Validation of an energy–size relationship obtained from a similarity solution to the batch grinding equation

• Batch grinding kinetics in the self-similar size distribution regime are analyzed.
• A wide range of particle breakage characteristics are considered.
• A comprehensive verification of the Kapur energy–size relationship is carried out.
• The relationship is found to be valid over a fairly broad size range of interest.
• In the context of ball mill scale-up, the merits of the relationship are discussed.

For a widely used combination of the functional forms for describing the size dependence of particle breakage rate and breakage distribution functions in the ball mill grinding operation, Kapur [13] has derived an energy–size relationship from a similarity solution to the fundamental size–mass balance equation of batch grinding kinetics. In spite of its significant relevance from the practical application point of view, this relationship has not been properly validated so far. Therefore, a detailed study was undertaken for its validation using some simulated batch grinding size distribution data as well as actual experimental data. The relationship has now been comprehensively validated. It is concluded that as compared to various known empirical energy–size relationships the one presented by Kapur can provide a more rational and sound basis for estimation of energy requirements for industrial ball milling operations.

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