On the dispersion of a solute by diffusion, convection and exchange between phases

Abstract

The method used in an earlier paper (Aris 1956) to discuss the dispersion of a solute in a fluid flowing through a tube is applied here to the case in which the solute can also pass into another fluid phase flowing in an annular region around the first. The apparent diffusion coefficient is the sum of the molecular and Taylor diffusion coefficients in the two phases and a term due to the finite rate of partition between them. It is shown how the Taylor diffusion coefficients depend on the ratio of amounts of solute held in the two phases and how this gives a connexion between the coefficient a$^{2}$U$^{2}$/48D found by Taylor (1953) for viscous flow in a circular tube and the 11 a$^{2}$U$^{2}$/48D found by Westhaver (1942) in his analysis of the distillation column. The use of these apparent diffusion coefficients in distillation and partition chromatography is illustrated.