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

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 ε and which are ε -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.