Limiting Conditions for Crystal–Crystallizer Collisions - American

Article Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Particle Breakage: Limiting Conditions for Crystal−Crystallizer Collisions Rory Tyrrell,* Brian De Souza, and Patrick J. Frawley Synthesis and Solid State Pharmaceutical Centre (SSPC), Bernal Institute, University of Limerick, Limerick, Ireland ABSTRACT: Two prominent theories surround the origin of secondary nuclei in batch crystallization experiments. Traditionally, the generation of secondary nuclei has been attributed to attrition breeding, resulting from collisions between crystals, impeller, and vessel geometry. Mechanistically, it is assumed that the collision of crystals leads to the generation of fine particles and nucleation sites. More recently, an alternative mechanism has received considerable attention, namely, cluster breeding secondary nucleation whereby the source of fine particles is attributed to clusters in solution. In the present work, a detailed experimental investigation of particle wall collisions of active pharmaceutical ingredient crystals is conducted. A pressurized test rig was developed whereby crystals in suspension were fired through a nozzle perpendicular to a stainless steel target. Using shadowgraphy, direct imaging particle-plane collisions are captured for crystals between 100−400 μm as they approach a target surface with initial velocities of up to 10 m/s. Crystals approaching a target surface are seen to be cushioned by a squeeze film boundary layer, greatly reducing their impact velocities. Furthermore, below a critical freestream particle Reynolds number, complete particle arrest was observed, preventing contact with the target surface entirely. This work provides further evidence to suggest that indeed secondary nucleation cannot be accounted for through particle−impeller breakage events. The alternative crystal breeding ideology is therefore further supported.

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INTRODUCTION Throughout the pharmaceutical industry, crystallization is used in order to produce active pharmaceutical ingredients (API) that are of the desired purity and polymorph and with a specified size and shape distribution, all of which contribute to the efficacy of the final drug product. The particle size distribution (PSD) is particularly relevant to bioavailability, with strict specifications on particle size commonly set by the governing drug regulatory authority. The crystallization PSD can also impact downstream pharmaceutical manufacturing unit operations such as isolation, drying, and tableting. The ability to control the particle size distribution, particularly when scaling processes from laboratory to industrial scale, is therefore a critical scientific and industrial challenge. Population balance (PB) based model predictions of the PSD evolution rely entirely upon kinetics to represent each of the mechanisms of the crystallization process. A detailed understanding of the underlying nucleation, both primary and secondary, growth, agglomeration, and breakage processes is thus essential to facilitate accurate modeling, allowing for tailoring of the PSD and to reduce the risk of batch failures. Secondary nucleation refers to the birth of nuclei at the interface of the parent crystals; the presence of at least one primary crystal is required and occurs at low to moderate levels of supersaturation. The issue of secondary nucleation has been the subject of much increased research attention in recent years. While the precise mechanism by which secondary nucleation occurs has eluded the scientific community, traditionally the formation of secondary nuclei has been largely attributed to contact nucleation or attrition breeding. Contact breeding © XXXX American Chemical Society

results from particle collision events such as collisions between particles and impeller blades, between crystals and vessel walls and mutual collisions between particles. The formation of secondary nuclei, which appear as fine particles, is attributed in this mechanism to attrition of the crystal corners, edges, and macro-steps on the crystal surface.1−5 An alternative mechanism has been proposed for secondary nucleation whereby the secondary nuclei do not originate from the crystal surface itself, but from clusters in solution making contact with a preordered layer adjacent to the crystal surface. These clusters are loosely bound to the parent crystal and can be easily sheared and thus act as new nuclei. The potential recursive nature of this mechanism lend to its description as autocatalytic. Recent molecular dynamic simulations conducted by Anwar et al.6 have elucidated this mechanism in detail. Furthermore, experimental studies carried out within our own research group have also provided significant supporting experimental evidence for the cluster breeding secondary nucleation mechanism.7 The focus of the present work is to specifically examine the issue of particle−plane collisions in order to discern whether or not such collisions can account for the rapid generation of particles, in seeded batch crystallization experiments at moderate supersaturations. Previously, the substantial increase in particle count would have been associated with the secondary nucleation attrition breeding mechanism. Should Received: January 25, 2017 Revised: October 2, 2017

