Pollutant transport in asymmetric velocity distributions influenced by phase exchange kinetics between two parallel plates

This study derives an analytical solution of the two-dimensional concentration distribution of a pollutant in a prismatic channel flow with asymmetric velocity pattern over its cross-section. This study also examines pollutant transport phenomena influenced by both irreversible and reversible reactions, along with the bulk chemical reaction of the pollutant with the channel boundaries and the fluid flows, respectively. The effects of mean and transverse concentration distributions are analyzed under the influence of various parameters, including adsorption, desorption, absorption, the asymmetric velocity distribution parameters (α and β), and the bulk chemical reaction parameter. The transverse concentration distribution up to the second-order approximation is derived using Mei's homogenization technique. Over the past two decades, researchers have emphasized that the Taylor dispersion model primarily predicts the longitudinal dispersion of the mean concentration. However, the study of transverse concentration distribution has gained significant importance due to its relevance in environmental engineering and industrial applications. According to the investigation’s findings, an increase in  α and β  enhances the overall velocity, resulting in a sharper velocity profile when α = β or a more asymmetric profile when α ≠ β . The dispersion coefficient  shows non-monotonic behavior influenced by the velocity parameters   α and β . Smaller   α and β  yield moderate velocity gradients and weaker shear, reducing dispersion. As   α and β  increase, sharper or asymmetric velocity profiles enhance shear effects, increasing dispersion. The mean concentration of the pollutant decreases with increasing   α and β  in both cases, but the decrease is more gradual in the asymmetric case. Increasing bed absorption and bulk chemical reaction parameters significantly reduces the transverse concentration, while increasing adsorption or desorption parameters raises the transverse concentration. Adsorption and desorption reactions at the boundaries reduce transverse concentration variation in both symmetric and asymmetric cases. The variation decreases with increased reaction rates, with slight non-uniformity observed when α ≠ β. The findings are crucial for enhancing natural stream quality, reducing pollution, and mitigating the effects of reactions.