Applicability of constitutive relations from kinetic theory for dense granular flows

The applicability of constitutive models based on kinetic theory for dense granular flows is examined. First, we calculate the average coordination number of a particle in a dense flow down an inclined plane using discrete element simulations that employ a linear spring-dashpot model for particle interactions. It is found that the average coordination number decreases as the spring constant increases at constant coefficient of restitution, and is less than 1 for the values of spring constant corresponding to materials such as sand and glass beads. The Bagnold coefficients, which are the ratios of the different components of the stress and the square of the strain rate, are calculated using both discrete element (DE) simulations and event driven (ED) simulations; collisions are considered to be instantaneous in the latter simulations. It is found that the theoretical predictions of the Bagnold coefficients are in quantitative agreement with both DE and ED simulations provided the pair distribution function obtained from the simulations is inserted into the theory. However, it is found that the pair distribution function in a sheared granular flow is significantly larger than that in an equilibrium fluid of elastic particles.