On scalar transport in an oscillatory Couette–Poiseuille flow under the effects of heterogeneous and bulk chemical reactions: A multi-scale approach

Abstract

This research presents an analytical solution to explore a two-dimensional concentration transport of solute in an oscillatory Couette–Poiseuille flow between two parallel plates in the presence of homogeneous and heterogeneous reactions. Mei's homogenization method up to second order approximation is used to find the multi-dimensional concentration distributions, namely, transverse concentration distribution, longitudinal concentration distribution, mean concentration distribution, Taylor dispersion coefficient, and the transverse uniformity simultaneously for three different flow conditions: steady, periodic, and the joint effect of steady and periodic Couette–Poiseuille flow for the first time. The distribution of transverse concentration of solute is studied due to its importance in oil lubrication and industrial applications. The transverse variation rate shows that the introduction of heterogeneous reactions cause transverse non-uniformity, but it is significant to note that homogeneous reaction has no effect on it. Furthermore, the maximum variation rate of the concentration cloud is obtained along the upstream and downstream directions when the boundary absorption is considered at steady and moving plates, respectively. To validate the present analytical model, a comparison is performed with the numerical solution and has achieved an excellent agreement. The outcomes of the present study may be helpful to develop a better understanding of the process of contamination and to prevent the pollution in the flow.