Transport properties of polydisperse fluids. I. Shear viscosity of polydisperse hard-sphere fluids

Abstract

The shear viscosity expressions for a polydisperse hard-sphere fluid in both the dilute and dense fluid regions have been obtained as the solution of a set of linear integral equations in the Enskog transport theory. In the monodisperse limit we recover the known Enskog result. Explicit analytical solutions have been obtained for the special case of equal-mass particles. For general mass-size distributions, a simple numerical method has been proposed. Computations have been performed for a mass-size relation of power-law form. The two size distributions we have looked at are the Schulz distribution and the log-normal distribution. It is found that both distributions show similar effects on the shear viscosity. In the dilute-gas region, for each given fractal dimension, there exists a critical variance of the size distribution at which the shear viscosity attains a maximum. In the dense-gas region, the shear viscosity increases as the variance and the density increase except for the low density and the high fractal-dimension region where the shear viscosity attains a minimum at some particular variance. The shear viscosity diverges at a close-packing density that decreases with increasing variance.