Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-18T07:14:11.477Z Has data issue: false hasContentIssue false
  • English
  • Français

A universal law for capillary rise in corners

Published online by Cambridge University Press:  06 January 2011

ALEXANDRE PONOMARENKO ,
DAVID QUÉRÉ  and
CHRISTOPHE CLANET
ALEXANDRE PONOMARENKO
Affiliation:
PMMH (Physique et Mécanique des Milieux Hétérogènes), UMR7636 du CNRS, ESPCI, 10 rue Vauquelin, 75005 Paris, and LadHyX, UMR7646 du CNRS, Ecole Polytechnique, 91128 Palaiseau, France
DAVID QUÉRÉ
Affiliation:
PMMH (Physique et Mécanique des Milieux Hétérogènes), UMR7636 du CNRS, ESPCI, 10 rue Vauquelin, 75005 Paris, and LadHyX, UMR7646 du CNRS, Ecole Polytechnique, 91128 Palaiseau, France
CHRISTOPHE CLANET*
Affiliation:
PMMH (Physique et Mécanique des Milieux Hétérogènes), UMR7636 du CNRS, ESPCI, 10 rue Vauquelin, 75005 Paris, and LadHyX, UMR7646 du CNRS, Ecole Polytechnique, 91128 Palaiseau, France
*
†Email address for correspondence: clanet@ladhyx.polytechnique.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the capillary rise of wetting liquids in the corners of different geometries and show that the meniscus rises without limit following the universal law: h(t)/a ≈ (γt/ηa)1/3, where γ and η stand for the surface tension and viscosity of the liquid while is the capillary length, based on the liquid density ρ and gravity g. This law is universal in the sense that it does not depend on the geometry of the corner.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 666 , 10 January 2011 , pp. 146 - 154
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bico, J. & Qur, D. 2002 Rise of liquids and bubbles in angular capillary tubes. J. Colloid Interface Sci. 247, 162–166.CrossRefGoogle ScholarPubMed
Boyle, 1682 New Experiments Physico-Mechanical Touching the Spring of the Air and Its Effects. Oxford H. Hall.Google Scholar
van Brakel, J. & Heertjes, P. M. 1975 Capillary rise in porous media. Nature 254, 585–586.CrossRefGoogle Scholar
Caps, H., Cox, S. J., Decauwer, H., Weaire, D. & Vandewalle, N. 2005 Capillary rise in foams under microgravity. Colloids Surf. Physicochem. Engng Asp. 261, 131–134.CrossRefGoogle Scholar
Caupin, F., Cole, M., Balibar, S. & Treiner, J. 2008 Absolute limit for the capillary rise of a fluid. EPL 82, 56004.CrossRefGoogle Scholar
Clanet, C. & Quéré, D. 2002 Onset of menisci. J. Fluid Mech. 460, 131–149.CrossRefGoogle Scholar
Depountis, N., Davies, M. C. R., Harris, C., Burkhart, S., Thorel, L., Rezzoug, A., Knig, D., Merrifield, C. & Craig, W. H. 2001 Centrifuge modelling of capillary rise. Engng Geol. 60, 95–106.CrossRefGoogle Scholar
Ferrero, F. 2003 Wettability measurements on plasma treated synthetic fabrics by capillary rise method. Polym. Test. 22, 571–578.CrossRefGoogle Scholar
Fries, N. & Dreyer, M. 2008 The transition from inertial to viscous flow in capillary rise. J. Colloid Interface Sci. 327, 125–128.CrossRefGoogle ScholarPubMed
Galet, L., Patry, S. & Dodds, J. 2010 Determination of the wettability of powders by the Washburn capillary rise method with bed preparation by a centrifugal packing technique. J. Colloid Interface Sci. 346, 470–475.CrossRefGoogle ScholarPubMed
de Gennes, P. G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.CrossRefGoogle Scholar
Hall, C. & Hoff, W. 2007 Rising damp: capillary rise dynamics in walls. Proc. R. Soc. A 463, 1871–1884.CrossRefGoogle Scholar
