Development of a Generalized Partition Curve Model for Hydrocyclones

Partition curves associated with hydrocyclone classification processes have been known to deviate from the typical S-shape by exhibiting asymmetric and non-monotonic behaviors, making their mathematical modeling challenging. In addition to the well-documented phenomenon of fish-hooks at the finer end, the partition curves can also sometimes exhibit fat-tailed behavior at the coarser end of the size spectrum, which has not been extensively highlighted in the literature. This study aimed to develop a parametric model for the partition curves which can systematically and effectively accommodate both these irregularities at the coarser and finer ends. Instead of adopting a piece-wise modeling approach for the task, a continuous model was successfully developed in the form of the addition of three component functions, each affecting different regions and features of the partition curve with a total of 7 fitting parameters. Two of the component functions were modified versions of the cumulative density functions of the Weibull distribution while the third was the modified solution of a single hyperbolic branch having a horizontal and a slant asymptote to accommodate the observed fat-tailed behavior. The model exhibited remarkable fitting performance for both experimentally generated and literature data. An alternative method of defining the separation cut size has also been proposed in this study to overcome the limitations of the classical concept of the d₅₀. It was also shown how the developed model can be utilized for quantitative analysis of the critical aspects of the partition curve such as the cut size, bypass, and the dip point.