TABLE OF CONTENTS We shall attempt to formulate a criterion for evaluating the quality of separation into any number of components. If the material is divided into n components in such a manner that each component contains only particles of the required class size without impurities, this separation is ideal. This means as the produced components become more homogeneous, the separation becomes closer to ideal.
In practice, there is no equipment ensuring ideal separation and, consequently, it is necessary to develop a criterion estimating the proximity of the actual separation to ideal separation. This criterion should reflect the extent by which the homogeneity of the produced components increased after separation, in comparison with the initial material.
Let us assume that it is required to separate material into n fractions (with the particle size within each fraction equal to the mean size of the particles constituting this fraction). Let us arrange all the particles of the material in a row and count the number of transpositions with returns for these particles. The number of transpositions with returns will give objective information on the degree of inhomogeneity of the system (it may be assumed that each size of the particle is some letter, and we obtain reports consisting of the same letters in different orders from, as in this case, the number of arrangements with returns is the number of reports which can be formed from these letters).
Let us assume that
