Application of the Rosin-Rammler function to describe quartz sandstone particle size distribution produced by high-pressure gas rapid unloading at different infiltration pressure

Abstract

Particle size distribution (PSD) is vital to particles as it determines the quality, safety, and performance of the final product. Rosin-Rammler function (R-R function) is probably the most suitable basic model to characterize the ore powders obtained from comminution. In this paper, we correlate the infiltration pressure with the R-R function to describe the PSD of quartz sandstone produced by high-pressure gas rapid unloading at different infiltration pressures. First, the pulverization experiments of quartz sandstone are conducted in the laboratory. As the infiltration pressure increases from 10 MPa to 25 MPa, producing more fine particles and the mass percentage of −0.5 mm and − 150 μm particles reach 85% and 45%, respectively. Then, based on Dimensional Analysis and assumptions, we assumed that the non-uniformity coefficient and the average particle size in the R-R function are both power functions of infiltration pressure. Finally, the experimental data is used as the learning sample to determine the undetermined parameters in the R-R function using Least Squares. By introducing the infiltration pressure the R-R function can describe and predict the PSD at different infiltration pressures. And the value of the parameters in the R-R function demonstrates that the higher the infiltration pressure, the smaller the average particle size and the more uniform particle distribution. In addition, we also discuss the application of Dimensional Analysis and Least Squares in solving complex problems. We hold that an appropriate basic model is key to obtaining good fitting results. This topic correlates the infiltration pressure with the R-R function to describe the PSD. On one hand, it reveals the significant influence of infiltration pressure on quartz sandstone pulverization. On the other hand, it also conveys the idea that Dimensional Analysis and Least Squares can indeed conduce to analyze complex problems under a reasonable basic model. • Pulverize quartz sandstone using high-pressure gas rapid unloading. • The infiltration pressure significantly affects the quartz sandstone pulverization. • Correlating the infiltration pressure with the R-R function. • Finally, the R-R function can depict PSD obtained at various infiltration pressures.