Extended hard-sphere model and collisions of cohesive particles.

In two earlier papers the present authors modified a standard hard-sphere particle-wall and particle-particle collision model to account for the presence of adhesive or cohesive interaction between the colliding particles: the problem is of importance for modeling particle-fluid flow using the Lagrangian approach. This technique, which involves a direct numerical simulation of such flows, is gaining increasing popularity for simulating, e.g., dust transport, flows of nanofluids and grains in planetary rings. The main objective of the previous papers was to formally extend the impulse-based hard-sphere model, while suggestions for quantifications of the adhesive or cohesive interaction were made. This present paper gives an improved quantification of the adhesive and cohesive interactions for use in the extended hard-sphere model for cases where the surfaces of the colliding bodies are "dry," e.g., there is no liquid-bridge formation between the colliding bodies. This quantification is based on the Johnson-Kendall-Roberts (JKR) analysis of collision dynamics but includes, in addition, dissipative forces using a soft-sphere modeling technique. In this way the cohesive impulse, required for the hard-sphere model, is calculated together with other parameters, namely the collision duration and the restitution coefficient. Finally a dimensional analysis technique is applied to fit an analytical expression to the results for the cohesive impulse that can be used in the extended hard-sphere model. At the end of the paper we show some simulation results in order to illustrate the model.