Modeling of precipitation of ultra-fine particles by pressure reduction over CO2-expanded liquids

Abstract

A mathematical model has been developed to describe the process of precipitation of ultrafine particles by pressure reduction over gas (CO2)-expanded liquids. A rapid pressure reduction over a CO2-expanded organic solution, from 30–70 to 1 bar at 303 K decreases the solution temperature by 30–80 K in a very short span of time (0.5–1.5 min), which generates a rapid, high, and uniform supersaturation of the dissolved solute in the solution and facilitates precipitation of ultrafine particles. The model developed in this work estimates the supersaturation attained, nucleation and growth rates obtained during the pressure reduction over CO2-expanded organic solutions, and the particle size distribution of the precipitated particles. Cholesterol has been chosen as a model solute to be precipitated, and acetone has been chosen as a solvent. A new method has been developed for prediction of equilibrium solubility of solute which is affected by a decrease in CO2 mole fraction as well as a simultaneous decrease in solution temperature during pressure reduction. This method combines the semi-empirical approach of using the partial molar volume fraction of solvent in a CO2-solvent binary mixture and solid–liquid equilibrium data for a solute–solvent system. Size distributions of the precipitated particles have been calculated assuming primary nucleation (homogeneous as well as heterogeneous nucleation) and diffusion-limited growth kinetics. The predicted mean average particle sizes are then compared with the size of cholesterol particles precipitated by pressure reduction of a CO2-expanded acetone solution of cholesterol. The particle sizes predicted assuming heterogeneous nucleation are found to be closer to the experimentally observed particle sizes, indicating that the heterogeneous nucleation could be the main mechanism of nucleation, which could occur at the gas–liquid interface of the CO2 bubbling out of CO2-expanded solution during pressure reduction.