Transport of reactive chemicals in sediment-laden streams

Abstract

This paper deals with the transport of chemicals in a turbulent stream when both sorbing suspended load and decay reactions are present. These conditions, which can be found quite commonly in rivers, give rise to interesting behaviour. Important and not trivial processes are added and interact with the classical diffusive, advective, and dispersive mechanisms. Due to the sorption process, the chemical divides into an aqueous and a sorbed phase which follow different evolutions: the aqueous phase is regulated by turbulent diffusion, advection and shear, while the sorbed one undergoes the same fluid dynamic mechanisms but through the evolution of suspended sediment, which is also subjected to sedimentation. The evolutions of the two phases are not separate, as the sorption–desorption exchanges between the aqueous and sorbed phases connect their dynamics. In turn, the decay reactions, being able to modify the concentrations in the two phases, influence the sorption process and therefore the entire transport dynamics. A complex picture results where several nonlinear interactions occur. The main objective of the work is to obtain the one-dimensional partial differential equation that describes the temporal and spatial dynamics of the depth-averaged concentration of the chemical. Due to the existence of three well separated time scales in the whole transport process, the mathematical homogenization theory is adopted to average the two-dimensional model, and the most general case is dealt with in which sediment transport is unsteady while the reactions are nonlinear and different for the aqueous and sorbed phases. Finally, some examples of real cases are discussed where the influence of unsteady suspended sediment dynamics and the nonlinearity of reactions is analyzed, while the role of the several nonlinear differential terms in the model is highlighted.