On the solute dispersion in a pipe of annular cross-section with absorption boundary

Abstract

The paper presents the longitudinal dispersion of passive tracer molecules released in a steady laminar flow through an annular pipe with heterogeneous reaction at the outer wall, which causes a depletion of contaminant in the flow. A finite-difference implicit scheme has been adopted to solve the unsteady advection-diffusion equation for all time period. Here, it is shown how the spreading of tracers is influenced by the shear flow, the aspect ratio (the ratio of the inner radius to the outer radius of the annular pipe), and the absorption parameter at the outer wall. The solute disperses in the annular region due to the interaction between advection and transverse diffusion. Three stages of longitudinal dispersion with time, named as diffusive regime, anomalous regime, and Taylor's regime observed for Poiseuille flow, are discussed for an annular pipe with absorption boundary. The axial distributions of mean concentration are determined from the first four central moments using Hermite polynomial representation. The results of this study are likely to be of interest for understanding the interaction between flow and dispersion in a catheterized artery with conductive walls.