Fractal Theory in Mineral Processing: Advances in Analyzing the Evolution of Cracks, Particles, Flocs, Bubbles and Their Aggregates

Fractal analysis provides scale-dependent descriptors of crack networks, particle size distributions, and aggregate structure in mineral processing. This review examines its application to crushing and grinding, flocculation and sedimentation, and flotation through an integrated crack–particle–floc–bubble framework. It compares characterization methods and aggregation models, including ballistic aggregation, diffusion-limited cluster aggregation, reaction-limited cluster aggregation, and coupled fluid–particle simulations. Particular attention is given to the distinction between image-based dimensions, particle size distribution exponents, and three-dimensional mass or surface dimensions. The reviewed studies associate structural evolution with loading, solution chemistry, shear, and interfacial interactions. These associations can help interpret fragmentation, settling, and bubble attachment, but they do not establish a universal relationship between fractal dimension and separation performance. Mineralogy, aggregate size, porosity, and measurement protocol constrain comparisons across systems. An integrated method–model–indicator map identifies how fractal descriptors can complement conventional process measurements. Future priorities include time-resolved three-dimensional characterization, experimentally validated multiphysics models, and data-driven methods that report uncertainty and generalization across mineral systems.