Contributions of Pore‐Scale Mixing and Mechanical Dispersion to Reaction During Active Spreading by Radial Groundwater Flow

Spreading and mixing are complementary processes that promote reaction of two reactive aqueous solutes present in contiguous plumes in groundwater. Spreading reconfigures the plume geometry, elongating the interface between the plumes, while mixing increases the volume of aquifer occupied by each plume, bringing the solute molecules together to react. Since reaction only occurs where the two solute plumes are in contact with each other, local mechanisms that drive flow and transport near the interface between the plumes control the amount of reaction. This work uses local characteristics of the plumes and the flow field near the plume interface to analyze the relative contributions of pore‐scale mixing and mechanical dispersion to instantaneous, irreversible, bimolecular reaction in a homogeneous aquifer with active spreading caused by radial flow from a well. Two solutes are introduced in sequence at the well, creating concentric circular plumes. We allow for incomplete mixing of the solutes in the pore space, by modeling the pore space as a segregated compartment and a mixed compartment with first‐order mass transfer between the two compartments. We develop semi‐analytical expressions for concentrations of the solutes in both compartments. We found that the relative contribution of mechanical dispersion to reaction increases over time and also increases due to increases in the Peclet number, in the relative source concentration of the chasing solute, and in the mass transfer rate from the segregated compartment to the mixed compartment of the pore space.