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The challenge of determining mixing extent of solutions undergoing advective-dispersive-diffusive transport is well known. In particular, reaction extent between displacing and displaced solutes depends on mixing at the pore scale, that is, generally smaller than continuum scale quantification that relies on dispersive fluxes. Here a novel mobile-mobile mass transfer approach is developed to distinguish diffusive mixing from dispersive spreading in one-dimensional transport involving small-scale velocity variations with some correlation, such as occurs in hydrodynamic dispersion, in which short-range ballistic transports give rise to dispersed but not mixed segregation zones, termed here ballisticules. When considering transport of a single solution, this approach distinguishes self-diffusive mixing from spreading, and in the case of displacement of one solution by another, each containing a participant reactant of an irreversible bimolecular reaction, this results in time-delayed diffusive mixing of reactants. The approach generates models for both kinetically controlled and equilibrium irreversible reaction cases, while honoring independently measured reaction rates and dispersivities. The mathematical solution for the equilibrium case is a simple analytical expression. The approach is applied to published experimental data on bimolecular reactions for homogeneous porous media under postasymptotic dispersive conditions with good results.

Plain Language Summary Computer models of the way that chemicals such as contaminants move in pipes, rivers, lakes, estuaries, and in groundwater, are important to science and engineering because this is how we predict water quality. These models also keep track of how the chemicals change due to reactions, and to do so they make big assumptions about how the chemicals mix. Experiments show that the models get the mixing part wrong, and as a result don't do a good job representing which chemicals occur where. This work fixes a part of the mixing error, with a simple fix that works in simple models.