Exponential decay of shear-driven surface erosion in confined abrasive swirling flow

Motivated by near-wall transport and flow-assisted surface evolution in particle-laden confined flows, this study examines the time-dependent decay of shear-driven surface erosion in a rotational abrasive flow configuration. Conventional formulations often treat the erosion rate as linear in time and thereby neglect the feedback between evolving boundary morphology and local near-wall transport. Here, we formulate a physics-informed exponential decay model by treating removable surface asperities as a gradually depleted population of effective erosion sites. In this interpretation, the measured decay of erosion rate is linked to the progressive weakening of morphology-induced transport enhancement as the surface smoothens. Experiments on a confined swirling abrasive flow platform show that both the instantaneous erosion rate and the boundary roughness decrease approximately exponentially with time. Least-squares fitting of the erosion rate gives R2 = 0.99, and the predicted erosion height agrees with experiments within 9.0 ± 1.5% relative error. The measurements also suggest three successive stages (stages I, II, and III): rapid initial removal of prominent defects, a smoother shear-dominated stage with reduced erosion efficiency, and a late stage in which prolonged interaction no longer improves the surface. The results provide a compact fluid-mechanical framework for interpreting transient surface evolution in shear-driven particle-laden flows beyond a process-specific time-correction formula.