Idealized Mathematical Model for Pharmaceutical Powder “Micronization” Using Compressed Gas Antisolvent (Re-)Precipitation (GASP): Predicted Performance for the Model Ternary System: Phenanthrene/Toluene/CO₂

Abstract

We consider pharma-motivated processes in which compressed gas (here, CO2) is employed as an “anti-solvent” (AS), causing drug particle (re)­precipitation from an injected presaturated organic solvent microdroplet assumed to be molecularly well-mixed at each instant. It is shown that conditions leading to appreciable homogeneous particle nucleation in this “expanded supersaturated liquid” environment can be sufficiently short-lived that they preclude appreciable particle growth because of encounters with solute molecules or other precipitate particles. This leads to relatively narrow predicted precipitated particle size distributions (PSDs), with a characteristic particle size determined by the typical critical nucleation size. Our mathematical techniques, which exploit the method of characteristics (MOC), make no presumption about PSD-shape and our numerical simulations employ realistic thermophysical properties for the previously studied model system: phenanthrene (surrogate “active pharmaceutical ingredient” [solute], toluene [solvent, S], and compressed CO2 [AS]). We explicitly consider initial solvent droplet diameters in the micrometer range and CO2 pressures of 52–64 bar and demonstrate the necessity of relaxing frequently made approximations (e.g., nucleation with constant surface energy, negligible Gibbs–Kelvin–Ostwald solubility corrections, solute diluteness, ...). Our new methods/parametrizations/performance results for this mathematical model should already help select optimal GASP/SASP operating conditions, and, with suitable extensions, ultimately lead to the development of nearly equally tractable yet sufficiently complete process models.