WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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.

A phenomenological multilayer adsorption model for a well-dispersed, homogeneous, nonporous adsorbent and a molecular adsorbate is presented. The model provides explicit kinetic expressions associating the adsorbed amounts to the fraction of the surface occupied and reduces to the first- and second-order adsorption models for special cases. Parameters of the model are a pair of true rate constants related to the adsorbate-adsorbent and adsorbate-surface adsorbate affinities. A general graphical procedure and analytical equations for special cases are provided to estimate the rate constants from kinetic adsorption data. Data from the adsorption of sodium stearate onto α-alumina from water were used to test the model. The predicted values of the rate constants suggested that the stearate was distributed homogeneously on the alumina surface and essentially adsorbed as a monolayer before starting to form the second layer.

WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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