Assessment of the parameter identifiability of population balance models for air jet mills

Abstract

Air jet mills are ubiquitous breakage devices not only in the pharmaceutical industry, but also in food and the toner manufacturing industry. The popularity of air jet mills arises due to its self-classifying, non-contaminating, and non-degrading operation while also maintaining a narrow particle size distribution. A popular approach towards mathematically modelling comminution devices like the jet mill is the population balance model framework. Population balance model for breakage is a semi-empirical framework in which several parameters are estimated from the experimental data. In many cases the experimental data available is insufficient, or of bad quality to guarantee the estimation of unique parameters. Thus it is imperative to assess the identifiability of such models to ensure that the chosen model structure is identifiable, both structurally and practically. In this study, we analyse the identifiability of the population balance model developed for the air jet mill. The identifiability analysis is carried out on basis of in-silico data generated by assuming certain parameter values to represent the true process. Based on several scenarios tested with data containing variety of information, it is shown that the model is practically non-identifiable for the situations in which the particle size measurement is available only at the end of the milling. The model becomes identifiable once continuous time measurements are available. The same holds for a reduced model with only the five breakage parameters.