Convective diffusion in steady flow through a tube with a retentive and absorptive wall

Abstract

This is a study on the mass transport, accomplished by reaction, advection, and dispersion, of a solute in steady Poiseuille flow through a circular tube with a reactive wall layer. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer and an irreversible component due to absorption into the wall. First, the generalized dispersion model is employed to deduce asymptotic steady-state values of the first three transport coefficients in terms of the strengths and kinetics of the two reactions, which can be of any magnitude. Second, a numerical simulation is performed to examine the time development of the fluid- and wall-phase concentration profiles starting from the initial release of the solute into the tube. The analytical deduction brings out not only results relevant to the asymptotic state when the transport coefficients become independent of time but also criteria that can be used to estimate the significance of the asymptotic steady state in the whole course of mass transport. The numerical simulation generates time-developing concentration profiles that can be used to explain some paradoxical behaviors exhibited by the transport coefficients under certain conditions.