Transverse concentration distribution in an open channel flow with bed absorption: A multi-scale approach

This study presents an analytical attempt to explore the two-dimensional concentration distribution in an open channel flow. Mei's homogenization technique is used to find the transverse concentration distribution up to third order approximations. It is well known that the Taylor dispersion model only predicts the longitudinal distribution of mean concentration and all the previous studies mostly focused on this. However, the transverse concentration distribution is important from environmental and industrial application view points. This study deduces an analytic solution of two-dimensional concentration distribution for an open channel flow with bed absorption by three-scale perturbation analysis that explores the pattern of scalar and its spreading across the channel under the effect of bed absorption. Results reveal that concentration of solute in the flowing fluid decreases with the increase in bed absorption parameter. It is also found that bed absorption causes large transverse concentration non-uniformity over the channel cross-section, especially in the downstream.