(220g) A Mechanistic Collision Model for Particle Breakage in Agitated Crystallization Experiments

Demonstrated here is a mechanistic approach to modelling particle breakage behaviour within mechanically agitated crystallization systems, gained from isolating fundamental fluid and particle behaviours. The role of fluid boundary layer effects in altering particle collision rates is coupled with a physical model for particle breakage probabilities. The proposed model combines the effects of fluid properties, operating conditions, particle impact velocities and sizes, and material properties. These factors are grouped into two governing behaviours: Hydrodynamics and Material Response. Firstly, the illustration of a material response boundary is quantified using a data classification technique.

Crystals were accelerated towards a target and impacted at various speeds and across a range of crystal sizes. This allowed construction of a failure probability heatmap, outlining the probability of damage occurring to the crystal after an impact had occurred. From this, the probability of failure for any crystal size and velocity pair was extracted and compared to theoretical forms for the expected failure probability distributions. A Multi Layer Perceptron (MLP) classifier was used to generate deterministic boundaries associated with previously observed experimental breakage data. This provides a clear proof of concept for the material response boundary, resulting in the successful mapping of size-velocity input pairs to expected breakage modes.

Limiting hydrodynamic factors from previous work are also shown alongside the new material response boundary, clarifying the role of both the fluid and solid phases at the macro scale. Through the use of shadowgraphy imaging it was shown that there exists a critical Reynolds threshold, below which collision between particles and an impeller blade is unlikely. Furthermore, those particles that do collide experience only a fraction of the nominal impeller tip-speed. Thus, this gives credit to the presence of a squeeze film boundary layer cushioning impacts at the impeller and around probes/baffles. As a result, the actual impact rate of particles with a typical crystallization system is often much lower than expected as the hydrodynamic conditions serve to protect the crystals from collision events.

From here, a Population Balance (PB) Finite Volume 1 Scheme (FVS) for pure breakage is compared against experimental breakage data for three unique pharmaceutical crystal populations in an agitated liquid-solid suspension.

The hydrodynamic and material response characteristics were combined using a physically relevant rate expression based on the characteristic circulation time of the system. It was found that by isolating important interactions in the system it is possible to construct physically based breakage modelling kinetics, without loss of generality to particulate processing as a whole. Good agreement with the mathematical model was found in all cases, even while each crystal material is chemically distinct.

This indicates that byfirst identifying key process behaviours, via such methods as the MLP classification technique used here, it is possible to construct a generalized particulate behaviour model. As such, this enables one to more accurately capture the behaviour of a range of materials without the need for more involved experimental testing. Importantly, the fundamental nature of the model is scale-independent, general across all materials well-defined by typical elastic moduli (such as Young's modulus and fracture toughness), and accounts for fluid dynamic parameters via a known Reynolds threshold for particle-plane collisions. Therefore, a key application of this methodology lay in process design, optimization, and scale-up where the need to produce reliable predictions in the smallest possible time frame is desirable.