Diffusion in a nonuniform velocity field

Abstract

The effect of a nonuniform velocity field on the diffusion process is examined. When the local passive admixture transport equation is averaged over the channel cross section, the differential equation for the average concentration over the cross section is obtained in the form of an infinite asymptotic series whose terms are linear combinations of the derivatives of the average concentration with respect to the coordinate and time, while the coefficients depend on the degree of transverse nonuniformity of the velocity field and the radial Peclet number. Estimates show that in most of the cases encountered in practice to ensure that the calculations have the necessary accuracy the series must include derivatives up to the third order. An approximate solution of the averaged equation is found by the method of asymptotic expansions and the initial moments of the residence time distribution function are determined.