A contribution to new measure for evaluation of a particle size distribution

Abstract

Many measures such as the percentiles, central tendency values, the inverse of specific surface area, and the parameters of distribution functions were used by many authors as indices for evaluation of the particle size distribution (PSD) resulted from different mineral processing operations such as comminution, classification, sedimentation and material handling. Many of these measures are not reliable and the others are not so accurate to differentiate between different PSDs because many sets of PSD data may have the same values of these measures. In the present paper, a new measure called median of the mean x₅₀ (mean) is used for evaluation of a PSD. This measure may be estimated easily by a simple expression using Gates–Gaudin–Schuhmann (GGS) distribution model. The value of this measure is defined as the particle size which divides the particles of a sample into two equal halves parts according to their mean. It can be stated that the value of this measure is lower if the sample is finer. In the present paper, the expressions for calculation median of the mean with arithmetic, quadratic and cubic means were estimated. Median of the mean measure may be considered more better over the other measures because it was based on the mean of PSD which takes into consideration all particle sizes and their corresponding distributions, as well as, the expression of this measure included the parameters of GGS distribution model. In this research, three groups of PSD data sets were studied. The results of first group showed that different PSDs, which have different values of x₅₀ (weight) and means, have also different values of x₅₀ (mean). The results of second group data revealed that different PSDs, which have the same values of x₅₀ (weight), have different values of this measure. The last PSDs data set, which have the same values of arithmetic means, showed larger differences in the values of this measure more than the values of x₅₀ (weight). Moreover, it was found that the values of x₅₀ (weight) increased as the values of quadratic and cubic means decreased, which is considered a non-logical behaviour where the x₅₀ (weight) must have lower values for the finer samples.

Keywords

PARTICLE SIZE DISTRIBUTION FUNCTION MEDIAN MEAN SURFACE AREA GATES-GAUDIN-SCHUHMANN MODEL

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