  Granular materials are characterized by large collections of discrete
particles of sizes larger than one micron, where the particle-particle
interactions are significantly more important than the particle-fluid
interactions. These flows can be successfully modeled by the existing Kinetic
Theory (KT) models when they are in the dilute regime with low
particle-particle collision frequencies, yielding results that agree well with
the simulation results of the event-driven hard sphere model or the more
sophisticated soft-sphere Discrete Element Method (DEM). However, these KT
models become less accurate for granular flows with soft particles (low
particle stiffness) at high particle-particle collision frequencies when the
predicted collision interval (the time of free flight for a particle prior to
the next collision) is comparable to the collision duration; there is a large
discrepancy between the results of these KT models and those from the DEM
models. In this work we develop a new KT model that could be used to model
granular systems of high collision frequencies with a finite particle
stiffness. This is done by modifying the fluctuation energy dissipation rate to
incorporate the ratio of collision duration to collision interval, a parameter
that is determined by both the collision frequency and particle stiffness. We
use a linear-spring-dashpot collision scheme to model the elastic potential
energy in the system and to uncover the relationship between the constitutive
relations of KT and the ratio of collision duration to collision interval.
