An asymptotic theory for dispersion of reactive contaminants in parallel flow

Abstract

The classic problem, first treated by Taylor [18], of the dispersion of inert soluble matter in fluid flow continues to attract attention from researchers describing the approach to the asymptotic state [5, 17]. The present article considers some of the complications caused when the solute is chemically active, Dispersing chemically active solutes occur in diverse fields such as chromatography, chemical engineering and environmental fluid mechanics.The asymptotic large-time analysis of Chatwin [5] is re-worked to handle the case of reactive solutes dispersing in parallel flow. Matching between moderate and large-time solutions requires consideration of the integral moments of the reactive contaminant could, and the Aris method of moments is therefore invoked and modified for reaction effects. The results are applied in detail to the outstanding paractical example—the chemical flow reactor (a device used to measure reaction rates for chemical reactions taking place between fluids). For this case, the paper provides a practical alternative to recent variable diffusion coefficient studies [6, 7, 15], and presents further results for the concentration distribution and for the limiting behaviour under weak and vigorous recactions at the boundary of the flow.