This study presents an analytical solution of the two-dimensional concentration distribution of a contaminant in a channel with a prismatic cross-section and asymmetric velocity distribution, influenced by reversible and irreversible reactions, along with the bulk chemical reaction. Recent works by Zhan et al. [J. Hydrol. 632, 130855 (2024)] have shown that weak desorption leads to complex transient dispersion behavior in open-channel flows, with a strong dependence on the initial distribution of contaminants and a delayed response compared to tube flows. Similarly, the present study examines contaminant transport in a channel with a prismatic cross-section and asymmetric velocity profile, incorporating reversible adsorption-desorption and irreversible absorption at the boundaries in both fluid and solid phases. Using Mei homogenization, analytical expressions for two-dimensional concentration up to second order are derived, and the influence of key transport parameters on both mean and two-dimensional concentrations is examined. The findings reveal that increasing the velocity parameters ($\alpha , \beta$) sharpens or skews the velocity profile, thus enhancing shear and increasing dispersion. Consequently, the dispersion coefficient $D_T^{*}$ varies nonmonotonically, while the mean concentration consistently decreases. Increased boundary absorption and bulk reaction parameters significantly reduce the two-dimensional concentration, while increasing the adsorption or desorption parameters raises the two-dimensional concentration. Increasing adsorption-desorption at the boundaries increases the two-dimensional concentration variation in both symmetric and asymmetric cases. It causes persistent nonuniformity when $\alpha \ne \beta$, while symmetry ($\alpha =\beta$) leads to uniform concentration profiles over time. The findings are crucial to improving the quality of the natural stream, reducing pollution, and mitigating the effects of reactions.

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• Fluid-particle interactions
• Laminar flows
• Mixing enhancement