Dispersive Growth in Batch Granulation

In many processes, such as coating or layering granulation, the width (or variance) of the particle property distribution is an important measure of product quality. The variance in particle size is directly related to the variance in thickness of the coating layers that has great influence on the product characteristics, for example the release time of active ingredients in pharmaceuticals. 

Coating, as well as layering granulation, has a well-established basis in mathematical modeling. Using a population balance approach for the particle property distribution, for example the distribution of size d, yields for the number density n the following type of population balance equation 

In modeling, the growth rate G is commonly considered to be independent of the particle property. For example, Mori et al. (2007) assume that the growth velocity of particles is directly related to their surface area in the fluidized bed, to obtain for spherical particles 

Msm denotes the mass flow rate of solid material entering the system with the spray, is the density of the solidifled layers, and (I2 is the second moment of the particle size distribution, so that n (i2 equals the total particle surface area. The population balance equation then reads as 

This fundamental assumption simplifles the structure of the mathematical problem significantly. Additionally, it is also backed by various experimental results - see for instance the references in Mori et al. (2007). 

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