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Wetting front dynamics in an isotropic porous medium

Published online by Cambridge University Press:  02 February 2012

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

A new approach to the modelling of wetting fronts in porous media on the Darcy scale is developed, based on considering the types (modes) of motion the menisci go through on the pore scale. This approach is illustrated using a simple model case of imbibition of a viscous incompressible liquid into an isotropic porous matrix with two modes of motion for the menisci, the wetting mode and the threshold mode. The latter makes it necessary to introduce an essentially new technique of conjugate problems that allows one to link threshold phenomena on the pore scale with the motion on the Darcy scale. The developed approach (a) makes room for incorporating the actual physics of wetting on the pore scale, (b) brings in the physics associated with pore-scale thresholds, which determine when sections of the wetting front will be brought to a halt (pinned), and, importantly, (c) provides a regular framework for constructing models of increasing complexity.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Porous media Mathematical Foundations: Topological fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 694 , 10 March 2012 , pp. 399 - 407
Copyright
Copyright © Cambridge University Press 2012

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