J. of Supercritical Fluids 41 (2007) 126–137 Mathematical modeling of the mass transfer from aqueous solutions in a supercritical fluid during particle formation A. Mart´ ın a , A. Bouchard b , G.W. Hofland b , G.-J. Witkamp b , M.J. Cocero a,∗ a Departamento de Ingenier´ ıa Qu´ ımica y Tecnolog´ ıa del Medio Ambiente, Facultad de Ciencias, Universidad de Valladolid, Prado de la Magdalena, 47011 Valladolid, Spain b Laboratory for Process Equipment, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands Received 21 December 2005; accepted 9 August 2006 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. © 2006 Elsevier B.V. All rights reserved. Keywords: Simulation; Phase equilibrium modeling; Peng Robinson Wong Sandler EOS; Lysozyme 1. Introduction Proteins are important therapeuticals and their stabilization is essential as they can undergo a variety of chemical and physical degradation reactions. Generally, the long-term storage stability of proteins is greatly enhanced when formulated as a dry rather than a liquid product. However, the transformation of liquid for- mulations into dry products is challenging since the conventional freeze- and spray-drying techniques can cause harmful stresses on the proteins. Supercritical fluid (SCF) drying can be an attrac- tive alternative because this technology allows carrying out the drying under mild conditions, thus avoiding the degradation of the proteins. Other advantages of the SCF drying technology are ∗ Corresponding author. Tel.: +34 983 423 174; fax: +34 983 422 013. E-mail address: mjcocero@iq.uva.es (M.J. Cocero). the cost effectiveness and the ease of scaling-up [1]. With this approach, the protein of interest is dissolved in a suitable sol- vent, and the solution is sprayed into SC-CO 2 . The evaporation of the solvent causes the precipitation of the protein. It can be seen that this process is similar to the relatively well-known SCF micronization processes [2]. A major difference between these processes arises from the fact that despite the poor solubility of water in supercritical carbon dioxide (SC-CO 2 ), the production of protein powders from aqueous solutions is favored over dry- ing from organic solutions, as organic solvents can affect the protein stability and might be poor at dissolving proteins. With the operating conditions commonly used in SCF micronization processes, the organic solvent and SC-CO 2 are completely mis- cible. In contrast, in the SCF drying process the solvent (water) and SC-CO 2 are only partially miscible. For this reason, the atomization of the solution and the mass transfer between the droplets and the gas are likely to have more influence on the SCF 0896-8446/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.supflu.2006.08.015