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

• The Fermi-Dirac distribution was shown to be equivalent to the Whiten Equation. • High-quality experimental data was used to support the analysis. • The experimental data adhered to the Fermi-Dirac distribution over a range of ± 5 E p . • The Rosin-Rammler equation showed departure from the data in the extremes. 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.