Tap Density Equations of Granular Powders Based on the Rate Process Theory and the Free Volume Concept

TL;DR

This paper develops tap density equations for granular powders using rate process theory and free volume concepts, unifying empirical models and potentially improving data fitting by introducing an adjustable parameter.

Contribution

It introduces a theoretical framework that derives tap density equations from fundamental principles, linking empirical models to physical mechanisms and applicable to both dry and wet particle systems.

Findings

Derived equations can fit experimental data better with an extra parameter.

Unified description of dry and wet particle systems based on free volume and rate control.

Equations reduce to widely used empirical models under certain conditions.

Abstract

Tap density of a granular powder is often linked to the flowability via Carr Index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in literature: The inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept, we obtain the tap density equations and they can be reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environment temperature are grouped into one parameter that weighs the pace of packing process. The current results, in conjunction with our previous findings, may imply that both dry(granular)and wet(colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).