Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficients

Analytical solutions to advection-dispersion equations are of continuous interest because they present benchmark solutions to problems in hydrogeology, chemical engineering, and fluid mechanics. In this paper, we examine solutions to two-dimensional advection-dispersion equation with time-dependent dispersion coefficients. The time- and space-dependent nature of the dispersion coefficient in subsurface contaminant transport problems has been demonstrated in the literature in both field and laboratory scale studies. Analytical solutions given in this paper could be used to model the transport of solute in hydrogeologic systems characterized by dispersion coefficients that may vary as a function of travel time from the input source. In particular, in this paper we develop instantaneous and continuous point-source solutions for constant, linear, asymptotic, and exponentially varying dispersion coefficients. The relationship between the proposed general solution and the particular solutions given in the relevant literature are discussed. Examples are included to demonstrate the effect of time-dependent dispersion coefficients on solute transport.