Power law scaling in a model for mass shedding dynamics in thin-film particle-laden flows

We propose a model for mass shedding events from a singular shock, known to occur in particle-laden flow. The model involves the regular release of i.i.d. mass clumps from the shock. The mass shedding process serves to prevent nonphysical mass accumulation that otherwise exists in the singular shock model. Such mass shedding has been observed in physical experiments. The mass shedding model leads to interesting dynamics. The basic assumptions are that (a) the speed of the clump is determined by simple lubrication theory (b) coalescence occurs when clumps collide. Statistical variation in the initial amounts of mass shed leads to dynamics that exhibits power law scaling of the mass distribution with respect to distance along the slope. Moreover this scaling is statistically stationary with respect to time. Such behavior is well-documented in classical models for avalanches and sand-piles but has not been observed or studied in slurry flow.