Multiphase systems are important in minerals processing, and usually include solid–solid and solid–fluid systems, such as in wet grinding, flotation, dewatering, and magnetic separation, among several other unit operations. In this paper, the current trends in the process system engineering tasks of modeling, design, and optimization in multiphase systems, are analyzed. Different scales of size and time are included, and therefore, the analysis includes modeling at the molecular level (molecular dynamic modeling) and unit operation level (e.g., computational fluid dynamic, CFD), and the application of optimization for the design of a plant. New strategies for the modeling, design, and optimization of multiphase systems are also included, with a strong focus on the application of artificial intelligence (AI) and the combination of experimentation and modeling with response surface methodology (RSM). The integration of different modeling techniques such as CFD with discrete element simulation (DEM) and response surface methodology (RSM) with artificial neural networks (ANN) is included. The paper finishes with tools to study the uncertainty, both epistemic and stochastic, based on uncertainty and global sensitivity analyses, which is present in all mineral processing operations. It is shown that all of these areas are very active and can help in the understanding, operation, design, and optimization of mineral processing that involves multiphase systems. Future needs, such as meso-scale modeling, are highlighted.

This research was performed to obtain high-value products from clay materials. High-grade nanometric delta-alumina (δ-Al₂O₃) was obtained from the modification of clay-based minerals, which could be potentially applied in the form of thin film for novel optoelectronic applications. The selective recovery process of alumina from clay materials presents an important advantage regarding the complete removal of other starting constituents such as silica, iron, titanium, alkali, and alkaline earth metals. To accomplish the selective removal of different species, an acid leaching route was used to extract the aluminum, then the iron impurities were eliminated by alkaline precipitation. The solution was acidized to precipitate the aluminum as aluminum chloride hexahydrate. Finally, the aluminum chloride hexahydrate was calcinated to obtain nano-delta-alumina with purity of over 98.5% Al₂O₃. The dominating crystalline phase was delta–gamma alumina (δ-phase and γ-phase), with a particle size of <140 nm. Then, these nanoparticles (NPs) were prepared as a stable colloidal dispersion to form a mesoporous layer employing the spin-coating technique. Initially, the synthesized alumina was characterized by atomic force microscopy (AFM) and TEM to determine the particle size and its morphology, whereas the colloidal dispersion was analyzed by rheological measurements. Finally, the findings of this investigation made it possible to get thin films with good porosity, which can be used in optoelectronic applications, specifically in perovskite solar cells.

The low recovery of fine chalcopyrite particles and the limited Cu/Fe selectivity with conventional thiol collectors prompted the evaluation of a Polystyrene–Divinylbenzene–Cetyltrimethylammonium Bromide–Potassium Amyl Xanthate (PS-DVB-CTAB-PAX) polymeric nanocollector. The copolymer was synthesized by emulsion polymerization and characterized using Total Organic Carbon (TOC) analysis, Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), Particle Size Analysis, and contact angle measurement. Its performance was tested in a Hallimond cell (150 mL) using a synthetic industrial water solution (0.010 mol/L NaCl + 0.005 mol/L CaCl₂) at a natural pH range of 6.0 to 8.0. PAX concentrations ranged from 0 to 16.19 mg L⁻¹, and nanocollector doses equivalent to 0 to 45 mg g⁻¹ of solid were tested. The nanocollector increased chalcopyrite recovery to 98 ± 1% for the −53 + 38 µm size fraction and maintained values greater than 95% in the coarse fractions, outperforming PAX across the entire dosage range. The PAX + nanocollector combination achieved the same recovery by reducing the total xanthate dosage by one-third, demonstrating a synergistic effect. TOC assays showed preferential adsorption of 96.6% on chalcopyrite versus 86.4% on pyrite, a difference that explains the observed Cu/Fe selectivity (pyrite floatability < 70%). The contact angle of chalcopyrite increased from 56.4° (water) to 86.5° in the presence of the nanocollector, demonstrating the generation of localized superhydrophobicity that reduces interfacial free energy and favors bubble–particle adhesion, whereas pyrite showed lower values of 51.1°, 58.3°, and 75.1°, confirming its more hydrophilic nature. These findings indicate that PS-DVB-CTAB-PAX enables optimized copper sulfide recovery, reduced thiol collector consumption, and improved metallurgical selectivity, making it a promising alternative for flotation circuits with high ionic strength water and for scaling up to pilot tests.