A non-linear mathematical model for an undisturbed soil-column experiment and source parameter identification

In this article, we put forward a non-linear transport model for an undisturbed soil-column experiment with the non-linear Freundlich's isotherm. As compared with ordinary models based on linear adsorption, the retardation factor is a non-linear functional of solute concentration, and the production term is a non-linear term related with the solute concentration and an unknown source/sink function. Furthermore, an actual undisturbed soil-column experiment in Zibo, Shandong Province, China is investigated, and an inverse problem of identifying the source/sink parameter is considered with the additional data of breakthrough curves. An optimal perturbation iteration algorithm is applied to determine the unknown source/sink parameter both in the cases of accurate and inaccurate data. The inversion results show that the optimal perturbation algorithm is efficient at least to the problem of this article, and the non-linear mathematical model here could be applied to describe undisturbed soil-column experiments with non-linear adsorption behaviours.