work of S. Balibar & al on homogeneous nucleation in water

  30. ∆Wc = 35 kBT

  31. LIQUIDES AUX INTERFACES

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