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DOI: 10.1021/acs.cgd.7b00125 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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film in time. A clear way to interpret this effect is to apply a mass conservation to the control volume:

collision breeding be unable to account for the rapid increase in particle count, it adds further evidence to support the cluster breeding ideology. Presented here is a detailed study of a generalized particle− plane interaction. The study focuses primarily in the area of particle−impeller interactions due to the more aggressive nature of a stirred impeller when compared to the flow around probes or baffles. Previous studies demonstrating particle− plane collisions at speeds consistent with industrial-scale impeller tip speeds have been conducted;2,8,9 however, particle sizes used in these studies ranged from 800 μm to 2 mm. Such particle size would be challenging to find throughout the pharmaceutical sector, with particle sizes rarely exceeding 800 μm during product crystallization, with final API products often milled to even smaller particle sizes. Clark and Burmeister10,11 reported on the effect of a boundary layer cushioning particles in experimental work with steel and glass spheres. In order to accurately study the effect of the impeller boundary layer on approaching crystals during stirred batch crystallization, it was necessary to carry out investigations using a more representative class of particle sizes. It was proposed that shadowgraphy imaging, a unique imaging platform based on the use of a high speed camera and planar illumination source, be used to allow for the direct observation and quantification of particle sizes and velocities in close proximity to the collision surface. The principle goals of the experimental work were to elucidate the effect of the squeeze film boundary effect, if any, on approaching particles; to investigate the potential for planar collisions; and to determine limiting criteria for collision events.

−πR2Vp = 2πRhVav

(1)

Evidently, the rate at which a particle can approach a target surface is directly linked to the rate at which fluid can escape the bounded cavity between them. The solution for Vp above can be found in ref 11. However, given briefly the extent to which particle−plane collisions are softened by this squeeze film is inversely proportional to the particle−fluid density ratio and freestream particle Reynolds number. Therefore, by simultaneously measuring particle sizes and velocities, it would be possible to determine the link between particle Reynolds numbers and squeeze film particle arrest experimentally.

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EXPERIMENTAL METHODS

Impact Tester. In order to quantify the effect of the squeeze film boundary layer, a shadowgraphy particle tracking technique was used to directly image particles as they approach a target surface with a specified inlet velocity (Figure 2). Individual particle tracking is

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SQUEEZE FILM BOUNDARY LAYER The theoretical foundations for predicting the cushioning-effect of squeeze films has been well documented in the literature.10−15 The squeeze film boundary layer can be considered as a volume of fluid that must “escape” the volume trapped between an approaching particle and the target surface. Illustrated in Figure 1 is this control volume trapped between the target surface and the approaching particle, with an equivalent cylinder used to simplify the definition of the control volume.

Figure 2. Impact testing schematic. enabled via a peak-searching algorithm tailored to identify specific particle sizes and shapes in a captured image sequence. Initial particle velocities of 1.0−10 m/s, consistent with those of impeller tip speeds, were developed through use of an impingement-jet of suspended particles accelerating particles toward the target surface. Now, rather than the impeller blade impacting the particles, the particles are “injected” at the impeller tip speeds, and their velocity can be tracked as a function of distance to the blade surface; the relative velocities of the particle−plane interaction remain equivalent, however. Furthermore, the constant inlet velocity ensures particle drag does not slow the particle to its terminal velocity before measurement can begin. In addition to this, the inlet nozzle was kept at a constant 10 mm distance from the target plane in order to ensure an approximately constant flow velocity normal to the target surface. Therefore, any measured particle deceleration is solely attributable to the squeeze film boundary layer interaction between the particle and target surface. The testing mechanism utilized a particle−fluid solution held at a desired pressure and released through a nozzle into the test chamber. A highspeed control valve allowed the inlet velocity of particles to be controlled accurately. Direct measurement of particle impact velocities can then be gained from the shadowgraphy imaging technique. Crystals of paracetamol (A5000 acetaminophen) were suspended in a saturated solution of deionized water as the use of solvents, or indeed nonsolvent suspension fluids, was seen to be unnecessary under the assumption that dimensionless parameters such as Reynolds and Stokes numbers can be correlated regardless of the choice of liquid phase (Table 1). A stainless steel target was used in order to accurately represent a typical industrial-scale impeller blade; however, the material properties of the target surface have a very minimal effect

Figure 1. Spherical particle approaching the target wall. Note the equivalent cylinder (dashed lines) used to denote distance, h, to the plane.

