Nuclei size distribution modelling in wet granulation

Abstract

Nucleation is an important wet granulation rate process that sometimes has a profound effect on granule attributes and which needs to be captured in process modelling studies. However, existing models fail to predict nuclei size distribution of a range of spray conditions typically used in industry. In this paper, the dimensionless nucleation number Ψn is used to develop two new nuclei size distribution models, one empirical and one semi-mechanistic. The empirical model assumes a log-normal distribution (LND), and the semi-mechanistic model is based on a approach proposed by Hapgood et al. (2009), which applies the Poisson distribution (PD) function. Modelling parameters are estimated using Monte Carlo simulations (MCS) data. From the models, the nuclei size distribution can be easily determined using analytical equations, which simplifies the inclusion in a population balance modelling (PBM) framework. The results of both models are assessed using MCS data as well as experimental data from literature. The empirical LND model is able to capture the MCS results accurately, and the predictions agree reasonably well with the experimental results over a wide range of dimensionless nucleation number (0<Ψn<3). The predictions of the semi-mechanistic modified Poisson distribution (MPD) model do not agree qualitatively with the MCS or experimental results. A sensitivity analysis shows that the MCS modelling assumptions need to capture the spatial drop distribution in the spray accurately, while the drop size distribution can be assumed to be uniform. Overall, we recommend that the LND model with the parameter values estimated be used in PBM frameworks to determine nuclei size distribution for a wide range of experimental conditions in mixers and fluidised granulators.