Application of multivariate Tromp functions for evaluating the joint impact of particle size, shape and wettability on the separation of ultrafine particles via flotation

Froth flotation predominantly separates particles according to their differences in wettability. However, other particle properties such as size, shape or density significantly influence the separation outcome as well. Froth flotation is most efficient for particles within a size range of about $20-200\mu m$, but challenges arise for very fine or coarse particles that are accompanied by low recoveries and poor selectivity. While the impact of particle size on the separation behavior in flotation is well-known by now, the effect of particle shape is less studied and varies based on the investigated zone (suspension or froth) and the separation apparatus used. A multidimensional perspective on the separation process, considering multiple particle properties, enhances the understanding of their collective influence. In this paper the two-dimensional case is studied, i.e., a parametric modeling approach is applied to determine bivariate Tromp functions from scanning electron microscopy-based image data of the feed and the separated fractions. With these functions it is possible to characterize the separation behavior of particle systems. Using a model system of ultrafine ($<10\mu m$) particles, consisting of differently shaped glass particles with different wettability states as the floatable and magnetite as the non-floatable fraction, allows for investigating the influence of particle size, shape and wettability, on the separation. In this way, the present paper contributes to a better understanding of the complex interplay between certain property vectors for the case of ultrafine particles. Furthermore, it demonstrates the benefits of using multivariate Tromp functions for evaluating separation processes, and points out the limitations of SEM based image measurements by means of mineral liberation analysis (MLA) for the studied particle size fraction.