QFlux: Quantile-resolved analysis of particle-size-distribution changes in comminution

Abstract

QFlux is a computational framework for turning particle-size-distribution (PSD) measurements into actionable information for comminution evaluation and optimization. Conventional comparisons based on a single passing size, such as P80P_{80}, cannot show how the rest of the product responds to added energy. QFlux quantifies cumulative transfer across selected size boundaries and the movement of passing-size quantiles, making changes in target-size production, fines generation and coarse-tail removal available for more focused engineering interpretation. The commercial opportunity is to build these capabilities into laboratory testing services, process-diagnostic software, comparative grinding studies and model-validation tools. Potential users include mine operators, metallurgical laboratories, engineering consultancies, equipment manufacturers and process-software developers. With suitable PSD and energy records, QFlux can add a distribution-resolved analytical layer to existing workflows without requiring replacement of the grinding equipment or the underlying process model. Commercial development can focus on screening operating conditions, comparing matched media or equipment trials using declared normalization conventions, identifying diminishing returns from further grinding, and selecting targeted interventions. Coupled with site-specific metallurgical, energy and cost information, these analyses provide a basis for pursuing lower specific-energy requirements, reduced avoidable overgrinding and better alignment between grinding and downstream product requirements. The opportunity is to translate richer test information into better-informed operating decisions, rather than rely on a single endpoint size. The preprint presents mathematical foundations, reproducible synthetic verification and analysis of three staged stirred-mill datasets. It provides the methodological basis for industrial evaluation, software integration and prospective technology licensing. The accompanying Supplementary Material documents detailed derivations, processed input tables, estimation procedures and numerical verification. Industrial collaboration and technology-licensing enquiries may be directed to the corresponding author.