| Popis: |
Practically all particle separation processes depend on more than one particulate property. In the case of the industrially important froth flotation separation, these properties concern wettability, composition, size and shape. Therefore, it is useful to analyze different particle descriptors when studying the influence of particle wettability and morphology on the separation behavior of particle systems. A common tool for classifying particle separation processes are Tromp functions. Recently, multivariate Tromp functions, computed by means of non-parametric kernel density estimation, have emerged which characterize the separation behavior with respect to multidimensional vectors of particle descriptors. In the present paper, an alternative parametric approach based on copulas is proposed in order to compute multivariate Tromp functions and, in this way, to characterize the separation behavior of particle systems. In particular, bivariate Tromp functions for the area-equivalent diameter and aspect ratio of glass particles with different morphologies and surface modification have been computed, based on image characterization by means of mineral liberation analysis (MLA). Comparing the obtained Tromp functions with one another reveals the combined influence of multiple factors, in this case particle wettability, morphology and size, on the separation behavior and introduces an innovative approach for evaluating multidimensional separation. In addition, we extend the parametric copula-based method for the computation of multivariate Tromp functions, in order to characterize separation processes, also in the case when image measurements are not available for all separated fractions. |
