WATER SUSPENSION INFILTRATION WITH ADSORPTION IN UNSATURATED-SATURATED POROUS MEDIA

Transportation of contaminated water suspension (water and silt) in unsaturated-saturated porous media is considered. Moreover, the water in suspension is contaminated and this contaminant is adsorbed by the porous media matrix. The deposition of silt in the matrix is characterized by a filtration function, and the contaminant adsorption is modeled by a sorption isotherm. The mathematical model includes a coupled system for the water suspension infiltration, silt, and contaminant (uniformly mixed in the water) transport with dispersion and their deposition and adsorption in porous media. Filtration function expresses the rate of silt deposition depending on the amount of (immobile) deposited silt. Contaminant adsorption is modeled in terms of the contaminant concentration in suspension, the amount of adsorbed contaminant, and the rate of adsorption. The main goal is to develop a suitable numerical approximation that can be applied to the solution of direct and inverse problems. In the numerical experiments, we demonstrate the correctness and the effectiveness of the used method.