On a generalized framework for turbulent collision frequency models in flotation: The road from past inconsistencies to a concise algebraic expression for fine particles.

Process modeling is a valuable tool for process design and optimization. Nonetheless, the extent of its use depends on the physical complexity of each particular application. Flotation is one of the most complex processes to model. In particular, in mechanical flotation cells, turbulent flow prevails and promotes bubble particle collisions. Many size and time scales of both hydrodynamic and physicochemical nature have to be resolved to model the process. The only way to achieve this is a combination of co-current (pulp and froth) and sequential multiscale modeling. A generalized framework for modeling the pulp phase from the device scale to thin film scale separating bubbles and particles is presented here. The core of the model is the term describing the collision frequency between bubbles and particles. Existing approaches to derive this term are reviewed and critically commented demonstrating several inconsistencies. A unified and consistent approach for deriving this collision frequency term is described overcoming all the inconsistencies of previous approaches. Specific results are presented for the case of flotation of fine particles, being practically the only case for which a simplified collision frequency expression of algebraic complexity can be derived.