Reaction and Anomalous Transport: Effective Reaction Rate Coefficients from the Multirate Model

One cause of anomalous transport is a distribution of exchange rates between fast- and slow-moving water. Slow-moving water is frequently the preferred location of the most significant reactions, such as in biofilms. We express transport and reaction using the multirate model and we assume first-order reaction from parent to daughter. In this case, the effective rate coefficient can be expressed λ _a = int_0^{infty } frac{alpha p(alpha) λ }{alpha +λ } dalpha where alpha is the mass transfer rate coefficient, ⪉mda is the reaction rate coefficient, and p(alpha) is the density function of mass transfer rate coefficients in the multirate model. Exchange rates much slower than ⪉mda contribute relatively little to the effective rate coefficient, while exchange rates similar to or faster than ⪉mda contribute most to the effective rate coefficient. Consequently, a conservative solute may experience anomalous transport, but a reacting solute may exhibit behavior that is not significantly different from Fickian transport with reaction.