On the anomalous dynamics of capillary rise in porous media

TL;DR

This paper presents a comprehensive theory explaining the complex, multi-regime dynamics of capillary rise in porous media by incorporating multiple menisci motion modes into continuum mechanics, aligning well with experimental observations.

Contribution

It introduces a novel theoretical framework that integrates dynamic wetting, threshold, and de-pinning modes into boundary conditions for porous media flow, covering a wide range of observed behaviors.

Findings

The theory describes all experimentally observed regimes over four orders of magnitude in time.

It identifies dominant physical mechanisms at different stages of capillary rise.

The model successfully predicts the anomalous dynamics of wetting fronts.

Abstract

The anomalous dynamics of capillary rise in a porous medium discovered experimentally more than a decade ago (Delker et al., Phys. Rev. Lett. 76 (1996) 2902) is described. The developed theory is based on considering the principal modes of motion of the menisci that collectively form the wetting front on the Darcy scale. These modes, which include (i) dynamic wetting mode, (ii) threshold mode and (iii) interface de-pinning process, are incorporated into the boundary conditions for the bulk equations formulated in the regular framework of continuum mechanics of porous media, thus allowing one to consider a general case of three-dimensional flows. The developed theory makes it possible to describe all regimes observed in the experiment, with the time spanning more than four orders of magnitude, and highlights the dominant physical mechanisms at different stages of the process.