The pivot phenomenon and difference-similarity of classifier particle distributions

Truncated analytical expressions for product size distributions of mechanical classifiers have been proposed recently by considering classifier feed distribution in terms of Gates–Gaudin–Schumann (GGS) function and classifier efficiency in terms of Plitt function. In this work it is shown from theoretical considerations that the distributions when expressed in density form pivot at a common size referred to as pivot-size. Under the specified operating conditions of the unit, the physical interpretation of this pivot phenomenon along with the mass balance considerations reveal that the size distributions are difference-similar and collapse onto a single curve when the mathematical difference between any two distributions is scaled with corresponding maximum value of the differences and thus make them invariant of shape effects of feed and product distributions. The procedure is explained in simple terms using an illustrative example.