Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-26T16:19:48.368Z Has data issue: false hasContentIssue false
  • English
  • Français

Forced dewetting on porous media

Published online by Cambridge University Press:  15 February 2007

OLIVIER DEVAUCHELLE ,
CHRISTOPHE JOSSERAND  and
STEPHANE ZALESKI
OLIVIER DEVAUCHELLE
Affiliation:
Laboratoire de Modélisation en Mécanique, CNRS-UMR 7606, Case 162, 4 place Jussieu, 75252 Paris Cédex 05, France
CHRISTOPHE JOSSERAND
Affiliation:
Laboratoire de Modélisation en Mécanique, CNRS-UMR 7606, Case 162, 4 place Jussieu, 75252 Paris Cédex 05, France
STEPHANE ZALESKI
Affiliation:
Laboratoire de Modélisation en Mécanique, CNRS-UMR 7606, Case 162, 4 place Jussieu, 75252 Paris Cédex 05, France
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the dewetting of a porous plate withdrawn from a liquid bath. The contact angle is fixed to zero and the flow is assumed to be almost parallel to the plate (lubrication approximation). The ordinary differential equation involving the position of the water surface is analysed in phase space by means of numerical integration. We show the existence of a stationary moving contact line with zero contact angle below a critical value of the capillary number η U/γ. Above this value, no stationary contact line can exist. An analytical model, based on asymptotic matching is developed, which reproduces the dependence of the critical capillary number on the angle of the plate with respect to the horizontal (3/2 power law), provided the capillary length is much larger than the square root of the porous-medium permeability. In addition, it is shown that the classical lubrication equation leads not only to the well-known Landau–Levich–Derjaguin films, but also to a family of films for which thickness is not imposed by the problem parameters.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 574 , 10 March 2007 , pp. 343 - 364
Copyright
Copyright © Cambridge University Press 2007

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

Aradian, A., Raphaël, E. & de Gennes, P.-G. 2000 Dewetting on porous media with aspiration. Eur. Phys. J. 2, 367–376.Google Scholar
Bacri, L. & Brochard-Wyart, F. 2001 Dewetting on porous media. Europhys. Lett. 56, 414–419.CrossRefGoogle Scholar
Beavers, S. & Joseph, D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.CrossRefGoogle Scholar
Blake, T. D. & Ruschak, K. J. 1979 A maximum speed of wetting. Natur. 282, 489–491.CrossRefGoogle Scholar
Charru, F., Mouilleron, H. & Eiff, O. 2004 Erosion and deposition of particles on a bed sheared by a viscous flow. J. Fluid Mech. 519, 55–80.CrossRefGoogle Scholar
Daerr, A., Lee, P., Lanuza, J. & Clément, E. 2003 Erosion patterns in a sediment layer. Phys. Rev. E 67, 065201.Google Scholar
Derjagin, B. V. 1943 On the thickness of a layer of liquid remaining on the walls of vessels after their emptying, and the theory of the application of photoemulsion after coating on the cine film. Acta Phys. Chem. USS. 20, 349–352.Google Scholar
Duffy, B. R. & Wilson, S. K. 1997 A third-order differential equation arising in thin-film flows and relevent to Tanner's law. Appl. Math. Lett. 10 (3), 63–68.CrossRefGoogle Scholar
Dussan, V. E. B. & Davis, S. H. 1974 On the motion of a fluid–fluid interface along a solid surface. J. Fluid Mech. 65, 71–95.CrossRefGoogle Scholar
Eggers, J. 2004 a Hydrodynamic theory of forced dewetting. Phys. Rev. Lett. 93, 094502.CrossRefGoogle ScholarPubMed
Eggers, J. 2004 b Toward a description of contact line motion at higher capillary numbers. Phys. Fluid. 16, 3491–3494.CrossRefGoogle Scholar
Fredsoe, J. & Deigaard, R. 1992 Mechanics of Coastal Sediment Transport. World Scientific.CrossRefGoogle Scholar
de Gennes, P., Brochard-Wyart, F. & Quéré, D. 2005 Gouttes, Bulles, Perles et Ondes. Belin.Google Scholar
de Gennes, P.-G. 1984 Dynamique d'étalement d'une goutte. C. R. Acad. Sci. Pari. 298 (4), 111–115.Google Scholar
de Gennes, P.-G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.CrossRefGoogle Scholar
Goyeau, B., Lhuillier, D., Gobin, D. & Velarde, M. G. 2003 Momentum transport at a fluid–porous interface. Intl J. Heat Mass Transfe. 46, 4071–4081.CrossRefGoogle Scholar
Hadjiconstantinou, N. G. 2003 Comment on Cercignani's second-order slip coefficient. Phys. Fluid. 15, 2352–2354.CrossRefGoogle Scholar
Hervet, H. & de Gennes, P.-G. 1984 Dynamique du mouillage: film précurseur sur solide ‘sec’. C. R. Acad. Sci. Pari. 299, 499–503.Google Scholar
Hocking, L. M. 1983 The spreading of a thin drop by gravity and capillarity. Q. J. Mech. Appl. Math. 36, 55–69.CrossRefGoogle Scholar
Hocking, L. M. 2001 Meniscus draw-up and draining. Eur. J. Appl. Math. 12, 195–208.CrossRefGoogle Scholar
Huh, E. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85–101.CrossRefGoogle Scholar
Landau, L. D. & Levich, B. V. 1942 Dragging of a liquid by a moving plate. Acta Phys. Chem. USS. 17, 42–54.Google Scholar
Manneville, P. 1990 Dissipative Structures and Weak Turbulence. Academic.Google Scholar
Maurer, J., Tabeling, P., Joseph, P. & Willaime, H. 2003 Second-order slip laws in microchannels for helium and nitrogen. Phys. Fluid. 15, 2613–2621.CrossRefGoogle Scholar
Neale, G. & Nader, W. 1974 Practical significance of Brinkman's extension of Darcy's law – coupled parallel flows within a channel and a bounding porous medium. Can. J. Chem. Engn. 52, 475–478.CrossRefGoogle Scholar
Raphaël, E. & de Gennes, P.-G. 1999 Imprégnation d'un ruban poreux. C. R. Acad. Sci. Pari. 327, 685–689.Google Scholar
Renardy, M., Renardy, Y. & Li, J. 2001 Numerical simulation of moving contact line using a volume-of-fluid method. J. Comput. Phys. 171, 243–263.CrossRefGoogle Scholar
Scherer, M. A., Melo, F. & Marder, M. 1999 Sand ripples in an oscillating annular sand-water cell. Phys. Fluid. 11, 58–67.CrossRefGoogle Scholar
Schorghofer, N., Jensen, B., Kudrolli, A. & Rothman, D. H. 2004 Spontaneous channelization in permeable ground: theory, experiment, and observation. J. Fluid Mech. 503, 357–374.CrossRefGoogle Scholar
Seppecher, P. 1996 Moving contact lines in the Cahn–Hilliard theory. Intl J. Engng Sci. 34, 977–992.CrossRefGoogle Scholar
Stegner, A. & Wesfreid, J. E. 1999 Dynamical evolution of sand ripples under water. Phys. Rev. E 60, R3487–R3490.Google ScholarPubMed
Strogatz, S. H. 1994 Nonlinear Dynamics and Chaos. Addison–Wesley.Google Scholar
Wilson, S. D. R. 1982 The drag-out problem in film coating theory. J. Engng Math. 16, 209–221.CrossRefGoogle Scholar