Understanding nucleation and oiling out through phase-field modelling

Abstract
Antisolvent crystallisation is a process widely applied within the pharmaceutical industry, reliant on the difference in solubility of a solute in two miscible liquids—the solvent and the antisolvent—to create supersaturation [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 undesired outcomes such as unwanted crystal phases or oiling out.
Mixing in the microscale is commonly described through Fick’s second law. However, this model considers composition gradients as the driving force for mass transfer, failing to explain non-idealities such as uphill diffusion [3]. Additionally, it assumes ideal behaviour, while the unwanted phenomena mentioned occur when non-idealities lead the system to unexpected regions of the phase diagram.
In this work, experimental micromixing studies of mixtures formed by water, ethanol and glycine are conducted, using Raman microscopy to generate composition maps of these binary and ternary systems. The maps are then used to compare the accuracy in predicting the mixing behaviour of two models: Fickian diffusion and a combination of the Cahn-Hilliard phase-field model with Maxwell-Stefan diffusion (CaHiMaS). The latter considers the minimization of the system’s free energy as the mass transfer driving force, can model non-ideal solutions and considers the interfacial free energy. Thus, it can potentially model the oiling-out phenomenon. Therefore, the hypothesis tested is that the CaHiMaS model and Fick’s law will adjust similarly to binary systems, while the former will allow to model the non-idealities and phase transformations in the ternary system.
This framework can greatly enhance our understanding of diffusive mixing processes and liquid-liquid separation phenomena in any chemical process involving diffusion of non-ideal solutions. Ultimately, this untapped knowledge will lead to safer and more robust manufacturing of chemical and pharmaceutical products.
References
[1] Lewis, A., Seckler, M., Kramer, H., van Rosmalen, G., Industrial Crystallization: Fundamentals and Applications. Cambridge University Press, 2015.
[2] Pirkle, C., et al. "Computational fluid dynamics modeling of mixing effects for crystallization in coaxial nozzles", Chem. Eng. Process., 97 (2015): 213-232.
[3] Krishna, R. "Uphill diffusion in multicomponent mixtures", Chem. Soc. Rev., 44 (2015): 2812-2836.
[4] Cahn, J. W. and Hilliard, J. E. "Free Energy of a Nonuniform System. I. Interfacial Free Energy", J. Chem. Phys., 28.2 (1928): 258-267.