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Recirculation zones (RZs) are common in many geophysical flows. These zones form near irregular solid boundaries and are separate from the main flow. Since mass can be trapped and later released locally from RZs, bulk transport can exhibit long tailsan anomalous behavior that is challenging to predict. The underlying RZ mass transfer and retention in this situation is poorly understood despite common parameterization by effective exchange coefficients in mobile-immobile (MIM) domain models. We analyzed the mass transfer process using computationally resolved flow and transport fields inside two-dimensional rough fractures. RZs were delineated by a novel technique followed by quantification of mass transfer across the interface with the main flow zone. The results showed that the first-order mass transfer coefficient is a function of Reynolds number and velocity difference between the RZ and bulk flow. A distributed mobile-immobile model with the directly estimated parameters accurately reproduced bulk anomalous transport. While the distributed mobile-immobile model is not yet predictive, its development showed that mass transfer coefficients for flows involving RZs are physically meaningful, potentially predictable, and useful for elucidating local mass transfer processes within the general framework of mobile-immobile transport modeling.

Plain Language Summary Mass transfer between a slow-flowing zone and a recirculation zone is a process found in many environmental and engineered settings. When present, these zones can substantially delay solute transport taking place in the moving bulk fluid. This usually results in the tailing of solutes, typically referred to as anomalous transport. By assuming that solute transport is diffusion-driven in the stagnant (immobile) region and advection-diffusion driven in the main flow (mobile) region, a classic mobile-immobile theory was developed and has been widely adopted to model this anomalous transport, despite loose physical background for its parameters. In this study, we present directly the mass transfer process at the interface between recirculation zone and its adjacent main flow channel. Recirculation zone volumes and mass transfer coefficients between recirculation zone and bulk flow were quantified and parameterized via an automated detection approach. This information was then fed into a parameterized distributed mobile-immobile domain transport model. The critical role of the local recirculation zones has been elucidated in capturing anomalous transport. The approaches and results in this study will be of interest to geoscientists and engineers who focus on the flow and transport phenomena in different geophysical settings with immobile zones.