RHEOLOGICAL EQUATIONS IN ASYMPTOTIC REGIMES OF GRANULAR FLOW

This paper assesses the validity of the generalized viscoplastic fluid (GVF) model in light of the established constitutive relations in two asymptotic flow regimes, namely, the macroviscous and grain-inertia r egimes. A comprehensive review of the literature on constitutive relat ions in both regimes reveals that except for some material constants, such as the coefficient of restitution, the normalized shear stress in both regimes varies only with the grain concentration, C. It is found that Krieger-Dougherty's relative viscosity, mu(C), is sufficiently coherent among the monotonically nondecreasing functions of C used in describing the variation of the shear stress with C in both regimes. I t not only accurately represents the C-dependent relative viscosity of a suspension in the macroviscous regime, but also plays a role of the radial distribution function that describes the statistics of particl e collisions in the grain-inertia regime. Use of mu,(C) alone, howeve r, cannot link the two regimes. Another parameter, the shear-rate numb er, N, is needed in modeling the rheology of neutrally buoyant granula r flows in transition between the two asymptotic regimes. The GVF mode l proves compatible with most established relations in both regimes.