The Taylor and hyperbolic models of unsteady longitudinal dispersion of a passive impurity in convection-diffusion processes

The problem of the dispersion of a passive impurity in a circular tube is c onsidered. Using an asymptotic method, similar to the Chapman-Enskog method of the kinetic theory of gases or the Krylov-Bogoloyubov averaging method of non-linear mechanics, an equation of steady diffusion is derived for the impurity concentration, averaged over the tube cross-section, which was ob tained by Taylor from physical considerations. Using the asymptotic method a recurrence system of equations is obtained for the expansion terms of arb itrary order. Estimates are made of the applicability of Taylor's model of longitudinal dispersion, which refines the estimated established by Taylor. To extend the limits of applicability of Taylor's model a two-term Bubnov- Galerkin representation is employed for the concentration, averaged over th e tube cross-section, which is now described by a hyperbolic-type telegraph equation. Green's function for this model is obtained, according to which the impurity concentration distribution is characterized by the presence of perturbation fronts with finite propagation velocities. The asymptotic agr eement between Green's function of the hyperbolic model and Green's functio n of the Taylor model is demonstrated. (C) 2000 Elsevier Science Ltd. All r ights reserved.