Pure Thermal Diffusion. I. Time-Dependent Phenomenological Theory for Binary Liquids

Abstract

Solutions to the partial differential equations which describe pure thermal diffusion in a binary liquid are obtained by means of perturbation and Fourier transform methods which retain explicitly the temperature and composition dependences of density, heat capacity, and the coefficients of diffusion, thermal diffusion, and thermal conductivity. Inclusion of the effects of time-dependent temperature and center-of-mass velocity gradients during the warming-up period yields unambiguous identification of zero time. Inclusion of the variability of the coefficients makes it possible to evaluate the effects of such variability. The theory provides clear criteria for experimental design. Practical formulas are given for both demixing and remixing experiments.