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