This paper presents the analysis of the batch flotation with regard to the size of the floated particles with coal as an example. Empirical studies were conducted on samples of bituminous coal from the Jankowice coal mine (33 type in Polish classification). Experimental includes fractional flotation of coal samples with various particle size, the float and sink analysis of flotation products and determination the ash content in each flotation and densimetric fractions. The evaluation of flotational upgrade was based on the partition curve and value of heterogeneity index (standard deviation) with the division into concentrate and tailings as a measure of flotation efficiency. From the partition curve, partition size, which is assumed in flotation as the maximum size of floatable particles under the given physicochemical conditions, was calculated. On the basis of float and sink analyses, it was found that floated particles are particles with hydrophobic properties corresponding to the density (related to the mineral matter content) below 1.6 Mg/m3. In this connection, the probability of detachment of a particle from a given particle size fractions, was calculated as a relation between the mass of particles with the density below 1.6 Mg/m3 in tailings and the mass of particles with this density in the feed. With the increase in particle size, the de-gree of heterogeneity increases and reaches the maximum value for particle size fractions 0.315–0.4 mm, then decreases for larger particles. The characteristics of the dependence of the degree of heterogeneity on particle size is analogous as in many flotation processes – the dependence of the flotation rate constant flotation on particle size.
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