Integral transform solution for solute transport in multi-layered porous media with the implicit treatment of the interface conditions and arbitrary boundary conditions

Abstract

Summary Solute transport in multi-layered porous media is of great importance in environmental engineering problems. Its important feature lies in the explicit existence of interface conditions. The previous analytical solutions require explicitly considering the interface conditions in the evaluation of coefficients or in the eigenvalue system. In the present study, an implicit treatment of interface conditions is presented to eliminate the interface conditions from the original system. The generalized integral transform technique is performed with respect to the transformed system to obtain the analytical solution. Compared to the pervious solution strategy, the present eigenfunctions are much simpler. The present analytical solution and eigenvalue system are expressed for the generalized boundary conditions by introducing two boundary factors in the boundary conditions, which applies to arbitrary assembly of boundary conditions without modification and can reduce the effort of programming. The developed analytical solution is validated against two experiments and one analytical solution. Good agreement is shown between the experimental data and analytical as well as numerical solutions.