Timothy R. Ginn

Phase exposure‐dependent exchange

Solutes and suspended material often experience delays during exchange between phases one of which may be moving. Consequently transport often exhibits combined effects of advection/dispersion, and delays associated with exchange between phases. Such processes are ubiquitous and include transport in porous/fractured media, watersheds, rivers, forest canopies, urban infrastructure systems, and networks. Upscaling approaches often treat the transport and delay mechanisms together, yielding macroscopic “anomalous transport” models. When interaction with the immobile phase is responsible for the delays, it is not the transport that is anomalous, but the lack of it, due to delays. We model such exchanges with a simple generalization of first-order kinetics completely independent of transport. Specifically, we introduce a remobilization rate coefficient that depends on the time in immobile phase. Memory-function formulations of exchange (with or without transport) can be cast in this framework, and can represent practically all time-nonlocal mass balance models including multirate mass transfer and its equivalent counterparts in the continuous time random walk and time-fractional advection dispersion formalisms, as well as equilibrium exchange. Our model can address delayed single-/multievent remobilizations as in delay-differential equations and periodic remobilizations that may be useful in sediment transport modeling. It is also possible to link delay mechanisms with transport if so desired, or to superpose an additional source of nonlocality through the transport operator. This approach allows for mechanistic characterization of the mass transfer process with measurable parameters, and the full set of processes representable by these generalized kinetics is a new open question.

Revisiting the Analytical Solution Approach to Mixing‐Limited Equilibrium Multicomponent Reactive Transport Using Mixing Ratios: Identification of Basis, Fixing an Error, and Dealing With Multiple Minerals

Multicomponent reactive transport involves the solution of a system ofnon-linear coupled partial differential equations. A number of methods have been developed to simplify the problem. In the case where all reactions are in instantaneous equilibrium and the mineral assemblage is constant in both space and time, de Simoni et al. (2007) provide an analytical solution that separates transport of aqueous components and minerals using scalar dissipation of “mixing ratios” between a number of boundary/initial solutions. In this approach, aqueous speciation is solved in conventional terms of primary and secondary species, and the mineral dissolution/precipitation rate is given in terms of the scalar dissipation and a chemical transformation term, both involving the secondary species associated with the mineral reaction. However, the identification of the secondary species is non-unique, and so it is not clear how to use the approach in general, a problem that is keenly manifest in the case of multiple minerals which may share aqueous ions. We address this problem by developing an approach to identify the secondary species required in the presence of one or multiple minerals. We also remedy a significant error in the de Simoni et al. (2007) approach. The result is a fixed and extended de Simoni et al. (2007) approach that allows construction of analytical solutions to multicomponent equilibrium reactive transport problems in which the mineral assemblage does not change in space or time and where the transport is described by closed-form solutions of the mixing-ratios.