Behavior of Contaminant in a Flow due to Variations in the Cross-Flow dispersion under a Dirichlet Boundary Conditions.

Abstract

The advection-dispersion equation (ADE) is mostly adopted in evaluating solute migration in a flow. This study presents the behavior of contaminant in a flow due to variations in the cross-flow dispersion under a Dirichlet boundary conditions. The analytical solution of a two-dimensional advection-dispersion equation for evaluating groundwater contamination in a homogeneous finite medium which is initially assumed not contaminant free was obtained. In deriving the model equation, it was assumed that there was a constant point-source concentration at the origin and a Dirichlet type boundary condition at the exit boundary. The cross-flow dispersion coefficients, velocities and decay terms are time-dependent. The modeled equation was transformed using some space and time variables and solved by parameter expanding and Eigen-functions expansion method. Graphs were plotted to study the behavior of the contaminant in the flow. The results showed that increase in the cross-flow coefficient decline the concentration of the contaminant with respect to increase in time, vertical distance and horizontal distance in different patterns.