Modeling of Coarse Particle Shape Evolution During Attrition in a Stirred Vessel

Particle breakage in stirred vessels is usually modeled using population balance equations (PBEs) to describe the evolution in particle size with time. Although shape has a strong effect on the particle properties and hence the product quality, changes in the particle shape distribution are typically neglected. To account for changes in both size and shape simultaneously, a multivariate population balance must be used. This multivariate PBE requires a multivariate breakage distribution function that accounts for the observed size and shape evolution in actual systems. A general mathematical framework that guarantees mass conservation and exchangeability for these breakage distribution functions has already been developed [1]. While the breakage distribution functions in this framework meet these constraints, they are not based on the fundamental physics of particle attrition. What is needed are breakage distribution functions based on fracture mechanics. Previous research [2-3] uses fracture mechanics to predict the total particle volume lost due to attrition. This information is incorporated into the new model by including it in the breakage distribution function. Starting with the original coarse particle size and shape, the model accounts for the material removed from the parent particles due to attrition. The approach is to model the breakage distribution function as a bivariate function of the particle volume and the shape factor. A comparison of the model with experimental results for several systems is presented. This work has wide applicability in that it directly affects any unit operation involving solids breakage in stirred vessels. This includes both stirred reactors with solid particles as well as crystallizers. Not limited to batch processes, this can also be used for continuous processes.