Thermally induced diffusion of chemicals under steady-state heat transfer in saturated porous media

Abstract

Thermally induced diffusion of chemicals is observed in many natural phenomena and engineering processes. We present analytical solutions to the non-isothermal diffusion of chemicals under combined effects of molecular and thermal diffusion processes and under variable diffusion coefficient with temperature. The generalized integral transform technique (GITT) is adopted to successfully derive the analytical solutions to the one-dimensional boundary problem under Neumann and Dirichlet outflow conditions. The accuracy of the analytical model developed is examined against three benchmarks including two experimental datasets. The analytical models are applied to develop an understanding of how the chemical transfer under non-isothermal conditions is governed by a combination of the Soret effect and temperature dependency of diffusion coefficient. We demonstrate that the mass transfer components due to thermal diffusion (or Soret effect) and the temperature dependency of diffusion coefficients are equally important to develop an accurate assessment of non-isothermal diffusion problem. Under the conditions of the case study considered, we show that a threshold for the Soret coefficient exists at which the temperature dependency of chemical diffusion coefficient can induce equally or larger influences on the chemical compared to the influence of thermal diffusion. The analytical solutions proposed also provide modelling benchmarks to examine the accuracy of alternative multiphysics numerical models for studying the non-isothermal diffusion problems in porous media.