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Dynamic contact angle of a liquid spreading on an unsaturated wettable porous substrate

Published online by Cambridge University Press:  09 January 2013

Yulii D. Shikhmurzaev  and
James E. Sprittles
Yulii D. Shikhmurzaev*
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK
James E. Sprittles
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK
*
†Email address for correspondence: yulii@for.mat.bham.ac.uk
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Abstract

The spreading of an incompressible viscous liquid over an isotropic homogeneous unsaturated porous substrate is considered. It is shown that, unlike the dynamic wetting of an impermeable solid substrate, where the dynamic contact angle has to be specified as a boundary condition in terms of the wetting velocity and other flow characteristics, the ‘effective’ dynamic contact angle on an unsaturated porous substrate is completely determined by the requirement of existence of a solution, i.e. the absence of a non-integrable singularity in the spreading fluid’s pressure at the ‘effective’ contact line. The obtained velocity dependence of the ‘effective’ contact angle determines the critical point at which a transition to a different flow regime takes place, where the fluid above the substrate stops spreading whereas the wetting front inside it continues to propagate.

JFM classification

Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 715 , 25 January 2013 , pp. 273 - 282
Copyright
©2013 Cambridge University Press

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References

Alleborn, N. & Raszillier, H. 2004 Spreading and sorption of a droplet on a porous substrate. Chem. Engng Sci. 59, 2071–2088.Google Scholar
Auriault, J.-L. 2010 About the Beavers and Joseph boundary condition. Transp. Porous Med. 83, 257–266.Google Scholar
Barenblatt, G. I., Entov, V. M. & Ryzhik, V. M. 1990 Theory of Fluid Flows through Natural Rocks. Kluwer.Google Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.Google Scholar
Blake, T. D. 2006 The physics of moving wetting lines. J. Colloid Interface Sci. 299, 1–13.Google Scholar
Blake, T. D. & Haynes, J. M. 1969 Kinetics of liquid/liquid displacement. J. Colloid Interface Sci. 30, 421–423.Google Scholar
Blake, T. D. & Shikhmurzaev, Y. D. 2002 Dynamic wetting by liquids of different viscosity. J. Colloid Interface Sci. 253, 196–202.Google Scholar
Clarke, A., Blake, T. D., Carruthers, K. & Woodward, A. 2002 Spreading and imbibition of liquid droplets on porous surfaces. Langmuir 18, 2980–2984.Google Scholar
Davis, S. H. & Hocking, L. M. 2000 Spreading and imbibition of viscous liquid on a porous base. II. Phys. Fluids 12, 1646–1655.Google Scholar
Dussan V., E. B. 1979 On the spreading of liquids on solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371–400.Google Scholar
de Gennes, P.-G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57, 827–863.Google Scholar
Huh, C. & Scriven, L. E. 1971 Hydrodynamic model of steady movement of a solid/liquid/fluid contact line. J. Colloid Interface Sci. 35, 85–101.Google Scholar
Jones, I. P. 1973 Low Reynolds number flow past a porous spherical shell. Proc. Camb. Phil. Soc. 73, 231–238.Google Scholar
Keshav, T. R. & Basu, S. 2007 Spreading of liquid droplets on proton exchange membrane of a direct alcohol fuel cell. Chem. Engng Sci. 62, 7515–7522.Google Scholar
Markicevic, B., D’Onofrio, T. G. & Navaz, H. K. 2010 On spread extent of sessile droplet into porous medium: numerical solution and comparison with experiments. Phys. Fluids 22, 012103.CrossRefGoogle Scholar
Murdoch, A. I. & Soliman, A. 1999 On the slip boundary condition for liquid flow over planar porous boundaries. Proc. R. Soc. Lond. A 455, 1315–1340.Google Scholar
Nield, D. A. 2009 The Beavers–Joseph boundary condition and related matters: a historical and critical note. Transp. Porous Med. 78, 537–540.Google Scholar
Probstein, R. F. 1989 Physicochemical Hydrodynamics: An Introduction. Butterworth.Google Scholar
Ralston, J., Popescu, M. & Sedev, R. 2008 Dynamics of wetting from an experimental point of view. Annu. Rev. Mater. Res. 38, 23–43.CrossRefGoogle Scholar
Reis, N. C. Jr., Griffiths, R. F. & Santos, J. M. 2004 Numerical simulation of the impact of liquid droplets on porous surfaces. J. Comput. Phys. 198, 747–770.CrossRefGoogle Scholar
Saffman, P. G. 1971 On the boundary condition at the surface of a porous medium. Stud. Appl. Maths 50, 93–101.Google Scholar
Shikhmurzaev, Y. D. 1993 The moving contact line on a smooth solid surface. Intl J. Multiphase Flow 19, 589–610.Google Scholar
Shikhmurzaev, Y. D. 2007 Capillary Flows with Forming Interfaces. Chapman & Hall/CRC.Google Scholar
Shikhmurzaev, Y. D. 2011 Some dry facts about dynamic wetting. Eur. Phys. J. 197, 47–60 (special topics).Google Scholar
Shikhmurzaev, Y. D. & Sprittles, J. E. 2012a Anomalous dynamics of capillary rise in porous media. Phys. Rev. E 86, 016306.Google Scholar
Shikhmurzaev, Y. D. & Sprittles, J. E. 2012b Wetting front dynamics in an isotropic porous medium. J. Fluid Mech. 694, 399–407.Google Scholar
Starov, V. M., Zhdanov, S. A., Kosvintsev, S. R., Sobolev, V. D. & Velarde, M. G. 2003 Spreading of liquid drops over porous substrates. Adv. Colloid Interface Sci. 104, 123–158.Google Scholar
Washburn, E. W. 1921 The dynamics of capillary flow. Phys. Rev. 17, 273–283.Google Scholar
Whitaker, S. 1999 The Method of Volume Averaging. Kluwer.Google Scholar
Wilson, M. C. T., Summers, J. L., Shikhmurzaev, Y. D., Clarke, A. & Blake, T. D. 2006 Non-local hydrodynamic influence on the dynamic contact angle: slip models versus experiment. Phys. Rev. E 73, 041606.Google Scholar