Analogous viscosity equations of granular powders based on Eyring's rate process theory and free volume concept

Abstract

Granular powders can be successfully treated with kinetic theory and statistical mechanics that are typically applicable to thermal systems, though the granular powders are athermal systems and the conventional environmental temperature is too weak to drive particles to move. Once the granular temperature is analogously defined in line with that in thermodynamics, the viscosity concept of thermal systems is naturally borrowed to describe the flowability of granular powders in this article. Eyring's rate process theory and free volume concept, which have been proved to be very powerful in dealing with many thermally activated phenomena in a wide variety of fields, are utilized to derive viscosity equations of granular powders under a simple shear. The obtained viscosity equations are examined only with empirical experimental observations in describing powder flowability, due to the lack of instruments and methodology for directly determining the viscosity of granular materials. Continuous shear thickening rather than discontinuous shear thickening is predicted and found to be dependent on the shear rate, the cohesive energy between particles, and the particle volume fraction, although the discontinuous shear thickening may still occur if certain conditions are met during shear, such as local particle volume fractions approaching the jamming point created by the shear induced inhomogeneity. A fundamental mechanism on how dry granular powders flow is proposed on the basis of what is demonstrated from the viscosity equations. The work presented in this article may lay a foundation to scale powder flowability in a more fundamental and consistent manner, at least providing an approach to consistently define the viscosity of granular powders. Since the same approaches are employed to derive the viscosity equations of granular powders as used to derive viscosity equations of liquids, colloidal suspensions, and polymeric materials, both athermal and thermal systems are thus unified with a single methodology.