Mathematical modeling of aerosol formation by rapid expansion of supercritical solutions in a converging nozzle

Abstract

A mathematical model of nucleation and particle growth during the partial expansion of a dilute supercritical solution in a sub-sonic converging nozzle is presented and solved numerically. The flow is assumed to be steady, one-dimensional and inviscid. The calculations suggest that the partial expansion of supercritical solutions is an effective route to the formation of monodisperse, sub-micron powders. The particle size is a very sensitive function of the temperature at which the solute is dissolved in the supercritical fluid (the extraction temperature), and of the temperature to which the saturated mixture is preheated isobarically prior to expansion (the pre-expansion temperature). Retrograde behavior (a decrease in solubility upon isobaric heating) is a common feature of supercritical solutions. It underlies the three most important trends predicted by the calculations: an increase in particle size upon increasing the pre-expansion temperature; and particle size decrease upon increasing the extraction temperature and pressure.