Distribution of Chemicals in Rivers during Contamination and Recovery

Differential equations that describe the fate of chemicals in rivers as they transfer, react, and volatilize, both during contamination and recovery are developed. Explicit analytical solutions are presented for the unsteady distribution of the substance in the aqueous and sediment phases assuming a constant partition coefficient. The solutions are expressed in terms of three parameters, dimensionless distance Z; dimensionless time T; and the conservation index K, which equals 1 for conservative nondegrading substances, and zero for infinitely fast loss or degradation. All three parameters are instrumental in defining limits for important asymptotic cases. Thus, for Z≤0.1, and under all conditions, the river compartmentalizes into sediment and aqueous phases of uniform concentration. T=10 is the minimum time scale for a steady profile to be developed during contamination. During recovery and for values of K≤0.1, the river (of whatever length) again reverts to compartments of uniform concentration.