Wet milling in rotor-stator mixers to reduce crystal size is an emerging practice with significant potential in crystallization and milling of active pharmaceutical ingredients. The complexities of crystal breakage behavior, the turbulent nature of flow, and multiscale geometry in rotor-stator mixers have limited the understanding of the milling process in these devices. The purpose of this work is to investigate the effect of milling conditions, crystal physical properties, and mixer geometry on the milling behavior of crystals, and to introduce a mechanistic framework on which to base mill design, scale up, and operating strategies.

A Silverson L4R rotor-stator mixer with a square-hole stator head was used to conduct systematic wet milling experiments. Three mill head geometries were studied. There are inline units with a standard shear gap (clearance between rotor and stator) and an enlarged shear gap, and a batch unit with a standard shear gap. Three different crystals with different elastic modulus, hardness, and fracture toughness were milled in an anti-solvent. Rotor speed and volumetric throughput were adjusted independently to vary energy input and mill head residence time. The milling rate was found to increase with higher rotor speed and lower throughput, while the ultimate particle size (maximum particle size at the end of milling) was only dependent on rotor speed. The effects of fluid agitation, particle-particle collisions, and particle-wall collisions on crystal breakage were assessed by changing particle concentration, coating the stator surfaces, and reducing rotor diameter. It was found that the concentration of particles in the slurry has a limited effect on milling rate and negligible effect on ultimate particle size. The effect of higher power input and smaller dispersion zone volume (the volume of the shear gap and stator hole regions), through changes to the mixing head geometry, showed to be more successful in concentrating the energy input, and hence, leads to higher milling rates and smaller ultimate particle size.

To quantitatively explain the experimental results, a class of mechanistic models for crystal breakage were developed that consider the influence of plastic deformation, elastic deformation, and fracture toughness on breakage resistance. These models are in agreement with classical grinding theories. Based on the particle size scale, two classes of disruptive forces were studied considering either macroscale velocity (proportional to rotor tip speed) or inertial subrange turbulent eddy velocity (given by Kolmogorov’s inertial subrange model). Four cohesive force definitions were studied, each with different dependence on physical properties and particle size. The disruptive and cohesive forces were employed to construct eight different correlations for ultimate crystal size and its rate of approach. Model discrimination is based on comparison to the wet milling experimental data. The best-fitting model was based on the combination of inertial subrange model as the disruptive force and elastic-plastic deformation model as the cohesive force.

For geometrically similar devices, a dimensionless comminution number was developed (ratio of disruptive to cohesive forces) to aid physical interpretation and scale up/down efforts. For devices without geometric similarity, the concept of local energy dissipation rate, defined as the power draw of the mixer per mass of fluid in shear gap and stator slot regions (calculated through computational fluid dynamics simulations), was introduced and exploited to compare the data from different mixers with different geometries. This approach was successful in correlating the maximum stable particle size resulting from wet milling of different crystals in a Silverson L4R inline mixer with standard and enlarged shear gap, and in a Silverson L4R batch mixer at different rotor speeds.

The mechanistic theory is further utilized to provide breakage kernels based on probability of collision and collision rate theories. Application of the breakage functions to predict the milling rate as well as their implementation within a population balance framework is discussed.