Irkutsk National Research Technical University, Irkutsk, Russia

K. V. Fedotov, Head of Department, Doctor of Engineering Sciences, Professor
G. I. Sarapulova, Doctor of Chemical Sciences, Professor, sara131@mail.ru
P. K. Fedotov, Doctor of Engineering Sciences, Professor

A review of publications on modeling the flotation process during ore benefication based on domestic and foreign journals over the past 25 years, including those from the open access MDPI, has been conducted. The increasing dynamics of describing and predicting flotation as a multi-speed and multi-phase physical and chemical continuum is demonstrated. A variety of linear and nonlinear relationships between the operating parameters of the flotation process, chemical reagents and mineral properties are identified, and various types of interactions and methods for describing the state of the foam are recorded. The quantitative assessment is carried out using mathematical models and numerical methods, neural network modeling, machine vision, as well as a new emerging field—the molecular–dynamic modeling. The purpose of the work is not to create an encyclopedic review, since there are quite a few tools and methods of modeling identified by publications, but to highlight the dominant trends and the most common techniques, to identify the more effective ones by the results of the works. Part I of this review presents a selective analysis of articles on mathematical and numerical modeling of the flotation process. The review will be useful for researchers studying flotation processes in ore benefication, as it reflects current trends in modeling complex multiphase flotation systems using various approaches based on global publications.

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