Empirical Evidence for Fermi-Dirac Classification of Minerals by Particle Size

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, alpha. An alternative descriptor was introduced by Scott and Napier-Munn (1992) based on the Whiten equation expressed in terms of the Ecart Probable, Ep. This paper examines the Fermi-Dirac distribution (Fermi, 1926; Dirac, 1926) used in quantum mechanics, identifying for the first time its equivalence to the simplified Whiten equation. Fermions are quantum particles that must choose between two electron spin states, exhibiting a probability that varies with a chemical potential difference. We see an analogy with the particle size classification of an efficient separator in terms of the probability of a particle reporting to either the overflow or the underflow. 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 (Fermi-Dirac distribution) over the commonly used Rosin-Rammler function. The raw data adhered to the distribution over a range of ±5Ep.