On the collision of rigid spheres in a weakly compressible fluid

Reliable representations for the interparticular collision laws for inertially dominated particulate flows remain elusive due to the complexity of this interaction. In this study, compressibility of both the solid and the containing fluid are considered in the context of pairwise collisions, and the conditions under which these are important are identified in terms of a regime map. To identify the suspension flow conditions under which compressibility effects are important, the map is presented in terms of granular flow quantities, which are derived from the parameters associated with the pairwise collision problem. After demonstrating that there exists a flow regime where the compressibility of the fluid is important, the collision of two rigid spherical particles in a weakly compressible fluid is investigated. Lubrication theory and a perturbation approach for the fluid density are applied to analytically determine the pressure correction due to weak fluid compressibility. It is shown that the first-order dynamical equation describing the collision process does not support rebounding particle trajectories, therefore characterizing rebound as an inherently nonlinear compressibility effect. © 1992 American Institute of Physics.