LAUSR

This study analytically examines solute concentration distribution in open-channel turbulent flows, considering the effects of reversible phase exchange kinetics (adsorption–desorption) and irreversible bed reactions (absorption). Using the multi-scale homogenization method, analytical expressions are derived for different transport coefficients, the mean concentration distribution, and the two-dimensional concentration distribution. Unlike the parabolic eddy vertical diffusivity [Elder, J. Fluid Mech. 5, 544–560 (1959); Guo, Jiang, Chen, Li, Alharbi, and Wakeel, J. Hydrol. 604, 127239 (2022); Wu, Zeng, Li, Gong, Zhan, Jiang, Xu, and Fu, Water Resour. Res. 60, e2024WR037586 (2024)], a more realistic exponential profile [proposed by Absi, Hydrology 8, 126 (2021)] has been chosen in this study. The transport process is modeled as involving two phases: a fluid phase, where the solute is carried by the flow, and a solid or stationary phase, where the solute can be retained on the bed. Adsorption at the bottom boundary allows solute to accumulate in the solid phase, while reversible desorption releases solute particles back into the fluid, enhancing dispersion. Additionally, solute may be depleted at the channel bed due to irreversible bed absorption. The model includes a comprehensive boundary condition at the channel bed, accounting for both solute exchange between the fluid and solid phases and depletion by the bed. Slow phase exchange kinetics lead to extensive solute dispersion, while fast kinetics limit dispersion. Initially, retention at the bottom boundary enhances the dispersion coefficient; however, beyond a certain threshold, it diminishes, leading to a more concentrated zone near the source. The combined effects of reversible and irreversible reactions at the channel bed significantly impact the solute dispersion. This model provides valuable insights into solute transport dynamics, making it useful for environmental management and engineering applications.