Collisional source of the second moment and pressure tensor for inhomogeneous rapid granular flows of highly inelastic spheres

By extending the constitutive theories for homogeneous granular flows of hi ghly inelastic spheres by Richman (J. Rheol 33 (1989) 1293), Chou (J. CSME 16-6 (1995) 577), and Chou and Richman (Physica A 259 (1998) 430), the coll isional source of the second moment of fluctuation velocity and pressure te nsor were developed in this study for inhomogeneous rapid granular flows of identical smooth highly inelastic spheres. The important mean fields in th is flow are the solid fraction, mean velocity, and full second moment of fl uctuation velocity. The collisional source of second moment and the collisi onal flux of momentum are based upon an anisotropic Maxwellian velocity dis tribution function. The constitutive theory was combined with the experimen tal results measured by Hsiau and Jang (Exp. Thermal Fluid Sci. 17 (1998) 2 02) so as to determine the profiles of pressure tensor and collision source of second moment in the inhomogeneous rapid granular shear flows of inelas tic spheres. The normal pressure discrepancies were also observed. (C) 2001 Elsevier Science B.V. All rights reserved.