Influence of Off-diagonal Dispersion on the Concentration of Contaminant in a Two-dimensional Contaminant Flow: A Semi-analytical Approach

Abstract

The equation which describes the two-dimensional contaminant flow model is a partial differential equation characterized by advection, dispersion, adsorption, first order decay and zero-order source. In this paper, the off-diagonal dispersion parameter is introduced into the two dimensional contaminant flow model in order to study its effect on the concentration of the contaminant. It is assumed that the adsorption term is modeled by Freudlich isotherm. The parameter expanding method is applied on the equation to obtain a set of differential equations which are then solved successively using the Eigen functions expansion technique to obtain the analytical solution. The results obtained are plotted into graphs to show the effect of change in the parameters on the concentration of the contaminants. Findings from this research show that the contaminant concentration decreases with increase in distance as the off-diagonal dispersion coefficient, zero-order source coefficient and vertical dispersion coefficient increases.