  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.
