A critical review on turbulent collision frequency/efficiency models in flotation: Unravelling the path from general coagulation to flotation

Abstract

Flotation is a very important separation process in the mining industry. In addition, it finds important application as a water treatment process. The better design of flotation devices and operation strategies requires development of reliable and consistent mathematical models. Flotation is much more complex than typical unit processes, involving physicochemical interactions in small size scale and hydrodynamic interactions between bubbles, particles and liquid in a variety of size scales. The only feasible integrated approach to modeling the flotation process is by incorporating multiple scales. In the heart of such an approach there is a submodel for the frequency of collisions between bubbles and particles. Literature on this subject in the absence of intense turbulence is very extensive and there are many well-accepted models. Yet, the situation is quite different for the case of turbulence being an important collision mechanism, which is exactly what happens in industrial dispersed air flotation devices. The corresponding literature models are limited and focused on different aspects of the process. The present work is a review study attempting to unify these models in a general framework. The review is not restricted to presenting existing models but all relevant physical principles and fundamental theories are examined and assessed properly. In this respect, there are two levels of classification of literature material in this work. The first is a classification as general collision models and flotation models. It is important to critically examine the general collision models of engineering and physics literature since they constitute the basis on which flotation models rely. The second classification is with respect to the level of detail and sophistication of models (from distributed multibubble/multiparticle model to lumped models based on statistical theory of turbulence). The outcome of the work comes to the conclusion that existing models focus only to specific parts of the phenomena leading to bubble-particle collisions and for this, further improvement is needed to integrate them to obtain a better and more general picture. The material and comments presented in this work are meant as a decisive milestone towards this integration procedure.

Keywords: Collision rate; Critical review; Flotation process; Mathematical model; Turbulent flow field.