Shear viscosity for a moderately dense granular binary mixture

摘要

The shear viscosity for a moderately dense granular binary mixture of smoothhard spheres undergoing uniform shear flow is determined. The basis for theanalysis is the Enskog kinetic equation, solved first analytically by theChapman-Enskog method up to first order in the shear rate for unforced systemsas well as for systems driven by a Gaussian thermostat. As in the elastic case,practical evaluation requires a Sonine polynomial approximation. In the leadingorder, we determine the shear viscosity in terms of the control parameters ofthe problem: solid fraction, composition, mass ratio, size ratio andrestitution coefficients. Both kinetic and collisional transfer contributionsto the shear viscosity are considered. To probe the accuracy of theChapman-Enskog results, the Enskog equation is then numerically solved forsystems driven by a Gaussian thermostat by means of an extension to dense gasesof the well-known Direct Simulation Monte Carlo (DSMC) method for dilute gases.The comparison between theory and simulation shows in general an excellentagreement over a wide region of the parameter space.