On the early development of dispersion in flow through a tube with wall reactions

Abstract

This is a study on numerical simulation of the convection-diffusion transport of a chemical species in steady flow through a small-diameter tube, which is lined with a very thin layer made up of retentive and absorptive materials. The species may be subject to a first-order kinetic reversible phase exchange with the wall material and irreversible absorption into the tube wall. Owing to the velocity shear across the tube section, the chemical species may spread out axially along the tube at a rate much larger than that given by the molecular diffusion; this process is known as dispersion. While the long-time dispersion behavior, well described by the Taylor model, has been extensively studied in the literature, the early development of the dispersion process is by contrast much less investigated. By early development, that means a span of time, after the release of the chemical into the flow, that is shorter than or comparable to the diffusion time scale across the tube section. To understand the early development of the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Flux Corrected Transport Algorithm (FCTA). The computation has enabled us to investigate the combined effects on the early development of the dispersion coefficient due to the reversible and irreversible wall reactions. One of the results is shown that the dispersion coefficient may approach its steady-state limit in a short time under the following conditions: (i) a high value of Damkohler number (say Da ≥ 10); (ii) a small but non-zero value of absorption rate (say Γ* ≤ 0.5).