Modeling comminution processes in ball mills as a canonical ensemble

TL;DR

This paper introduces a novel statistical mechanics-based model for comminution in ball mills, integrating internal dynamics and external forces, enabling numerical simulations and potentially more verifiable experimental predictions.

Contribution

The paper presents a new canonical ensemble approach to model ball mill processes, combining mechanical and external forces within a Hamiltonian framework.

Findings

Monte Carlo simulations of particle number evolution

Model accounts for electromagnetic and gravitational effects

Potential for improved experimental verification

Abstract

A new approach to describe comminution processes in general ball mills as a macroscopic canonical ensemble is proposed. Using hamiltonian method, the model is able to take simultaneously into account the internal dynamics from mechanical motions inside the vial and external effects like electromagnetic and gravitational forces. Relevant physical observables are extracted using statistical mechanics approach through partition function at finite temperature. The method enables numerical calculation using Monte Carlo technique to obtain, for instance particle number evolution in term of system temperature. It is argued that the method is experimentally more verifiable than the conventional approaches based on geometrical displacements. An example of simulation for typical spex mill is also given.