A Phenomenological Kinetic Flotation Model: Intrinsic Floatability Profiling for Batch and Continuous Flotation Systems

Abstract

This study presents a mechanistic flotation kinetics model that unifies the description of mineral particle floatability in both batch and continuous systems. Building on a physically explicit interpretation of bubble-particle interactions, the model introduces the concept of intrinsic floatability, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upphi }_{\text{P},\text{ij}}<^>{\text{s}}$$\end{document}, defined as the size-and composition-dependent probability that a particle within a bubble's sweep volume reports to the froth. A central feature of the framework is that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upphi }_{\text{P},\text{ij}}<^>{\text{s}}$$\end{document} is decoupled from system-level rate-determining factors, such as bubble-particle encounter frequency, transport limits, and bubble surface crowding-that otherwise confound attempts to extract floatability distributions from kinetic data. This separation is achieved through three explicit, time-dependent parameters: the encounter rate kappa(t), the limiting flotation rate mu(t), and the bubble saturation factor chi(t). Together, these parameters isolate intrinsic particle behavior from external constraints. The model naturally reduces to the classical first-order rate law in dilute pulps, while in concentrated suspensions it predicts systematic deviations, approaching zero-order kinetics as bubble surfaces saturate. Importantly, the same formulation applies seamlessly to batch tests and multi-stage continuous circuits, enabling a consistent theoretical framework across scales and ore types. Requiring only standard flotation data and known system parameters, the model is practical for both laboratory coal flotation studies and industrial non-coal applications. Validation using batch coal data and continuous plant-scale copper flotation results demonstrates its robustness and broad relevance.