Study of the key factors affecting the dispersion of dust particles in the atmosphere

Abstract

A mathematical model has been developed to provide a more accurate description of atmospheric dust particle transport. Unlike most existing models that assume the particle velocity matches the wind speed, this work considers the case where particles possess inertia and their velocity differs from the flow velocity. The equations of motion are derived from Newton’s second law, accounting for the Stokes drag force, ambient air flow, and gravity. A three-stage numerical algorithm based on the second-order backward differentiation formula (BDF2) with an initial Crank–Nicolson startup substep is constructed, ensuring second-order accuracy; the convergence rate observed in computational experiments was approximately two. The motion dynamics of three typical categories of dust particles – ????????2.5, ????????10, and coarse particles (50 ????m) – were investigated across various wind speeds and release heights. Relaxation times, terminal settling velocities, horizontal transport ranges, and trajectory inclination angles were determined. The results demonstrate that inertial lag causes particles to lag behind the air flow, with the relative error of the simplified model reaching its maximum immediately after release and decaying as velocities equalize, whereas for ????????2.5 and ????????10 particles, this simplification has virtually no effect on the outcome. Practical recommendations are formulated for applying the model to construction dust monitoring, industrial emission forecasting, and urban air quality management.