On thermal diffusion separation in binary mixtures with variable transport coefficients

The stationary heat transfer and Soret separation of a binary mixture between parallel plates with different constant temperatures is studied allowing for variable transport properties. The mixture is described by non-linear one-dimensional equations of heat and mass transfer, where the density, thermal conductivity, and Soret coefficient depend on temperature and concentration. A general procedure for integrating these equations is proposed. The problem is reduced to the ordinary differential equation of first order, which describes the trajectory of the system in the concentration–temperature plane, and implicit dependence of temperature on space coordinate. It is shown that the solution for concentration is unique if the density and thermal conductivity do not depend on concentration. Analytical solutions of the problem are derived in a number of cases, while the most general case is treated numerically. The non-linear temperature and concentration profiles in different binary mixtures (aqueous solutions, colloidal suspensions, polymer blend) are constructed and analyzed. A procedure for extracting the dependence of Soret coefficient on temperature and concentration from the experimentally measured thermal and compositional profiles is suggested.