(146c) Modelling Diffusive Mixing in Antisolvent Crystallisation

Mass transfer plays an important role in many chemical processes, and it is essential to develop a better fundamental understanding, in order to design more efficient processes. This paper focuses on the molecular diffusion aspect of mass transfer and on diffusive mixing in the context of anti-solvent crystallization processes. In anti-solvent crystallization, the mixing of the solution and anti-solvent has a significant impact on local compositions and, hence, the local supersaturation profiles. Crystal nucleation and growth rates are sensitive functions of supersaturation, and, therefore, the resulting crystal properties, such as crystal size distribution and shape, are dependent on the supersaturation. Thus, the control of mixing is crucial for an effective crystallization process.

Mixing can occur via two main mechanism - diffusive and advective. Diffusion can be described as mixing at a molecular level and occurs via random thermal motion (i.e brownian motion), while advection is mixing at a bulk scale. At small length scales or at laminar flow conditions, the mass transport is diffusion dominated, and easier to control. This can be applied to microfluidics¹, which offers high level of control over mixing, and thus crystal properties. In turbulent mixing, regions or layers exist in which there is a larger concentration gradient than in the bulk fluid. At small length scales, mixing is diffusion controlled within these layers, and a better understanding of diffusion will assist in the development of industrial anti-solvent processeses

In previous work, researchers^2,3 have modelled the mixing step during anti-solvent crystallization processes using approaches based on Fickian diffusion. In this work, mixing is modelled using Maxwell-Stefan diffusion, where species activities, rather than concentrations, act as the driving force. This model was then used to investigate the effect of activity on diffusive mixing with respect to local solution composition and the corresponding supersaturation profiles. Using the extended Scatchard-Hildebrand activity model, phase diagrams are calculated allowing for the possibility of spinodal decomposition two liquid phases during mixing.

Methods

We study ternary solutions of water (solvent), glycine (solute), and ethanol (anti-solvent). The diffusive mixing occurs in a static microfluidic channel, with advective considered negligible. Figure 1(a) shows the initial composition of the channel in terms of volume fraction. The multi-component Maxwell-Stefan⁴ equations were solved via the finite volume (FiPy v3.4) method to determine spatial-temporal volume fraction profiles over a range of conditions for the model system. From the volume fraction profiles, supersaturation profiles can be generated from solubility data for glycine in water-ethanol mixtures (Figure 1(b)).

Figure 1: (a) Initial composition profile, and (b) solubility of glycine in water/ethanol mixtures.

The mixing process was modelled for both ideal and non-ideal – in the case for non-ideal, regular solution theory was used to determine the activity coefficient of components in the system. Diffusion in ideal and non-ideal liquid mixtures were compared to highlight qualitative differences. Parametric sensitivity analysis was performed to determine how the variation of diffusion coefficients impacted diffusive fluxes and local supersaturation profiles. The role of antisolvent choice on diffusive mixing will be investigated through the consideration of various antisolvents, e.g. Methanol and propanol.

Results

Diffusive mixing was simulated for a ternary component antisolvent system consisting of water (solvent), ethanol (antisolvent) and glycine (solute). To investigate the role of activity gradients on diffusion, mixing was examined for both ideal and non-ideal solutions, with Figure 2 offering a comparison of the qualitative behaviors. Figure 2(a) shows the magnitude and location of the ‘peak’ supersaturation within the channel. Each dot represents a time step of 1 second. In the ideal solution (green), the driving force is the composition gradient, resulting in glycine diffusing into the anti-solvent. A large overshoot in supersaturation is predicted, due to the low solubility in the anti-solvent mixture. As mixing proceeds, this overshoot collapses, and the final, fully mixed supersaturation limit is approached. When the activity gradient is considered as the driving force (pink), key differences are observed. Glycine no longer diffuses into the anti-solvent and instead retreats into the solution. The interdiffusion of anti-solvent and solution generates supersaturation, however, the overshoots seen previously are absent. Ideal and non-ideal solutions predict substantially different conditions for crystallization.

Solvent-solute interactions can influence crystal properties, and as a consequence, the local composition becomes an important consideration. To gain insight into how activity impacts local composition profiles, the composition of the peak supersaturation was plotted on a ternary diagram (mass) with respect to time, Figure 2(b). This further emphasizes the effect of activity on mixing. The non-ideal model predicts that the peak supersaturation, and hence the most probable region for nucleation, occurs on the solution side. The opposite is observed for ideal solutions. For non-ideal solutions, spinodal decomposition is also predicted to occur, further complicating efforts to control nucleation. These were plotted for the results of parametric study undertaken on the diffusion coefficients to explore the range of predicted behaviors. These ternary plots gave insight into the effect of antisolvent choice on diffusive mixing in terms of the magnitude and composition of the peak supersaturation and the prediction of liquid-liquid demixing.

Figure 2: (a) Plot showing position and value of the peak supersaturation within the channel with respect to time. With each dot representing a time step of 1 second. Arrows show movement direction of peak. (b) Compositional trajectory of the 'peak' supersaturation during diffusive mixing shown on ternary phase diagram. The green line shows Ideal diffusion, while magenta shows non-ideal diusion. Purple and green crosses indicates starting point of diffusion, and the fully mixed composition is shown with a black cross. The orange crosses indicate where simulations were stopped due to the path hitting the spinodal region. A mixed anti-solvent was used (80% ethanol & 20% water by mass), and equal amounts of water and ethanol were initially present within the channel. The initial solution supersaturation was 0.85.

Conclusions

A thermodynamically consistent diffusion model for multi-component systems has been analyzed to improve our understanding of the influence of diffusive mixing and its effect on anti-solvent crystallization. It is hoped that this will assist in the design of crystallization processes, by allowing for a screening of process conditions to control supersaturation profiles that provide better control over anti-solvent crystallization processes. These models were applied to various systems to gain insight into the role of solvent choice on the mixing step in anti-solvent processes.