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

A. Martín, A. Bouchard, G. W. Hofland, G. J. Witkamp, M. J. Cocero*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


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 CO2-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 CO2 due to the extraction. Since lysozyme is poorly soluble in ethanol and CO2, particle formation may already begin in the initial swelling stage. It was also found that the maximum concentration of ethanol and CO2 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/CO2 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.

Original languageEnglish (US)
Pages (from-to)126-137
Number of pages12
JournalJournal of Supercritical Fluids
Issue number1
StatePublished - May 1 2007
Externally publishedYes


  • Lysozyme
  • Peng Robinson Wong Sandler EOS
  • Phase equilibrium modeling
  • Simulation

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Materials Science (miscellaneous)
  • Physics and Astronomy (miscellaneous)


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