Dynamic behavior of collision of elastic spheres in viscous fluids

Abstract

The dynamic behavior of the collision of two elastic spheres in a stagnant viscous fluid is investigated in this study for particle Reynolds numbers ranging from 5 to 300. The interactive behavior of these particles is examined both experimentally and theoretically. Specifically, the trajectory and velocity of a moving particle in collinear and oblique collisions with a fixed particle are measured using a high speed video system and an Infinity lens. The lattice-Boltzmann (LB) simulation is conducted to obtain the detailed three-dimensional flow field and the forces around the particles during the course of collision. Furthermore, a mechanistic model is developed which accounts for four stages of collision processes, including: (1) immediately before the collision, (2) compression during the collision, (3) rebound during the collision, and (4) immediately after the collision. The LB simulation and experimental results lead to an empirical expression for the drag force on the particle during the close-range particle–particle interaction. This close-range interaction between two approaching particles is taken into account in the equation of motion of the particle. The pressure force and added mass force are derived, based on collisions in inviscid fluids, as a function of separation distance. Results of the LB simulation and prediction by the mechanistic model are in good agreement with the experimental results. The viscous effects on the compression and rebound processes of colliding particles with regard to the elasticity properties of the particle are examined. The studies are also conducted for simulation based on a hard sphere model, which is commonly used in accounting for the particle collision behavior in gas. The study concludes that the key to proper quantification of the particle collision characteristics in liquid is the ability to accurately predict the particle velocity upon contact.