Mathematical modeling of nucleation and growth of particles formed by the rapid expansion of a supercritical solution under subsonic conditions

The size distribution of fine powders formed during the rapid expansion of supercritical solutions (RESS) depends on the operating conditions, as well as on the geometry of the expansion device. In order to meet product specifications and improve process control, a fundamental understanding of the interplay between nucleation, condensation, and coagulation during this type of expansion is needed. In this work, we model the particle dynamics resulting from homogeneous nucleation, condensation and coagulation during the subsonic expansion of a non-volatile solute in a supercritical fluid inside a cylindrical capillary. The calculations show that subsonic RESS is a very effective technique for producing particles in the 10-50 nm diameter range. The particle formation process is characterized by delayed nucleation, low particle number concentrations, precipitation of a comparatively small fraction of the total solute mass, and by a narrow size distribution. In a few cases where the expansion trajectory enters the fluid's vapor-liquid coexistence region, the particle formation exhibits early nucleation, strong coagulation, and higher particle number concentrations. In order to explain and describe quantitatively the much larger particle diameters found in actual RESS experiments, additional condensation and coagulation processes that occur in the transonic flow field outside the expansion device, and their interaction with this complex flow field, would also need to be incorporated.