Advancing models of bubble-particle contact times: A comprehensive review of flotation attachment efficiency prediction.

Bubble-particle attachment is a fundamental process in flotation, critical for determining separation efficiency, based on surface hydrophobicity and many other aspects of colloid and surface chemistry. This review examines and refines models of contact time - encompassing collision, sliding, and attachment interactions - to quantify attachment efficiency in flotation systems. It begins by exploring the underlying colloidal physics of bubble-particle collision and sliding interactions during attachment, emphasising the velocity components of particles at bubble surfaces, including water flow and particle settling. Approximate models for water velocity near bubble surfaces are critically assessed, considering the influence of gas holdup and bubble surface mobility. The review also evaluates sliding time models, addressing their role in predicting attachment efficiency under varying conditions, such as changes in Reynolds number, bubble surface mobility, flow asymmetry, gas holdup, and inertial forces. Experimental validation of these models is discussed, highlighting key insights into how water flow fields at the bubble surface and particle dynamics influence attachment processes. While interfacial interactions, microhydrodynamics, and particle morphology are not directly reviewed, this paper identifies them as critical factors to consider in future modelling efforts. By synthesising current models and emphasising areas for further development, this review advances understanding of bubble-particle attachment mechanisms and provides a foundation for optimising flotation efficiency through improved analytical and computational approaches.