Flow-cell studies of thermal diffusion in liquids. Part 2.—Phenomenological equations and their solution

Abstract

Equations are developed describing the attainment of Soret equilibrium in two-component liquid systems flowing in a laminar fashion through a rectangular duct. The resulting diffusion equation is solved in a simplified form, valid for small temperature intervals, by a suitable finite difference approximation. A complementary solution yielding an explicit expression for the separation and valid for large times is derived from the calculus of variations. Use of this expression for interpreting practical results, as in the calibration experiments, is shown in part 1. Consideration of the errors involved in the simplified diffusion equation leads to an upper limit on the temperature interval for the validity of the solution. Errors arising from finite thermal and velocity entry lengths are shown to be negligible.