An analytical solution for contaminant transport against the flow with periodic boundary condition in one-dimensional porous media

The transport of pollutants in porous media, is of hydrodynamic dispersion phenomena, has been the major research subject for more than four decades. The present paper is an attempt to describe analytically the solute transport in one-dimensional homogeneous porous medium of finite domain. The effects of time-periodic pulse-type inlet contaminant concentration and groundwater flow velocity against the contaminant transport are investigated analytically. The temporally dependent dispersion proportional to seepage velocity and retardation factor is also taken into account. The governing transport equation is solved analytically by employing Laplace transformation technique. The effects of various physical parameters on solute transport and their importance are discussed and are also illustrated graphically.