Kinetic model for the hard-sphere fluid and solid

The revised Enskog kinetic theory (RET) for a system of hard spheres provides an exceptionally broad description of mesoscopic and macroscopic dynamics, applicable for both fluid and solid phases, long and short wavelengths, low and high densities, and exact at short times. This gnat potential is compromised by the difficulty of obtaining solutions outside the domain of linear response, In the present work a simpler kinetic model based on the RET is proposed with the same scope of application but accessible to solution for more general states. As a test of this model the rheological properties of a fluid under shear far from equilibrium are calculated as a function of the density and shear rate. Comparisons with Monte Carlo simulations of the RET show excellent agreement for transport properties but some limitations of the model for predicting velocity distributions at large shear rates. The model is discussed critically and its potential for several future applications is noted.