Viscometric effects in a dense hard-sphere fluid

A recently proposed Monte Carlo simulation method for the Enskog equation is applied to uniform shear flow. This state is characterized by uniform density n and temperature T and a linear velocity profile: u(r)= a.r, a(alpha beta) = a delta(alpha x)delta(beta y). In each unit time step dt, the peculiar velocities (V-i) of N particles are updated in two stages. In the free streaming stage, the velocity V-i is changed into V-i --> V-i - a.V-i Delta t; in the collision stage, V-i --> V-i - (<(sigma)over cap>(i).g(ij))<(sigma)over cap>(i) with probability equal to 4 pi sigma(2) Theta(<(sigma)over cap>(i).g(ij))(<(sigma)over cap>(i).g(ij))chi(n)n Delta t, where;i, is a random unit vector, a is the diameter of the spheres, g(ij) = V-i - V-j - sigma a.<(sigma)over cap>(i), V-j being the velocity of a random partner j, and chi(n) is the equilibrium pair correlation function at contact. The kinetic and collisional transfer contributions to the pressure tensor are calculated as functions of density. The Navier-Stokes shear viscosity is seen to agree with the theoretical value. Furthermore, the nonlinear Burnett coefficients associated with normal stresses are obtained.