Dispersion in open-channel flow subject to the processes of sorptive exchange on the bottom and air-water exchange on the free surface

Abstract

An analytical study is presented of dispersion in steady and oscillatory open-channel flow under the combined effects due to reversible sorptive phase exchange with the bed and irreversible air-water exchange on the free surface. The free-surface reaction is assumed to be so weak that the asymptotic mean concentration can be developed well before undue substantial loss to the air occurs. The effective advection-dispersion transport equation, which is derived using a multiple-scale homogenization technique, contains formal expressions for the various components of the dispersion coefficient arising from the two chemical effects. Numerical calculations demonstrate that, as long as the bed is sorbing, the kinetics of the sorptive exchange plays a key role in controlling the overall dispersion mechanism. The otherwise weak effects of the free-surface loss can be significantly enhanced by the presence of kinetic phase exchange on the bottom.