Analytical solutions to thermal gradient enhanced diffusion of organic contaminants through unsaturated composite liner: considering the existence of capillary fringe

The capillary fringe (CF) is a well-known zone of tension saturation immediately above the water table and has significant influence on solute transport in soil profile, yet the CF has not been included in available models for contaminant transport in composite liners. This study presents an exact analytical solution to thermal gradient enhanced diffusion of organic contaminants through unsaturated composite liner considering the existence of CF. The exact solution is obtained by the separation of variables method and validated by two existing analytical solutions and a numerical model. The influence of CF on the diffusion of two organic contaminants is analyzed under different desaturation coefficients, Soret coefficients, and the temperature difference between the upper and the bottom surfaces of the composite liner. A corresponding simplified solution is also proposed by using a new Robin-type boundary and evaluated for engineering practice. The mass flux by thermal diffusion is considered when developing the new Robin-type boundary. The results show that the CF has a remarkable influence on contaminant diffusion in unsaturated composite liners and the influence is more distinct for unsaturated composite liners with higher desaturation coefficient. The enhancement of thermal diffusion process by the increase of Soret coefficient and the temperature difference between the upper and the bottom surfaces of the composite liner is more significant if the CF is included in the diffusion model. The simplified solution shows excellent performance when the CF is not considered and when the desaturation coefficient is low (e.g., 0.1 m−1) regardless of the variations of CF and Soret coefficient. The results are useful for analyzing organic contaminants diffusion through unsaturated composite liners considering the existence of CF and thermal effects in both theory and engineering practice.