Viscosity of a mixture of soft spheres

Abstract

The viscosity of a 50% mixture of soft spheres (i.e., particles which interact according to the force law $\phi =\frac{d}{r^{12}}$) has been simulated by applying nonequilibrium molecular dynamics to a system of 108 particles. Results for several size (actually $d$) and mass differences are given and compared with the predictions of a conformal-solution Van der Waals 1 theory. To construct this theory, it was necessary to derive a mixing rule for the mass. Overall, agreement between theory and simulation is satisfactory to size differences of about 14% and to mass differences of about 5%. It is pointed out that nonequilibrium molecular dynamics is a powerful technique and appears well suited to this particular application: The simulated viscosity of the mixture can be obtained to within about 5% accuracy for the 108-particle system by applying a shear to the system and following its behavior for about 7000 time steps.