A novel mathematical method for prediction of rapid expansion of supercritical solution (RESS) processed ibuprofen powder size distribution

A fundamental understanding of the interplay among the variables involved in a rapid expansion of supercritical solution (RESS) process is necessary in order to achieve control of product within the desired specifications. A model is proposed where the experimental data are fitted to a 2-D Sp-line equation that results in a mathematical pattern matching function that can easily be processed analytically to yield a continuous motion estimate. This model presents a novel promising method to interpolate between any two experimental results. Comparison of the mean particles size values which are calculated as a function of nozzle temperature (TN) and pre-expansion pressure (Ppre-expansion) with the experimental data, results in a ±8% accuracy. The optimum operational point that leads to the minimum mean particles diameter (40 nm) is determined through mathematical optimization of this equation and confirmed experimentally. Furthermore, 600 more values of mean particle size are predicted by varying the nozzle temperature and dissolution pressure and the results are presented in the form of a 3-dimesional curve.