Here we present and benchmark an analytical model to describe the radial extent of erosion of settled particle beds by radial wall jets as a function of time. The extent of erosion is an essential measure of the performance of vessels mixed by arrays of radial wall jets because portions of vessel floors not cleared of settled particles may accumulate undesirable constituents. We derive a model of the cleared radius as a function of time scaled so that fits may be described using only two free parameters. We find remarkably good agreement between experimental data and the model upon fitting. Extracted fitting parameters are shown to be reasonable. The influence of nozzle transience on erosion transience has also been evaluated. We find that nozzle transience explains the initially slower rate of erosion and decreases the final extent of erosion by one to three nozzle diameters for the cases considered. Future work remains to evaluate the dimensionless groups from conservation laws and account for vessel curvature.

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