One-Dimensional Pollutant’s Advective-Diffusive Transport from a Varying Pulse-Type Point Source through a Medium of Linear Heterogeneity

Abstract

Analytical solutions of one-dimensional (1D) advection-diffusion equations (ADE) are obtained subject to an initially pollutant-free domain and varying pulse-type input conditions. The medium is considered heterogeneous and of semi-infinite extent. The heterogeneity is defined by considering the velocity as a spatially dependent, linear, non homogeneous increasing function. It is interpolated in a finite domain in which concentration values are to be evaluated. The unsteadiness of the exponential form of velocity and dispersivity is also considered. The expression for velocity is written in degenerate form. Analytical solutions are obtained when dispersivity depends upon the velocity. The Laplace integral transform technique (LITT) has been used.