Flow Equations for Free-Flowable Particle Fractions of Sorbitol for Direct Compression: An Exploratory Multiple Regression Analysis of Particle and Orifice Size Influence

Abstract

Flowability is among the most important properties of powders, especially when fine particle size fractions need to be processed. In this study, our goal was to find a possibly simple but accurate mathematical model for predicting the mass flow rate for different fractions of the pharmaceutical excipient sorbitol for direct compression. Various regression models derived from the Jones–Pilpel equation for the prediction of the mass flow rate were investigated. Using validation with experimental data for various particle and hopper orifice sizes, we focused on the prediction accuracy of the respective models, i.e., on the relative difference between measured and model-predicted values. Classical indicators of regression quality from statistics were addressed as well, but we consider high prediction accuracy to be particularly important for industrial processing in practice. For individual particle size fractions, the best results (an average prediction accuracy of 3.8%) were obtained using simple regression on orifice size. However, for higher accuracy (3.1%) in a unifying model, valid in the broad particle size range 0.100–0.346 mm, a fully quadratic model, incorporating interaction between particle and orifice size, appears to be most appropriate.

Keywords

• mass flow rate
• flow equation
• powders properties
• orifice diameter
• hopper
• particle size