Assessment of kinetic theories for moderately dense granular binary mixtures: Shear viscosity coefficient

Two different kinetic theories [J. Solsvik and E. Manger (SM-theory), Phys. Fluids \textbf{33}, 043321 (2021) V. Garz\'o, J. W. Dufty, C. M. Hrenya (GDH-theory), Rev. E \textbf{76}, 031303 (2007)] are considered to determine the shear viscosity $\eta$ for a moderately dense granular binary mixture of smooth hard spheres. The is subjected simple flow heated by action an external driving force (Gaussian thermostat) that exactly compensates energy dissipated in collisions. set Enskog equations starting point obtain dependence on control parameters mixture: solid fraction, concentration, mass diameter ratios, coefficients normal restitution. While expression found SM-theory based assumption Maxwellian distributions velocity distribution functions each species, GDH-theory solves equation means Chapman--Enskog method first order rate. To assess accuracy both theories, numerically solved direct simulation Monte Carlo (DSMC) method. carried out under flow, using thermostat cooling effects. Given predicts vanishing contribution viscosity, comparison between theory simulations essentially made at level collisional $\eta_c$ viscosity. results clearly show compares with much better than over wide range values restitution, volume (masses, diameters, concentration).