On the Early Development of Dispersion in Flow Through a Tube with Wall Reactions

This dissertation, "On the Early Development of Dispersion in Flow Through a Tube With Wall Reactions" by Mei-wan, Lau, 劉美雲, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled On the Early Development of Dispersion in Flow through a Tube with Wall Reactions Submitted by Mei-wan, Lau for the Degree of Master of Philosophy at The University of Hong Kong in September 2007 The aim of this thesis is to study the convection-diffusion transport of chemical species in steady flow through a small-diameter tube lined with a very thin layer made up of a retentive and absorptive material. The species may be subject to a first-order kinetic reversible phase exchange with the wall and irreversible absorption into the 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, which is well described by the Taylor model, has been extensively studied in the literature, the early development of the dispersion process has so far received little attention. Short-time dispersion refers to 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. i The study found that, during the initial development, the radial variation of the concentration was as significant as the axial variation, and that therefore the transport was essentially two-dimensional. The early-time dispersion problem, therefore, is not amenable to the same analytical approach that can be applied to the long-time problem, namely modeling a one-dimensional transport in terms of the section-averaged concentration. It has to be solved numerically. A numerical algorithm, known as the Flux-Corrected Transport Algorithm (FCTA) was adopted in this study to solve the present short-time dispersion problem. The FCTA is a scheme that applies artificial diffusion to the numerical solution of convection-diffusion problems. This method can give accurate numerical solutions for the transport of a slug when convection dominates, as in the present problem. In order to understand the behavior of the early phases of dispersion due to convection and diffusion in steady flow along a tube, numerical simulations were generated following the sequence (i) different forms of initial slugs in flow with no wall reactions, (ii) flow with reversible wall retention only, (iii) ii flow with irreversible wall absorption only, and (iv) flow with coupled effects of both wall reactions. We present the numerical results in the forms of mean breakthrough curves, snapshots of the axial distribution of the mobile-phase concentration at different times, and the first three spatial moments of the distribution as functions of time. We show that the dispersion coefficient may approach its steady-state limit in a short time if the Damkohler number is high enough or the absorption rate is small but non-zero. The study should help to enhance the understanding of short-time dispersion behavior and the transport coefficients as functions of the wall reaction parameters. The detailed numerical work presented in this thesis fills a theoretical gap in the linking of short-time and long-time dispersions. iii DOI: 10.5353/th_b3899485 Subjects: Dispersion - Mathematical models Fluid dynamics