Analogous Viscosity Equations of Granular Powders Based on Eyrings Rate Process Theory and Free Volume Concept

TL;DR

This paper develops viscosity equations for granular powders using Eyrings rate process theory and free volume concept, predicting shear thickening behavior and proposing a fundamental flow mechanism, unifying thermal and athermal systems.

Contribution

It introduces a novel approach to derive viscosity equations for granular powders based on thermally activated process theories, unifying the description of flow in thermal and athermal systems.

Findings

Predicted continuous shear thickening dependent on shear rate and particle cohesion.

Found conditions under which discontinuous shear thickening may occur.

Proposed a fundamental mechanism for dry granular powder flow.

Abstract

The viscosity concept of thermal systems is borrowed to describe the flowability of granular powders in this article with the granular temperature is defined analogously. Eyrings 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. The continuous shear thickening rather than the discontinuous shear thickening are predicted and found to be dependent on shear rate, the cohesive energy between particles, and the particle volume fraction, though the discontinuous shear thickening may still occur if certain conditions are met during shear, such as local particle volume fractions approach to 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 are 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.