Reactive transport in channel flows with bed adsorption and desorption

Researches on the solute dispersion process with adsorption and desorption at boundaries are common in various fields, such as chemistry, biology and hydraulics. However, the Laplace transform as an available method for the adsorption-desorption boundary conditions, is complicated and difficult to apply. Recently, Jiang et al. (J. Fluid Mech., vol. 947, 2022, A37) proposed a much simpler analytical method based on the classic framework of separation of variables to derive solutions of concentration moments for a tube flow, which is valid for the entire range of the reactive transport process. The key of this approach is to solve the eigenvalue problem for the bulk and surface concentration distributions with the adsorption-desorption boundary conditions. Compared with the Laplace transform method, this new method can effectively avoid the complexity caused by the inverse Laplace Transform. Here we apply this simple approach to solute transport in channel flows with bed adsorption and desorption. We investigate the effect of adsorption-desorption on the dispersion process, and the influence of initial conditions on the non-uniformity of dispersion characteristics over the cross-section before the Taylor dispersion regime.