Transient dispersion of a reactive solute in an oscillatory Couette flow through an anisotropic porous medium

Abstract

This research discusses the significance of reactive solute dispersion relevant to ecological, biological, and geological contexts. It examines solute movement under oscillatory Couette flow through anisotropic porous media between parallel plates under the effect of heterogeneous boundary reactions. The flow is driven by the combined effect of upper plate oscillation in its plane and time-dependent pressure gradient. The lower plate is assumed rough, which introduces slip velocity. A semi-analytical approach, with the method of moments and finite difference scheme, is utilized to explore the transient dispersion in steady and oscillatory flows with or without a non-zero mean. Using the Hermite polynomial, the mean concentration for purely oscillatory and combined flow is obtained, highlighting notable variations based on flow factors. The results suggest that increment in anisotropic angle ϕ reduces dispersion and enhances mean concentration for permeability ratio K < 1, but this reverses for K > 1. Three dispersion phases emerge: diffusive, anomalous, and Taylor's regimes. Gaussian cloud distribution occurs at small and large times, with intermediate stages displaying anomalous dispersion and asymmetric longitudinal distribution. Effects of boundary absorption stabilize over time. The research focuses on the practical significance of different permeabilities of porous media, emphasizing applications of anisotropic porous media in fields such as chemical engineering and industrial processes.