A mathematical model of the erosion process in a channel bend

We develop a mathematical model for the cumulative erosion of a micro-particle in a channel system. At 90∘ bends in the system, a particle may deviate from the flow, impact the wall, and erode material. We highlight the case of the eroded material adhering to the particle, growing in size, and thus imgdemonstrate how the damage accumulates exponentially with time. We describe and quantify the statistical nature of the evolution of particle growth and erosion (mass and location). We perform this analysis according to a number of realistic particle concentration distributions: uniform, Gaussian, and bimodal. A bimodal distribution, corresponding to the tubular pinch effect in suspension flows, results in unequal peak zones of erosion due to the flow characteristics.