Stefan's Problem Applied to Solution Crystallization

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  • Silva José Marcos F.
    Laboratory of Separation Process Development, Faculty of Chemical Engineering, State University of Campinas (UNICAMP)
  • Lopes Carlos E.
    Laboratory of Fermentation Processes, Department of Antibiotics, Federal University of Pernambuco (UFPE)
  • Meirelles Antonio J. A.
    Laboratory of Extraction, Applied Thermodynamics and Equilibrium (EXTRAE), Faculty of Food Engineering, State University of Campinas (UNICAMP)
  • Wolf-Maciel Maria Regina
    Laboratory of Separation Process Development, Faculty of Chemical Engineering, State University of Campinas (UNICAMP)

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A one-dimensional model for the crystallization of a binary or pseudo-binary solution was developed. Usually, the Stefan’s problem is associated with the crystallization of melted solids, in which the energy transfer (heat diffusion) dominates the process. In the present work, the Stefan’s problem was solved for the crystallization from solutions, i.e., a situation in which mass transfer is the most important phenomenon. An analytical solution was obtained for the equation describing the process. From this solution, a mathematical expression for the crystal growth was obtained as a function of time, degree of supersaturation, liquid diffusivity and solution molar concentration. It was also observed that the expression for the crystal growth agrees qualitatively well with experimental data reported in the literature.

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