Asymptotic analysis of pollution filtration through thin random fissures between two porous media

TL;DR

This paper analyzes how pollutants pass through thin, randomly distributed fissures between two porous media, determining the asymptotic flow velocity and pollutant flux as fissure thickness diminishes.

Contribution

It provides a novel asymptotic analysis of pollutant filtration through randomly distributed thin fissures, including explicit limit behaviors of flow and pollutant flux.

Findings

Limit velocity of flow computed

Limit pollutant flux determined

Asymptotic behavior characterized

Abstract

We describe the asymptotic behaviour of a filtration problem from a contaminated porous medium to a non-contaminated porous medium through thin vertical fissures of fixed height h>0, of random thinness of order {\epsilon} and which are $\epsilon$-periodically distributed. We compute the limit velocity of the flow and the limit flux of pollutant at the interfaces between the two porous media and the intermediate one.