(4bo) The Study of Micromixing and Phase Transition Phenomena in Pharmaceutical Processes: A Phase-Field Modelling and Raman Microscopy Approach

Introduction

Anti-solvent crystallization is a widely used purification method in the pharmaceutical industry, which exploits the difference in solubility of a solute in two miscible liquids: a solvent and an anti-solvent [1]. In this process, the local values of the supersaturation are dictated by the local compositions. Variations in the supersaturation can greatly affect the properties of the final crystalline product, and, consequently, mixing plays a major role in these processes. Unfortunately, mass transfer is not well understood in these systems, often leading to the formation of unwanted crystal phases or to undesired phenomena such as liquid-liquid phase separation (LLPS) (i.e. the separation of the solute via the formation of a secondary liquid phase).

Traditionally, mixing at the microscale has been described through Fick’s law, which considers composition gradients to be the driving force for mass transfer, instead of the thermodynamically accurate chemical potential. This significant limitation prevents this model from correctly describing more nuanced aspects of mass transport, such as "uphill diffusion" [2] — the diffusion of species against its concentration gradient — which is important in anti-solvent crystallization. More realistic models can be employed, such as the less common Maxwell-Stefan, which is based on chemical potential gradients. Nonetheless, these approaches still cannot adequately describe anti-solvent crystallization as they do not consider the contribution of the interfaces within a system to the free energy, and, thus, to the species chemical potentials and mass transfer. Interfaces can appear when new phases nucleate, such as in unwanted phenomena like LLPS, which arise as non-idealities in the system lead it towards unexpected regions of the phase diagram (see Figure 1(a)).

For these reasons, these models clearly do not suffice when it comes to the modelling and description of microscale mass transfer in crystallization systems, which inherently involve multiphase phenomena. Developing a model capable of doing so is crucial for the understanding and prevention of unwanted phenomena.

Also preventing the complete understanding of anti-solvent crystallization is the lack of accurate thermodynamic data and detailed mixing measurements, which is one of the main bottlenecks for the application of more accurate models, such as phase-field models, to the pharmaceutical field. Traditionally, mixing behavior has been reported in the form of Fickian diffusion coefficients, vastly reducing a complex phenomenon to a simple, but not always representative number, and increasing the difficulty of describing the system through a simplified model.

In this work, we propose a model of nucleation and LLPS based on a combination of the coupled Cahn-Hilliard/Allen-Cahn (CHAC) phase-field model [3] with a nucleation model. Phase-field models have been extensively applied in materials science to describe precipitation and growth [4]. They base their dynamics on the free energy functions of each phase of the system, thus including in their description the interfacial free energy. This provides a much more solid thermodynamic base for modelling multiphase mass transfer, making these models robust candidates for the description of this phenomenon in the crystallization field. In this context, this work focuses on the modelling of liquid-liquid phase separation in a salicylic acid-acetonitrile binary system, studying the influence of the different model parameters on process outcomes. Particularly, the effects of the interfacial free energy coefficient, the CHAC mobilities, and the minima of the phase free energy curves will be investigated.

To support the modelling work, we have also conducted experimental mixing studies in a microfluidic device, using Raman microscopy to map diffusive mixing in ethanol-water mixtures of different compositions. We propose a new standard manner for reporting mixing data, in the form of space-resolved composition maps. These effectively constitute digital fingerprints of the mixing process, and information, such as Fickian diffusion coefficients, can be easily extracted from them.

Methodology

2D phase-field model simulations were performed, using the PRISMS library [5], coupling the Wheeler, Boettinger and McFadden (WBM) nucleation model [6] with the CHAC dynamics. Adaptive meshing and periodic boundary conditions were selected. The nucleation constants of the model were estimated through already available kinetic data for salicylic acid-acetonitrile mixtures undergoing LLPS (see Figure 1(b) (left)), following the method outlined in [7]. The remaining model parameters are estimated through optimization with available in-line images of the evolution of the system, by extracting the phase fraction and the percentiles of the particle size distribution.

The setup for the experimental micromixing studies was formed by a Harvard Apparatus PHD ULTRATM 4400 remote syringe pump, used to infuse liquid from two Hamilton Gastight 1/4-28 UNF glass syringes connected via PTFE tubing to a hydrophilic glass Y-junction chip. The channel volume and length are 0.2µL and 12.5mm, and its depth and width are 100 µm×205 µm, respectively.

Raman spectra were captured using the Horiba XploRA+ confocal Raman microscope. Linear maps were obtained by collecting spectra in 5 µm steps in the direction perpendicular to the flow every 1250 µm along the channel length, building a 2D map of the mixing process. The spectra were collected using a 532 nm laser through a 50x objective with an acquisition time of 3 s and a grating of 1200 gr/mm. They were converted into composition values through fitting with a partial least-squares method. The resulting maps, which capture the evolution of the mixing process along the microchannel, are fed to an optimization loop that allows the estimation of the Fickian diffusion coefficients.

Results and discussion

The composition and phase-variable maps obtained from the phase-field model simulations, a sample of the latter given in Figure 1(b) (right), prove the far higher suitability of this approach to describe nucleation and LLPS in the microscale within crystallization systems in comparison to more common diffusion models. The qualitative comparison of the simulated maps and the available experimental images provide sufficient reason to believe in the feasibility of this approach for the parameter estimation of the model.

The experimental microfluidic composition maps, an example of which is presented in Figure 1(c) (right), show a steady mixing of ethanol and water solutions, with the vertical composition profile flattening progressively along the channel due to the increased contact time. Additional composition maps have been captured for ethanol-water mixtures at different compositions and flow rates, as summarised in Figure 1(d). Preliminary results show an error <5% between literature and experimental values for the Fick diffusion coefficient of ethanol-water mixtures. The experiments also show the formation of an interface that disappears gradually, as seen in Figure 1(c) (left). This most likely corresponds with the laminar flow diffusion interface, commonly observed between co-flowing liquids in microfluidic systems [8]. The Raman maps allow us to monitor the composition of the interface as the liquids mix, albeit with a certain unavoidable uncertainty, especially at the edges of the microchannel, due to the complexities and nuances of the setup. Nonetheless, they successfully prove the feasibility and usefulness of the methodology, and its great potential for future applications to more complex systems.

Conclusions

In this work, we prove the suitability of describing mass transfer in binary crystallization systems through the CHAC phase-field models in combination with WBM nucleation, given the similarities between the simulated and experimental evolution of a salicylic acid-acetonitrile system. A workflow to identify the required model parameters is proposed, consisting on a combination of kinetic data and optimization via the comparison of relevant key performance indicators obtained from available experimental data. Finally, a novel experimental setup is proposed as a means of conducting information-rich mixing studies, that could be used in the future to further fit these models for multicomponent, multiphase systems. The versatility of these maps is proven by extracting Fick’s diffusion coefficient for ethanol-water mixtures, with preliminary results indicating an error <5%. Overall, the proposed modelling and experimental framework has the potential to greatly enhance our understanding of mixing processes and LLPS in any chemical process involving diffusive mixing of non-ideal solutions. Ultimately, this will lead to safer, more robust manufacturing of chemical and pharmaceutical products.

References

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