Understanding solvent-induced phase transformations driven by anomalous mass transfer

Antisolvent crystallisation is a process widely applied within the pharmaceutical industry. It relies on the difference in solubility of a solute in two miscible liquids—the solvent and the antisolvent—to create the supersaturation required for crystallisation to occur [1]. Since local supersaturation values affect the properties of the final product [2], mixing plays a major role in this process. However, mass transfer in this context is not well understood, leading to the formation of unwanted crystal phases or to undesired phenomena such as oiling out (i.e. separation of the solute via the formation of a second liquid phase).
Traditionally, mixing in the microscale has been described through Fick's second law. However, this model considers composition gradients as the driving force for mass transfer, instead of the more physically accurate gradient in chemical potential. Thus, it fails to explain non-idealities such as uphill diffusion [3], which is the diffusion of a species against its concentration gradient. Additionally, this model assumes ideal behaviour, but unwanted phenomena, such as oiling out, can occur when non-idealities lead to unexpected regions of the phase diagram. Thus, developing a model that accurately predicts and describes micromixing is essential for understanding and preventing these undesired events.
In this work, we propose the modeling of an antisolvent crystallisation system through the Cahn-Hilliard phase-field model [4], coupled with either the Fickian or the Maxwell-Stefan diffusion coefficient. The system, in which the appearance of undesired phenomena has been reported, is formed by water, ethanol, and glycine.
Since the Cahn-Hilliard model considers the driving force for mass transfer to be the minimization of the free energy, a better description of the mixing process is expected than through Fickian diffusion. Regarding its comparison with the Maxwell-Stefan model [3], a similar outcome is expected except when
close to the spinodal region, in which the Cahn-Hilliard model will prove to be superior. Since this model considers the interphase free energy, it is suitable for the description of phase changes such as spinodal decomposition. Thus, it is also potentially capable of simulating oiling-out. The simulation results will be
compared to experimental diffusion measurements obtained through Raman spectroscopy, with the expectation that the Cahn-Hilliard model will adjust better to the experimental results.
This framework can greatly enhance our understanding of diffusive mixing processes and liquid-liquid separation phenomena in any chemical process in which diffusion of non-ideal solutions takes place. Ultimately, this will lead to safer, more robust manufacturing of chemical and pharmaceutical products.
References
1. A. Lewis, M. Seckler, H. Kramer, G. van Rosmalen, Cambridge University Press, 2015, 255-256
2. C. Pirkle, L. C. Foguth, S. J. Brenek, K. Girard, R. D. Braatz, Chem. Eng. Process., 2015, 97, 213-232
3. R. Krishna, Chem. Soc. Rev., 2015, 44, 2812-2836
4. J. W. Cahn and J. E. Hilliard, J. Chem. Phys., 1928, 28(2), 258-267