An analytical model for diffusion of chemicals under thermal effects in semi-infinite porous media

An analytical solution for one-dimensional diffusion of chemicals under coupled chemical and thermal potentials is presented. The theoretical formulation considered includes heat conduction and chemical diffusion due to both molecular and thermal diffusion potentials. Laplace transformation technique has been used to derive the analytical solution to the problem in a semi-infinite domain. The results obtained by the proposed analytical solution have a good agreement with those obtained from the laboratory tests of thermal diffusion of a salt solution in a compact clay. Comparisons with the numerical model were also carried out to investigate the effects of transient heat conduction and temperature-dependency of diffusion coefficient on the chemical transport due to a thermal gradient. An application of the model to study the effects of thermal diffusion on chemical transport in a compacted clay liner (CCL) is presented. The results show that the base concentration and flux of the chemical in the CCL increases with the increase of the temperature and Soret coefficient. The 40-year bottom fluxes for the case with thermal diffusion are 2-11 times greater than the case with only molecular diffusion for a 0.6 m compacted clay liner. Based on the results achieved, thermal diffusion demonstrates considerable effect in the landfill design. In the simulation scenario with ST = 5 × 10−2 1/K, the base concentration and the flux of the chemical at 100 years is 1.5 times and 8 times larger, respectively than those obtained from the simulation without considering thermal diffusion. Using the analytical model presented, a series of dimensionless design charts are presented that can be used to estimate the thickness of the CCL, under non-isothermal conditions. The proposed analytical solution provides a simple method for the verification of alternative numerical models, evaluation of groundwater/soil remediation methods and preliminary design of landfill clay liners.