Transient storage model: the impact of temporally varying reaction rate

The transient storage model (TSM) has been widely used to interpret solute transport in river corridors. Its key components are a mobile domain, representing the main channel, and an immobile domain, accounting for solute storage within the hyporheic zone, where biogeochemical transformations are known to occur. In this study, we consider a reactive immobile compartment characterized by a linear reaction whose rate fluctuates over time. We systematically explore combinations of characteristic storage times, reaction-rate fluctuation periods, and the relative importance of advection and dispersion in the mobile domain to identify the regimes in which temporal fluctuations exert a significant control on solute dynamics. Furthermore, we derive a semi-analytical expression for the effective reactivity of the river corridor, highlighting deviations from the classical scenario assuming a time-invariant reaction rate in the immobile domain.