The fundamental flotation models are useful for understanding flotation mechanisms. However, these models cannot be used for design and optimization of flotation circuits because it is very difficult to determine induction times experimentally during flotation despite using advanced high-speed cameras. Thus, there is a need to develop the model that can be used for practical applications, which is the main objective in this work. The developed models were successful in predicted P-a (attachment efficiency) and ti (induction time) at various chemical conditions. The values of P-a (attachment efficiency) were strongly affected by particle size, collector concentration and pulp pH while the values of t(i) (induction time) were affected by particle size and collector concentration and the values of k (flotation rate constant) were affected by collector concentration only. It means that P-a is much more sensitive than ti and k to detect the changes in the flotation experimental conditions. The slopes ofti vs P-a functions were larger at different particle sizes than those at different collector concentrations, demonstrating that the effect of particle size was more dominant than the effect of collector concentration on P-a. This paper demonstrated that understanding of P-a is essential for better analysing flotation mechanisms. (c) 2020 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.