A renewal theory approach to understanding interparticle coating variability

•Mann's equation predicting coating variance is amended to handle small spray sizes.•The new renewal theory equation is applied to other coating distribution predictions.•In contrast to other methods, intermediate model parameters are physically meaningful.•In contrast to other methods, the renewal theory result is an algebraic expression.

Many models, both analytical and numerical, have been derived for predicting coating mass variability of particle coating operations (e.g. tablet pan coating, spouted bed coating). These existing models require lengthy simulation times or artificial discrete time scales, diminishing their utility. In this work, a simple alternative is proposed. Here an alternating dependent renewal theory model is presented to predict the interparticle coating mass distribution for spray coating processes. By accounting for the variability of coating mass per visit to the spray and cycle time in the mixing vessel, the new model gives an explicit equation for the coating mass distribution. Comparisons are made against other modeling approaches including Bernoulli trial models, the Monte-Carlo models, and population balance models. It is shown that all existing modeling methods can be more easily and compactly expressed under the modeling approach developed in this work.

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