Over the last years, inverse gas chromatography (IGC) proved to be a versatile and sensitive analytical technique for physicochemical properties. However, the comparability of results obtained by different users and devices remains a topic for debate. This is the first time, an interlaboratory study using different types of IGC instruments is reported. Eight organizations with different IGC devices defined a common lab measurement protocol to analyse two standard materials, silica and lactose. All data was collected in a standard result form and has been treated identically with the objective to identify experimentally observed differences and not potentially different data treatments. The calculated values of the dispersive surface energy vary quite significantly (silica: 22 mJ/m² - 34 mJ/m², lactose 37 mJ/m² - 51 mJ/m²) and so do the ISP values and retention volumes for both materials. This points towards significant and seemingly undiscovered differences in the operation of the instruments and the obtained underlying primary data, even under the premise of standard conditions. Variations are independent of the instrument type and uncertainties in flow rates or the injected quantities of probe molecules may be potential factors for the differences. This interlaboratory study demonstrates that the IGC is a very sensitive analytical tool, which detects minor changes, but it also shows that for a proper comparison, the measurement conditions have to be checked with great care. A publicly available standard protocol and material, for which this study can be seen as a starting point, is still needed to judge on the measurements and the resulting parameters more objectively.

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.

Froth flotation faces increasing challenges in separating particles as those become finer and more complex, thus reducing the efficiency of the separation process. A lab flotation apparatus has been designed combining the advantages of agitator-type froth flotation for high turbulences and column flotation with a deep froth zone for a fractionating effect, also enabling a study on the effect of different particle property vectors. A model system of ultrafine (<10 µm) particles was used for flotation to study how the separation process is influenced by the ultrafine property vectors of shape and wettability. To evaluate the new apparatus, flotation tests were carried out in a benchmark mechanical flotation cell under comparable conditions. Higher wettabilities result in higher recoveries, but the results show that optimum levels of hydrophobicity vary for different particle shapes. Different behaviours are observed for differently shaped particles, depending on their wettability state. The entrainment of unwanted gangue is reduced with increasing froth depth. While higher recoveries are obtained for the benchmark cell, the newly developed apparatus produces concentrates with higher grades. Our findings contribute to ultrafine flotation techniques and especially our understanding of the complex effect of particle shape in combination with the other property vectors.

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 μm, 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 separation apparatus used. Beyond these complexities, many particle properties are correlated, making it challenging to analyze the isolated impact of individual properties on the separation behavior. Therefore, 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 μm) particles, consisting of either glass spheres or glass fragments with different wettability states as the floatable fraction and magnetite as the non-floatable fraction, allows for the investigation of the influence of descriptor vectors consisting of size, shape and wettability, on the separation. In this way, the present paper contributes to a better understanding of the complex interplay between certain descriptor 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.

Particle systems and their efficient and precise separation are becoming increasingly complex. Therefore, instead of focusing on a single separation feature, a multidimensional approach is needed where more than one particle property is considered. This, however, requires the precise characterization of the particle system, which is especially challenging for fine particles with sizes below 10 µm. This paper discusses the benefits and limitations of different characterization techniques, including optical contour analysis, inverse gas chromatography, flow cytometry, and SEM-based image analysis. The separation of ultrafine particles was investigated for a binary system using froth flotation, where a novel developed flotation apparatus is used. A special focus was placed on the multidimensional evaluation of the separation according to the particle properties of size, shape, and wettability, which was addressed via multivariate Tromp and entropy functions. The results emphasize the intricacy of the flotation process and the complex interaction of the individual particle properties and process parameters. The investigations contribute to the understanding of the characterization of particulate properties as well as the separation behavior of ultrafine particles via froth flotation, especially in the case of a multidimensional approach.