A phenomenological model of the increase in solute concentration in ground water due to evaporation

We present a new phenomenological model of the evaporation of ground water containing a polluting material in the dissolved form. Only the one-dimensional case is treated. It is assumed that there exists a sharp evaporation front separating between the dry and the water-saturated soil. The water-saturated soil is assumed to occupy a semi-infinite domain x > X(t), where x is a vertical coordinate directed downward and X(t) is a position of the evaporation front. The mathematical description is based on four linear diffusion equations coupled through four boundary conditions, one of which is nonlinear, on the free moving evaporation front. We use a similarity solution of the governing equations and analyze it qualitatively showing that the solute concentration increases in the upward vertical direction and reaches its maximum on the evaporation front. The dependence of the solute concentration at the evaporation front and of the velocity of the front on the initial solute concentration and the temperature of the ground surface are computed. It is shown that for not high values of the initial solute concentration that are below the concentration value c(d) at which a deposition of the pollutant sets in, the solute concentration on the evaporation front can reach values that are above the deposition value c(d). These results point to a possible mechanism of pollutant deposition in ground water caused by the evaporation.