Effect of shear rate on primary nucleation of para-amino benzoic acid in solution under different fluid dynamic conditions

Step-By-Step Standardization of the Bottom-Up Semi-Automated Nanocrystallization of Pharmaceuticals: A Quality By Design and Design of Experiments Joint Approach

Nanosized drug crystals have been reported with enhanced apparent solubility, bioavailability, and therapeutic efficacy compared to microcrystal materials, which are not suitable for parenteral administration. However, nanocrystal design and development by bottom-up approaches are challenging, especially considering the non-standardized process parameters in the injection step. This work aims to present a systematic step-by-step approach through Quality-by-Design (QbD) and Design of Experiments (DoE) for synthesizing drug nanocrystals by a semi-automated nanoprecipitation method. Curcumin is used as a drug model due to its well-known poor water solubility (0.6 µg mL-1, 25 °C). Formal and informal risk assessment tools allow identifying the critical factors. A fractional factorial 24-1 screening design evaluates their impact on the average size and polydispersity of nanocrystals. The optimization of significant factors is done by a Central Composite Design. This response surface methodology supports the rational design of the nanocrystals, identifying and exploring the design space. The proposed joint approach leads to a reproducible, robust, and stable nanocrystalline preparation of 316 nm with a PdI of 0.217 in compliance with the quality profile. An orthogonal approach for particle size and polydispersity characterization allows discarding the formation of aggregates. Overall, the synergy between advanced data analysis and semi-automated standardized nanocrystallization of drugs is highlighted.

The interplay between nucleation and patterning during shear-induced crystallization from solution in a parallel plate geometry

Cooling crystallization of small organic molecules from solution is an important operation for the separation and purification of drug products. In this research, shear-induced nucleation from a supersaturated solution is studied in a parallel plate geometry. Under conditions of shear and small gap sizes, narrow mesoscale circular bands of small crystals appeared spontaneously and reproducibly on the plate's surface. We have investigated the connection between nucleation and the emergence of these circular patterns. Our results show that nucleation occurs preferably in zones with high local shear rate (located at the outer edges of the plates), compared to zones with low local shear rate (at the center of the plates). The time before nucleation occurs decreases significantly for increasing mean shear rate and time. The circular crystalline patterns appear at the plate's surface, where heterogeneous nucleation first occurs. Multiple hypotheses are explored to understand the pattern formation in crystallization. Since no satisfactory explanation is found, a new mechanism is proposed. This hypothesis involves crystals initially forming on the surface of the plates and undergoing stick-slip motion, which influences the local nucleation kinetics. This results in an interplay between (secondary) nucleation and stick-slip motion at the start of the crystallization process. By modifying the surface of the plates, their ability to act as a heterogeneous nucleation site can be altered, allowing control over the formation of patterns.

Machine Learning-Derived Correlations for Scale-Up and Technology Transfer of Primary Nucleation Kinetics

Scaling up and technology transfer of crystallization processes have been and continue to be a challenge. This is often due to the stochastic nature of primary nucleation, various scale dependencies of nucleation mechanisms, and the multitude of scale-up approaches. To better understand these dependencies, a series of isothermal induction time studies were performed across a range of vessel volumes, impeller types, and impeller speeds. From these measurements, the nucleation rate and growth time were estimated as parameters of an induction time distribution model. Then using machine learning techniques, correlations between the vessel hydrodynamic features, calculated from computational flow dynamic simulations, and nucleation kinetic parameters were analyzed. Of the 18 machine learning models trained, two models for the nucleation rate were found to have the best performance (in terms of % of predictions within experimental variance): a nonlinear random Forest model and a nonlinear gradient boosting model. For growth time, a nonlinear gradient boosting model was found to outperform the other models tested. These models were then ensembled to directly predict the probability of nucleation, at a given time, solely from hydrodynamic features with an overall root mean square error of 0.16. This work shows how machine learning approaches can be used to analyze limited datasets of induction times to provide insights into what hydrodynamic parameters should be considered in the scale-up of an unseeded crystallization process.

Microfluidic Platform with Serpentine Geometry Providing Chaotic Mixing in Induction Time Experiments

We present a droplet microfluidic platform mixing the contents of the droplet chaotically in microfluidic induction time measurements, a promising method for quantifying nucleation kinetics with minute amounts of solute. The nucleation kinetics of aqueous potassium chloride droplets dispersed in mineral oil without surfactants is quantified in the presence and absence of chaotic mixing. We demonstrate the ability of the proposed platform to dictate droplet size, to provide a homogeneous temperature distribution, and to chaotically mix the droplet contents. Chaotic mixing in induction time measurements is facilitated by the motion of droplets through serpentine micromixer bends, while the extent of mixing is controlled by how much droplets move. Different nucleation kinetics are observed in experiments where the droplets are static, mixed, and in motion. We hypothesize that the droplet motion induces formation of a thin-liquid Bretherton film surrounding the droplets. The thin film shields droplets from solid boundaries that are more efficient heteronucleant surfaces compared to liquid-liquid interfaces. We observed that repeated microfluidic induction time measurements, particularly with moving droplets, produce significantly distinct cumulative nucleation probability curves, indicating that the measured nucleation kinetics depend strongly on the details of the experimental procedure, which we discuss in detail. Finally, we compare the microfluidic experiments to well-mixed, milliliter volume, turbidity-based measurements in the context of classic nucleation theory.

Self-assembly of millimeter-scale magnetic particles in suspension

Self-assembly is ubiquitous at all scales in nature. Most studies have focused on the self-assembly of micron-scale and nano-scale components. In this study, we explore the self-assembly of millimeter-scale magnetic particles in a bubble-column reactor to form 9 different structures. Two component systems (N-N and S-S particles) assemble faster than one-component systems (all particles have N-S poles) because they have more numerous bonding pathways. In addition, two-components add control to process initiation and evolution, and enable the formation of complex structures such as squares, tetrahedra and cubes. Self-assembly is collision-limited, thus, the formation time increases with the total number of bonds required to form the structure and the injected power. The dimensionless Mason number captures the interplay between hydrodynamic forces and magnetic interactions: self-assembly is most efficient at intermediate Mason numbers (the system is quasi-static at low Mason numbers with limited chances for particle interaction; on the other hand, hydrodynamic forces prevail over dipole-dipole interactions and hinder bonding at high Mason numbers). Two strategies to improve yield involve (1) the inclusion of pre-assembled nucleation templates to prevent the formation of incorrect initial structures that lead to kinetic traps, and (2) the presence of boundaries to geometrically filter unwanted configurations and to overcome kinetic traps through particle-wall collisions. Yield maximization involves system operation at an optimal Mason number, the inclusion of nucleation templates and the use of engineered boundaries (size and shape).

Inclusion of shear rate effects in the kinetics of a discretized population balance model: Application to struvite precipitation

The effect of mixing in the modelling of processes based on mass transfer phenomena is commonly ignored in wastewater treatment industry. In this contribution, the effect of the average shear rate in the nucleation and growth rates of struvite is analyzed by combining experimental data with simulation results obtained with a previously presented mass-based discretized population balance model. According to the obtained results, the effect of the average shear rate is identifiable for the selected data and mechanisms. Therefore, it should be considered when a detailed modelling of the process is needed. Consequently, in this contribution, the average shear rate has been decoupled from the kinetic constants. In addition, kinetic rates where it is explicitly included as a power law function have been proposed. The exponents in these power law functions for the primary homogeneous nucleation and growth are 1.3 and 0.3, respectively. Considering shear rate effects allowed to see in the simulation outputs experimentally observed effects: a faster pH decay and smaller particle distribution for increasing mixing intensities.