Multi-scale approach to analyze the dispersion of solute under the influence of homogeneous and inhomogeneous reactions through a channel

The present study deduces an analytical solution to explore a two dimensional transport of solute concentration in a fluid flowing between two parallel plates in appearance of a homogeneous and first order inhomogeneous reactions. Mei's homogenization method is used to get the transverse concentration distribution up to third order approximation. Taylor dispersion model can only predict the longitudinal dispersion of mean concentration and this fact mainly focused by many researchers over the last two decades. Nowadays, due to its importance in environmental engineering and industrial applications, the spread of transverse concentration is quite significant. The outcomes of the investigation reveal that the Taylor dispersion coefficient decreases with the enhancement of both the homogeneous and inhomogeneous reactions. It is found that the reaction rates cause transverse non-uniformity of the solute cloud. However, the centroid of the concentration cloud moves when the inhomogeneous reaction is applied at any one or both of the channel plates. Interestingly, the centroid gradually shifts towards the upstream direction whenever reaction is taken at both the walls.