Redistribution of a passive tracer in a porous medium under a surface-washing flow at high Péclet number.

The cleaning of porous materials is a ubiquitous and complex problem. Contaminant redistribution is the process by which cleaning can lead to contamination of previously ‘clean’ parts of the porous material. In the case of surface washing, absorption of the contaminant from the washing flow into the porous medium may lead to potential exposure to the contaminant in regions downstream of the contamination source. To obtain a quantitative understanding of contaminant redistribution in porous media, we propose a two-dimensional model for the surface-washing of a wet porous medium contaminated by a drop of a single-species contaminant using a thin film flow. A quasi-steady diffusive boundary layer equation describes mass transport in the thin film flow and a macroscopic diffusion equation is used to describe mass transport in the porous medium. We focus our analysis on asymptotic regimes that exhibit contaminant redistribution in the porous medium and substantiate our asymptotic results through a comparison with numerical simulations performed in COMSOL Multiphysics. The results of this investigation are used to suggest ways in which the cleaning process in porous materials can be improved to reduce the impact of contaminant redistribution.