Transport of pollutant in a channel flow under the influence of homogeneous and inhomogeneous reactions

This paper presents an analytical study that explores the two-dimensional concentration distribution of a pollutant in a fluid flowing with an asymmetric velocity profile across the channel cross-section. The pollutant may undergo first-order homogeneous and inhomogeneous reactions within the flowing fluid and channel boundaries, respectively. This work utilizes Mei's multiscale homogenization technique to derive analytical expressions for the mean and transverse concentration distribution up to the third-order approximations. The study also examines the impact of flow and reaction parameters on pollutant distribution. Results reveal that as the asymmetric velocity parameter decreases, dispersion increases and consequently reduces mean concentration. The concentration of the pollutant cloud decreases due to increased inhomogeneous reactions. Moreover, it is observed that inhomogeneous reactions introduce non-uniformity in the transverse concentration distribution, while in the absence of such reactions, the distribution remains uniform. The asymmetric velocity parameter indirectly impacts concentration variation by shifting the location of peak variation downstream or upstream. Inhomogeneous reactions notably reduce the peak of transverse concentration variation by increasing the homogeneous reaction. The results are vital as they can improve the natural stream quality, decrease pollution, and alleviate the influence of homogeneous reactions.