Interaction Law for a Collision Between Two Solid Particles in a Viscous Liquid

Citation

Yang, Fu-Ling (2006) Interaction Law for a Collision Between Two Solid Particles in a Viscous Liquid. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/VFD0-C413. https://resolver.caltech.edu/CaltechETD:etd-05262006-120244

Abstract

This thesis addresses the problem of inter-particle collisions in a viscous liquid. Experimental measurements were made on normal and oblique collisions between identical and dissimilar pairs of solid spheres. The experimental evidence supports the hypothesis that the normal and the tangential component of motions are decoupled during a rapid collision.

The relative particle motion in the normal direction is crucial to an immersed collision process and can be characterized by an effective coefficient of restitution and a binary Stokes number. The effective coefficient of restitution monotonically decreases with a diminishing binary Stokes number, indicating a particle motion with less inertia and higher hindering fluid forces. The correlation between the two parameters exhibits a similar trend to what is observed in a sphere-wall collision, which motivates a theoretical modeling.

The collision model developed in the current work includes a flow model and a revised rebound scheme. The flow model considers the steady viscous drag, the added mass force, and the history force. How the presence of a second nearby solid boundary affects these forces is investigated. A flow model is proposed with wall-correction terms and is used to predict an immersed pendulum motion toward a solid wall. General agreement with the available experimental data validates the model. The rebound scheme considers the magnitude of the surface roughness and the minimum distance of approach resuling from an elastohydrodynamic contact.

The performance of the collision model in predicting the effective coefficient of restitution is evaluated through comparisons with experimental measurements and an existing elastohydrodynamic collision model that the current work is based on.

Based on the current experimental findings, the tangential component of motion can be described by a dry collision model, provided that the material parameters are properly modified for the interstitial liquid. Two pertinent parameters are the normal effective coefficient of restitution and an effective friction coefficient.

Thesis Files