Convective–diffusive macrotransport processes in the presence of an inhomogeneous volumetric chemical reaction: Perturbation expressions for the effective reaction and transport coefficients in terms of comparable nonreactive properties

Abstract

A systematic perturbation solution scheme is developed for calculating the laterally averaged effective reaction velocity constant K* for a chemically reactive solute undergoing a laterally inhomogeneous chemical reaction within a laterally bounded (but longitudinally unbounded) domain through which the solute is transported by convection and diffusion. This is accomplished by use of a perturbation operator technique which is used to obtain a time-dependent effective reaction velocity constant via a systematic perturbation expansion about the nonreactive, purely convective–diffusive Taylor dispersion state. The generally nonequilibrium initial spatial solute distribution requires use of a ‘‘fictitious’’ macroscale initial condition in the first-order macroscale linear decay law governing the total amount of solute present in the system at any time. This fictitious value differs from the true value of the total amount of solute initially present. Comparison is made between the present formalism and that developed by Wilemski-Fixman and others in the analysis of partially diffusion-controlled reactions of tracer corpuscles and polymers diffusing within laterally unbounded domains (from which convection is absent). An example drawn from this field confirms the viability of the scheme. Perturbative expressions are also derived for the mean tracer velocity vector U* and Taylor dispersion dyadic D* about this mean. The asymptotic expression obtained for the convective contribution to D* explicitly manifests the effect of the inhomogeneous chemical reaction upon this effective transport coefficient.