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Imbibition in Disordered Media
The physics of liquids in porous media gives rise to many interesting
phenomena, including imbibition where a viscous fluid displaces a less viscous
one. Here we discuss the theoretical and experimental progress made in recent
years in this field. The emphasis is on an interfacial description, akin to the
focus of a statistical physics approach. Coarse-grained equations of motion
have been recently presented in the literature. These contain terms that take
into account the pertinent features of imbibition: non-locality and the
quenched noise that arises from the random environment, fluctuations of the
fluid flow and capillary forces. The theoretical progress has highlighted the
presence of intrinsic length-scales that invalidate scale invariance often
assumed to be present in kinetic roughening processes such as that of a
two-phase boundary in liquid penetration. Another important fact is that the
macroscopic fluid flow, the kinetic roughening properties, and the effective
noise in the problem are all coupled. Many possible deviations from simple
scaling behaviour exist, and we outline the experimental evidence. Finally,
prospects for further work, both theoretical and experimental, are discussed.Comment: Review article, to appear in Advances in Physics, 53 pages LaTe