Viscometric effects in a dense hard-sphere fluid

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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 αβ=aδ αxδ βy . In each unit time step Δt, 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 Δt ; in the collision stage, V i → V i − ( σ i · G ij) σ i with probability equal to 4πσ 2Θ( σ i · G ij)χ(n)nΔt , where σ i is a random unit vector, σ is the diameter of the spheres, G ij ≡ V i − V j − σ a · σ i , V j being the velocity of a random partner j, and χ( 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.