A mathematical model is advanced to simulate dynamically and spatially varied shallow water flow and soil detachment, transport, and deposition in rills. The model mimics the dynamic process of rill evolution, including variable rates of sediment redistribution along the bed and changes in local bed morphology. The sediment source term in the model uses a point scale, probabilistic relationship based on turbulent flow mechanics and a recently developed sediment transport relationship for rills based on stream power. The interdependent feedback loops between channel bed morphology, local flow hydraulics, and local scour and deposition, within the framework of the full hydrodynamic equations with inertial terms, constitute a mathematical model with the capacity to represent spatial variability and temporal evolution of the rill. Finite elements were applied to numerically solve the hydrodynamic and sediment continuity equations. A series of laboratory flume experiments were performed to evaluate the model. Initial bed slopes were 3, 5, and 7% with step increases of water inflow rates of 7.6, 11.4, and 15.2 L min−1. The soil material used in the flume was a kaolinitic, sandy‐clay loam. The rill model equations were solved for increasingly complex cases of spatial and temporal variabilities. The model followed measured patterns of morphological changes as the rill evolved, which suggests that the feedback loops in the model between erosion, bed morphological changes, and hydraulics were adequate to capture the essence of rill evolution.

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Although ion-exchange resins have been used widely as drug delivery systems, their exact release kinetics has not been reported yet. Usually only the rate-limiting step has been taken into account and the rest of the steps have been ignored as instantaneous processes. To investigate the exact release kinetics of polymer-coated drug/ion-exchange resin complexes for sustained drug delivery, the results of new mathematical modeling were compared with experimental results. Drug/resin complexes with a model drug, dextromethorphan, were prepared and used as cores for fluid-bed coating. An aqueous colloidal dispersion of poly(vinyl acetate) was applied for the coating. A comprehensive mathematical model was developed using a mechanistic approach by considering diffusion, swelling, and ion-exchange processes solved by numerical techniques. The rate-limiting factor of the uncoated resin particles was diffusion through the core matrix. Similarly, in the coated particles the rate-limiting factor was diffusion through the coating membrane. The mathematical model has captured the phenomena observed during experimental evaluations and the release dynamics from uncoated and coated (at different coat levels) particles were predicted accurately (maximum RMSE 2.4%). The mathematical model is a useful tool to theoretically evaluate the drug release properties from coated ion-exchange complexes thus can be used for design purposes.

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