The rheology of dense, polydisperse granular fluids under shear

TL;DR

This paper develops a generalized moment method to solve the Enskog equation for dense, polydisperse granular fluids under shear, accurately predicting bulk properties but less so temperature distributions.

Contribution

It introduces a novel generating function technique for the Grad moment method, improving accuracy in modeling dense, inelastic granular mixtures under shear.

Findings

Enskog theory accurately predicts pressure and viscosity.

Generalized moment method outperforms simple Grad method.

Temperature distribution predictions are less accurate.

Abstract

The solution of the Enskog equation for the one-body velocity distribution of a moderately dense, arbitrary mixture of inelastic hard spheres undergoing planar shear flow is described. A generalization of the Grad moment method, implemented by means of a novel generating function technique, is used so as to avoid any assumptions concerning the size of the shear rate. The result is illustrated by using it to calculate the pressure, normal stresses and shear viscosity of a model polydisperse granular fluid in which grain size, mass and coefficient of restitution varies amoungst the grains. The results are compared to a numerical solution of the Enskog equation as well as molecular dynamics simulations. Most bulk properties are well described by the Enskog theory and it is shown that the generalized moment method is more accurate than the simple (Grad) moment method. However, the description of the distribution of temperatures in the mixture predicted by Enskog theory does not compare well to simulation, even at relatively modest densities.