Analysis of mathematical models for description of the fractional composition of disperse elastic fillers

The paper presents a comparative analysis of integral and differential mathematical models describing the particle size distribution of dispersed elastic fillers. Crushed vulcanizates obtained by high temperature shear grinding were studied as objects of research. Technogenic waste – waste passenger car tires and rubber elements of gas mask facepieces – were used as raw materials. Data on the distribution of the crushed vulcanizate particles were obtained by laser diffraction using the particle size analyzer Fritsch Analysette 22 Microtec plus (“Fritsch”, Germany). It was found that the distribution curves are unimodal asymmetric curves. Search and analysis of mathematical models were carried out using a specialized software product TableCurve 2D v5.01 (Jandel Scientific). Four- and five-parameter equations pertaining to the class of logistic models were tested to describe the integral cumulative distribution curves of the rubber powder particles. In order to justify the choice of a suitable mathematical model to describe the fractional composition of the crushed vulcanizes, the adequacy of the models was assessed, the structural characteristics of the variation series, the statistical moments of distribution and the indicators of its shape were determined. It was found that according to a number of criteria it is appropriate to use the logarithmically normal distribution function for the description and analysis of the rubber powders fractional composition. It is suggested that regardless of the nature of the feedstock, the described implementation of high temperature shear grinding provides products having an identical shape of rubber powder particles size distribution.