An Experimental and Numerical Study of Normal Particle Collisions in a Viscous Liquid

When two solid bodies collide in a liquid environment, the collision process is influenced by viscous effects and the increased pressure in the interstitial liquid layer between the two solid boundaries. A normal collision process is investigated for a range of impact Stokes numbers using both experimental and numerical methods. Experiments of a steel sphere falling under gravity and colliding with a Zerodur wall with Stokes number ranging from 5 to 100 are performed, which complement previous investigations of immersed particle-wall collision processes. The incompressible Navier-Stokes equations are solved numerically to predict the coupled motion of the falling particle and the surrounding fluid as the particle impacts and rebounds from the planar wall. The numerical method is validated by comparing the numerical simulations of a settling sphere with experimental measurements of the sphere trajectory and the accompanying flow-field. A contact model of the liquid-solid and solid-solid interaction is developed that incorporates the elasticity of the solids to permit the rebound trajectory to be simulated accurately. The contact model is applied when the particle is sufficiently close to the wall that it becomes difficult to resolve the thin lubrication layer. The model is calibrated with measured particle trajectories and is found to represent well the observed coefficient of restitution over a range of impact Stokes numbers from 1 to 1000. In addition, the model is modified to simulate the normal collision of two spheres. The effective coefficient of restitution obtained from the simulation shows a strong dependence on the binary Stokes number accordant with other researcher's experimental results. The unique behaviors of the two spheres at low binary Stokes number including target motion prior to contact and group motion after collision are simulated by the current work.