Granular-Flow Rheology: Role of Shear-Rate Number in Transition Regime

Abstract

This paper examines the rationale behind the semiempirical formulation of a generalized viscoplastic fluid (GVF) model in the light of the Reiner-Rivlin constitutive theory and the viscoplastic theory, thereby identifying the parameters that control the rheology of granular flow. The shear-rate number ( N ) proves to be among the most significant parameters identified from the GVF model. As N → 0 and N →∞, the GVF model can reduce asymptotically to the theoretical stress versus shear-rate relations in the macroviscous and grain-inertia regimes, respectively, where the grain concentration ( C ) also plays a major role in the rheology of granular flow. Using available data obtained from the rotating-cylinder experiments of neutrally buoyant solid spheres dispersing in an interstitial fluid, the shear stress for granular flow in transition between the two regimes proves dependent on N and C in addition to some material constants, such as the coefficient of restitution. The insufficiency of data on rotating-cylinder experiments cannot presently allow the GVF model to predict how a granular flow may behave in the entire range of N ; however, the analyzed data provide an insight on the interrelation among the relevant dimensionless parameters.