Mathematical modeling of the mass transfer from aqueous solutions in a supercritical fluid during particle formation

Abstract

A solved mathematical model of the mass transfer between a droplet of water and a gas mixture of supercritical fluid and co-solvent is presented. This model is applicable to the study of the precipitation from drying of aqueous solutions with a supercritical fluid. The model takes into account the two-way mass transfer of water into the gas phase, and of the supercritical fluid and co-solvent into the droplet. The energy balance is also included in the calculations. The resolution of the model allows the determination of the radial profiles of composition and temperature as a function of time, both inside and outside of the droplet, and the variation of the droplet radius with time. The model has been used for the interpretation of experimental results of the precipitation and drying of lysozyme from aqueous solutions with a mixture of supercritical carbon dioxide and ethanol. The phase behavior of the ternary system CO 2–water–ethanol was modeled with the Peng–Robinson Equation of State with Wong–Sandler mixing rule, while mass and energy transport properties were calculated with suitable empirical correlations. The calculations show that the droplet undergoes an initial stage of swelling due to the condensation of ethanol, followed by a decrease in the droplet radius after saturation of the droplet with ethanol and CO 2 due to the extraction. Since lysozyme is poorly soluble in ethanol and CO 2, particle formation may already begin in the initial swelling stage. It was also found that the maximum concentration of ethanol and CO 2 in the droplet is strongly dependent on the initial concentration of ethanol in the gas phase. This could explain the variations in particle morphology observed experimentally when the ethanol/CO 2 flow ratio is varied. Pressure variations only have a small effect on the time required for the complete evaporation of the droplet. An increase in temperature causes a large variation in the saturation composition of the droplet and enhances the evaporation rate.