A modified kinetic theory for frictional granular flows in dense and dilute regimes

Continuum modeling of granular and gas-solid flows generally involves the use of a kinetic-theory (KT) model for the particulate phase, and the most widely used KT models have been derived for dilute flows of smooth, frictionless spheres. In reality, however, granular particles are frictional and can achieve dense packing, and these features must be taken into account to improve rheological predictions in these flow scenarios. Existing approaches in the literature for producing closed-form KT-based models employ empirical modifications to adapt the original models for use in dense and frictional systems. In this article, we investigate the capacity for such modifications to improve the rheological predictions of the Garzó-Dufty (GD) KT model [V. Garzó and J. W. Dufty, "Dense fluid transport for inelastic hard spheres," Phys. Rev. E59, 5895-5911 (1999)]10.1103/PhysRevE.59.5895. On the basis of molecular dynamics simulations of homogeneous, simple shear flows of soft, frictional spheres, we propose a new expression for the radial distribution function at contact as well as modifications to the GD expressions for shear stress and energy dissipation rate. These changes account for dense-regime scalings observed in inertial-number models as well as the effects of interparticle friction while preserving the dynamic nature of the KT model.