Work

Empirical evidence for Fermi-Dirac classification of minerals by particle size

Year: 2025

Type: article

Abstract: In mineral processing , partition curves are used to describe the probability of a particle of a given size or density reporting to the overflow or the underflow stream. One simple descriptor is the Rosin-Rammler (Weibull) functional form, based on a sharpness parameter, α. An alternative descriptor was introduced by Scott and Napier-Munn (1992) based on the simplified Whiten equation expressed in terms of the Ecart probable, E p . Curiously, this simplified Whiten equation has functional equivalence to the Fermi-Dirac distribution ( Fermi, 1926 , Dirac, 1926 ), an exact equation used in quantum mechanics to describe the probability of Fermions residing in either the valency or the conduction band . In this study, the particle size classification data from Starrett and Galvin (2023) , produced using the REFLUX™ Classifier, provided powerful empirical evidence supporting the application of the simplified Whiten equation over the commonly used Rosin-Rammler function. The raw data adhered to the simplified Whiten equation over a range of ± 5E p , much wider than the Rosin-Rammler function. Hence the simplified Whiten equation, with its equivalence to the fundamental Fermi-Dirac distribution, offers prospects for a stronger theoretical framework for describing the role of a hydrodynamic driving force in particle size classification.

Source: Minerals Engineering

DOI: 10.1016/j.mineng.2025.109277

Authors: J.B. Starrett, S.M. Iveson, K.P. Galvin

Institutions: ARC Centre of Excellence for Enabling Eco-Efficient Beneficiation of Minerals, University of Newcastle Australia

Language: English

Topic: Mineral Processing and Grinding

Subfield: Mechanical Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,220

Funder: Australian Research Council