Incorporation of Velocity-dependent Restitution Coefficient and Particle Surface Friction into Kinetic Theory for Modeling Granular Flow Cooling

TL;DR

This paper enhances kinetic theory for granular flows by incorporating velocity-dependent restitution and surface friction, significantly improving predictions of free cooling in inelastic, frictional granular media under microgravity conditions.

Contribution

The study introduces a modified kinetic theory model that accounts for velocity-dependent restitution and surface friction, improving accuracy in modeling granular flow cooling.

Findings

Modified KT aligns better with experimental data.

Velocity-dependent restitution is crucial for accurate modeling.

Surface friction significantly affects granular cooling predictions.

Abstract

Kinetic theory (KT) has been successfully used to model rapid granular flows in which particle interactions are frictionless and near elastic. However, it fails when particle interactions become frictional and inelastic. For example, the KT is not able to accurately predict the free cooling process of a vibrated granular medium that consists of inelastic frictional particles under microgravity. The main reason that the classical KT fails to model these flows is due to its inability to account for the particle surface friction and its inelastic behavior, which are the two most important factors that need be considered in modeling collisional granular flows. In this study, we have modified the KT model that is able to incorporate these two factors. The inelasticity of a particle is considered by establishing a velocity-dependent expression for the restitution coefficient based on many experimental studies found in the literature, and the particle friction effect is included by using a tangential restitution coefficient that is related to the particle friction coefficient. Theoretical predictions of the free cooling process by the classical KT and the improved KT are compared with the experimental results from a study conducted on an airplane undergoing parabolic flights without the influence of gravity [Y. Grasselli, G. Bossis, and G. Goutallier, EPL (Europhysics Letters) 86, 60007 (2009)]. Our results show that both the velocity- dependent restitution coefficient and the particle surface friction are important in predicting the free cooling process of granular flows; the modified KT model that integrates these two factors is able to improve the simulation results and led to a better agreement with the experimental results.