Powder Ball Milling: An energy balance approach to particle size reduction

TL;DR

This paper presents an energy balance model for particle size reduction in milling, explaining the lower size limit and grinding inhibition through energy equilibrium and phase transformation concepts.

Contribution

It introduces a novel energy balance approach linking milling mechanics to particle size limits, incorporating phase transformation kinetics for better prediction.

Findings

Validated model with experimental data

Identified energy equilibrium as key to size limit

Connected milling behavior to phase transformation kinetics

Abstract

Milling of brittle materials shows a lower limit in size reduction, below which grinding cannot proceed further. Experimentally, the smallest particle size is determined by the milling media energy, and it is time-independent. Rittinger's law, which applies to fine grinding, does not consider any lower limit in size, leading to nonphysical results. A damping factor gradually inhibiting grinding efficiency has already been suggested as a modification. Milling mechanics and changes in material properties at small sizes have been associated to this behavior. In this work, the grinding inhibition is linked to an energy balance between the powder's specific surface energy and the energy density, calculated as the kinetic energy of the milling media divided by the impacted volume. By introducing the idea of energy equilibrium, comminution behaves as a phase transformation characterized by a JMAK kinetics. Validation of this formulation has been conducted on published and original data.