The effect of relative position on the motion and interactions of particle sedimentation under gravity in a finite-width vertical channel

Understanding the settling behaviour of particles and the interactions between fluid and particles in channelled fluids is crucial for various natural and industrial processes. The research presented in this study focuses on elucidating the sedimentation modes of dual particles within finite-width channels, employing the Arbitrary Lagrangian-Eulerian (ALE) method in conjunction with Hertz contact theory. We aim to understand how the initial relative position affects the dynamic characteristics of particle settlement. The threshold values of α = 35° and gap ratio (the distance between particles relative to their diameter) L/D = 3.5 are deemed critical. The phenomenon of particles ‘kissing’ does not manifest when the initial angle α ≤ 35°. As the α increases, the DKT (Drafting-Kissing-Tumbling) process recurs at earlier stage. In all cases where dual-particle are arranged in a vertically aligned pattern (DP1 = DP2 or DP1> DP2), the settling behaviour of particles will eventually achieve a steady state characterized by the DKT process when L/D ≤ 4.0. As the gap ratio (L/D) increases, the time taken for the kissing phenomenon is prolonged. Additionally, the two particles exchange positions and the larger particle taking the lead in the settling process. In scenarios where dual particles are arranged side by side, the kissing phenomenon does not occur. Instead, the trajectory of the particles deviates from the centreline and shifts towards the channel wall due to the Magnus effect when L/D ≤ 2.0. When L/D ≥ 3.0, particles settle as though they were a single particle. In cases involving multiple particles, the hindering effect of the wall becomes significant and can not be ignored, leading to the observation of Rayleigh-Taylor instability development. As a result, the overall settlement pattern tends to be ‘concave’.