Analytical Solution for Pollutant Diffusion in Soils with Time-Dependent Dispersion Coefficient

Abstract

According to the characteristics of the time-dependent dispersion coefficient of pollutant migration in soils, a one-dimensional pollutant migration model considering solute decay is established in the finite thickness soil. Based on the proposed model, the time-dependent boundary condition variable is considered, and different types of time-dependent dispersion coefficients are also assumed. The variable parameter k for pollutant diffusion time is used to control the time-dependent model. The analytical solution is obtained by separating the variable method. The results calculated by the presented analytical solution compared with those in the literature indicate solution accuracy and program reliability. According to the parameter study, variable k in the time-dependent model has a particular influence on the results, and the time-dependent and constant boundary conditions have a significant difference. The proposed method can be a reference for the landfill liner design.