Dispersion of reacting settling particles in ice-covered channels: transient behaviour and asymptotic analysis

Abstract

This study investigates the dispersion of reacting fine settling particles in ice-covered channels, considering both laminar and turbulent flow regimes. The concentration distribution and transport dynamics of fine settling particles are analysed by incorporating the combined effects of settling velocity and reaction rate. Unlike previous studies, this work extends Mei’s multiscale homogenization approach to incorporate the effect of settling velocity on long time dispersion. The transient behaviour of the transport process, including advection, dispersion, skewness, kurtosis and concentration distribution, is analysed using Aris’s method of moments. In addition, an implicit finite-difference scheme is employed to validate the analytical results, demonstrating good agreement. The present results predict that increasing the reaction rate reduces the total mass in the flow, while the dispersion characteristics remain unaffected. An increase in particle settling velocity enhances upstream movement in both laminar and turbulent flows. However, this effect is predicted to be more pronounced under turbulent conditions. In the presence of the settling velocity, the particles tend to form a concentrated layer near the channel bed, which can eventually lead to the accumulation of pollutants and sediments. This behaviour poses a serious risk to the aquatic environment. Understanding the dispersion of reacting and settling particles is essential for managing environmental pollution in ice-covered rivers, estuaries and similar systems.