Hardy, W. B. 1922 Historical notes upon surface energy and forces of short range. Nature 109, 375–378.CrossRefGoogle Scholar
Higuera, F. J., Medina, A. & Linan, A. 2008 Capillary rise of a liquid between two vertical plates making a small angle. Phys. Fluids 20, 102102.CrossRefGoogle Scholar
Hoffman, R. L. 1974 A study of the advancing interface. J. Colloid Interface Sci. 50, 228–241.CrossRefGoogle Scholar
Ishino, C., Reyssat, M., Reyssat, E., Okumura, K. & Quéré, D. 2007 Wicking within forest of micro-pillars. EPL 79, 56005.CrossRefGoogle Scholar
Jurin, J. 1718 An account of some experiments shown before the Royal Society; with an enquiry into the cause of the ascent and suspension of water in capillary tubes. Philos. Trans. R. Soc. Lond. 30, 739–747.Google Scholar
Karoglou, M., Moropoulou, A., Giakoumaki, A. & Krokida, M. K. 2005 Capillary rise kinetics of some building materials. J. Colloid Interface Sci. 284, 260–264.CrossRefGoogle ScholarPubMed
Kistler, F. 1993 Hydrodynamics of wetting. Wettability, Surfactant Science Series (ed. Berg, J. C.), vol. 49. Dekker.Google Scholar
Lago, M. & Araujo, M. 2001 Capillary rise in porous media. J. Colloid Interface Sci. 234, 35–43.CrossRefGoogle ScholarPubMed
Laplace, P. S. 1878 Traité de mécanique céleste. Bachelier Librairie Paris.Google Scholar
Lucas, R. 1918 Rate of capillary ascension of liquids. Kolloid Z. 23, 15.CrossRefGoogle Scholar
Marmur, A. 2003 Kinetics of penetration into uniform porous media: testing the equivalent-capillary concept. Langmuir 19, 5956–5959.CrossRefGoogle Scholar
Princen, H. M. 1968 Capillary phenomena in assemblies of parallel cylinders. J. Colloid Interface Sci. 30, 69–75.CrossRefGoogle Scholar
Princen, H. M. 1969 Capillary phenomena in assemblies of parallel cylinders. J. Colloid Interface Sci. 30, 359–371.CrossRefGoogle Scholar
Quéré, D. 1997 Inertial capillarity. Europhys. Lett. 39, 533–538.CrossRefGoogle Scholar
Quéré, D., Raphael, E. & Ollitrault, J.-Y. 1999 Rebounds in a capillary tube. Langmuir 15, 3679–3682.CrossRefGoogle Scholar
de Ramos, A. L. & Cerro, R. L. 1994 Liquid filament rise in corners of square capillaries: a novel method for the measurement of small contact angles. Chem. Engng Sci. 49, 2395.CrossRefGoogle Scholar
Ramrez-Flores, J. C., Bachmann, J. & Marmur, A. 2010 Direct determination of contact angles of model soils in comparison with wettability characterization by capillary rise. J. Hydrol. 382, 10–19.CrossRefGoogle Scholar
Siebold, A., Nardin, M., Schultz, J., Walliser, A. & Oppliger, M. 2000 Effect of dynamic contact angle on capillary rise phenomena. Colloids Surfaces A 161, 81–87.CrossRefGoogle Scholar
Steen, P. H. 1996 Capillarity and interfacial phenomena, wetting and spreading. In Research Trends in Fluid Mechanics (ed. Lumley, J. L., Acrivos, A., Leal, L. G. & Leibovich, S.), vol. 48. AIP.Google Scholar
Tang, L. H. & Tang, Y. 1994 Capiflary rise in tubes with sharp grooves. J. Phys. II 4, 881–890.Google Scholar
Tanner, L. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D. Appl. Phys. 12, 1473–1484.CrossRefGoogle Scholar
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273–283.CrossRefGoogle Scholar
Weislogel, M. M. & Lichter, S. 1998 Capillary flow in an interior corner. J. Fluid Mech. 373, 349–378.CrossRefGoogle Scholar
Wolf, F. G., dos Santos, L. O. E. & Philippi, P. C. 2010 Capillary rise between parallel plates under dynamic conditions. J. Colloid Interface Sci. 344, 171–179.CrossRefGoogle ScholarPubMed