A phenomenological model of the increase in solute concentration in groundwater 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-dimensi onal case is treated. It is assumed that there exists a sharp evaporation f ront separating between the dry and the water-saturated soil. The water-sat urated soil is assumed to occupy a semi-infinite domain x > X(t), where x i s a vertical coordinate directed downward and X(t) is a position of the eva poration front. The mathematical description is based on four linear diffus ion equations coupled through four boundary conditions, one of which is non linear, on the free moving evaporation front. We use a similarity solution of the governing equations and analyze it qualitatively showing that the so lute concentration increases in the upward vertical direction and reaches i ts maximum on the evaporation front. The dependence of the solute concentra tion at the evaporation front and of the velocity of the front on the initi al solute concentration and the temperature of the ground surface are compu ted. It is shown that for not high values of the initial solute concentrati on 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 r each values that are above the deposition value c(d). These results point t o a possible mechanism of pollutant deposition in ground water caused by th e evaporation.