Analytical solution and timescale for transport of reacting solutes in rivers and streams

Abstract

A number of biogeochemical reactions and lateral hydrodynamic mixing affects the transport of solute elements in streams and rivers. The combination of the various mechanisms gives rise to an accumulation of the solute in temporary storage zones and a retardation of solute migration. A new model framework is proposed from which an analytical solution is derived describing the concentration as a function of distance along the stream, depth into storage zones, and time. The model includes the effects of sorption of solutes to suspended solids and bed sediments, a lateral exchange with the storage zones, first‐order reactions, and dilution. The migration velocity is close to the advection velocity of the stream for a short travel distance, but it continuously decreases as the distance increases. The timescale of the process is linearly related to a modified Damköhler number; a dimensionless form of the lateral exchange coefficient. The analytical solution has been verified for two tracer experiments with both a sorbing and a nonreactive tracer and the Cr transport in the Vistula River, Poland. The lateral diffusion coefficient can be tentatively evaluated from the transport of Chernobyl Cs in several European rivers as a special case of the interpretative model. The lateral mixing coefficient varies with stream conditions in the order of 0.1 × 10−6 < Ds < 10 × 10−6 (m2/s).