An analytical model for diffusion of chemicals under a thermal gradient in finite clayey soil

An analytical solution to non-isothermal diffusion of chemicals in finite porous medium with different combinations of boundary and initial conditions is presented. The average degree of diffusion was proposed to assess the contaminant removal efficiency from polluted soil with different initial contaminant concentration distribution conditions considering chemical and thermal diffusion. The dimensionless time factor for the average degree of diffusion U = 90% can be decreased by a factor of 8.4 in the case with rectangular initial solute concentration distribution considering thermal diffusion. An application of the model to study the effects of initial solute concentration distribution and adsorption on the average degree of diffusion show that both the adsorption performance of clayey soil to the contaminant and the initial solute concentration distribution have a significant effect on the average degree of diffusion. In the cases with rectangular and inverse triangular initial solute concentration distributions, when U = 50%, the times increase by factors of 2.2 and 5.3, respectively, compared to the case with triangular initial solute concentration distribution. An application of the model to study the effects of temperature on the average degree of diffusion of contaminant in polluted soil show that the temperature difference has a significant effect to promote the contaminant transport in clayey soil by increasing both of the thermal diffusion and chemical diffusion effect. It may be an effective method to remove contaminant from polluted soil by thermal diffusion.