Correlating mean particle size of pure solids in supercritical antisolvent processes using dimensional analysis with the Buckingham π-theorem

In supercritical antisolvent processes, two correlations have been proposed to estimate the mean particle size of precipitated pure solid compounds. These easy-to-use correlations, each with six adjustable coefficients were developed by applying dimensional analysis based on the Buckingham π-theorem, relating the particle size to feeding, thermodynamic, and mechanical process parameters. These correlations can help in scaling-up microparticle production processes; however, they do not conceptually explain the influence of process parameters on particle sizes, and remain limited by the experimental available data. The two correlations are differentiated by employing either solute supersaturation data or molar volumes of CO₂+solvent systems. These correlations were evaluated by testing seventeen ternary systems, with deviations from experimental values ≤ 88 %. They proved capable of correlating all solutes grouped by the same solvent. Pilot-scale data were estimated using coefficients adjusted with laboratory-scale data. Finally, the correlations successfully reproduced the particle size as a function of temperature and pressure.