Mixing, entropy and reactive solute transport

Mixing processes significantly affect reactive solute transport in fluids. For example, contaminant degradation in environmental aquatic systems can be limited either by the availability of one or more reactants, brought into contact by physical mixing, or by the kinetics of the (bio)chemical transformations. Appropriate metrics are needed to accurately quantify the interplay between mixing and reactive processes. The exponential of the Shannon entropy of the concentration probability distribution has been proposed and applied to quantify the dilution of conservative solutes either in a given volume (dilution index) or in a given water flux (flux-related dilution index). In this work we derive the transport equation for the entropy of a reactive solute. Adopting a flux-related framework, we show that the degree of uniformity of the solute mass flux distribution for a reactive species and its rate of change are informative measures of physical and (bio)chemical processes and their complex interaction. Citation: Chiogna, G., D. L. Hochstetler, A. Bellin, P. K. Kitanidis, and M. Rolle (2012), Mixing, entropy and reactive solute transport, Geophys. Res. Lett., 39, L20405, doi:10.1029/2012GL053295.