Constitutive theory for homogeneous granular shear flows of highly inelastic spheres

A constitutive theory is developed in this present steady, homogeneous, granular shear flows of identical, smooth and highly inelastic spheres. The important mean fields in these flows are the solid fraction, mean velocity and full second moment of fluctuation velocity. The constitutive theory, which consists of the pressure tensor and the collisional source of second moment, is based upon an anisotropic Maxwellian velocity distribution function. The constitutive relation for the pressure tensor contains contribution coming from both kinetic transport between collisions and collisional transport between particles. Consequently, it applies toward the full range of the solid fractions. The constitutive theory is combined in this study with the balance equation for full second moment so as to determine each component of the second moment and the pressure tensor. Most strikingly, normal pressure discrepancies, which increase with particle inelasticity, are observed here.