Looking at Figure 1, it is clear that the displacement of fluid from this control volume will extract a considerable amount of work from the approaching particle, thus reducing its velocity. Furthermore, considering that the suspension phase here is liquid water, the assumption of constant density is implicit. Therefore, with compressibility effects negated, the particle must be slowed to allow for the fluid to escape from the squeeze B

DOI: 10.1021/acs.cgd.7b00125 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Table 1. Experimental Conditions for Particle and Solvent Phases acetaminophen (A5000) 3

density [g/cm ] solubility16 [g/kg]

1.297 10.97

deionized water 3

density [g/cm ] temperature [°C] dynamic viscosity [Pa·s]

1.0 15 1.1344 × 10−3

on the magnitude of the cushioning effect. It was considered that polytetrafluoroethylene targets be employed in order to reflect laboratory-scale reactions; however, the harder stainless steel targets were deemed to provide a harsher environment and thus a more stringent test of any collision events. Impact angles were chosen as a “worse-case” scenario at 90°, as a more oblique angle of impact would merely result in greater deflection of incoming particles. Therefore, the conditions under which the impacts were carried out are representative of the most aggressive conditions a particle could come to expect in practice. Thus, if breakage remained unseen in theses cases, it could easily be stipulated that it would also not occur under the majority of similar crystallization processes. Furthermore, crystals used here are within a nominal range of 100−400 μm, representative of typical paracetamol size distributions in stirred, isothermal, batch crystallizations. Shadowgraphy Technique. In the shadowgraphy imaging technique, the fluid jet is uniformly backlit and the resulting particle silhouettes are tracked though an image inversion process. Particle velocity vectors and sizes can be determined and tracked through the entire capture sequence. Images are acquired via long-range microscopy coupled with a high-speed camera capable of capturing images at over 50,000 Hz, providing excellent temporal resolution for particles approaching at high initial speeds. Using this method, it is possible to track particles down to 1 μm in resolution, allowing precise measurement of both the parent crystals and any possible fragments resulting from collision with the target surface. As the raw image being captured is of particle silhouettes, a highquality background image must first be taken in order for an image inversion process to yield a photographic negative that transforms particle shadows to light-intensities; this process is outlined in Figure 3. Through this inversion, a peak-searching algorithm can then identify particle boundaries, and calculate sizes and velocities between sequential frames.

Figure 4. Shadowgraphy global segmentation (particle identification).

Figure 5. Shadowgraphy secondary segmentation (particle filter). In this case, the particle is either above or within the high- and lowpass bands, i.e., the particle is sufficiently focused. The limits of these high- and low-pass filters are tuned manually and should be fixed at a point where, ideally, all background particles are neglected and only the particle of interest is tracked. As an additional step, image noise is reduced by normalizing the camera sensor before each capture sequence, and background noise is reduced by averaging a background reference image over 10 images in order to yield a more uniform background image. Specific particle sizes can also be filtered to eliminate any remaining micron-scale noise being misrepresented as particles and affecting subsequent image calculations. Furthermore, particles can be filtered by area, minimum or maximum diameter, circularity, and velocity in order to filter out any unwanted data. Individual particle velocities are found quite readily as each particle’s location is known between frames, and the time-step value is fixed by the image capture rate known to the system.

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RESULTS AND DISCUSSION Particle Size Effect. As is evidenced in Figure 6, the velocity gradient proved to be largely independent of particle size. Particles of 400 to 100 μm for initial velocities of 2 and 6 m/s are presented here for comparison; yet it is only within approximately 500 μm of the target surface that a difference in particle sets manifests itself in either a collision event or particle arrest. This is highly characteristic of a squeeze film boundary layer effect cushioning particles in close proximity to the target surface. Furthermore, if additional factors such as Stokes drag were to play a significant role in particle arrest there would be a more observable particle size dependency between sets. Qualitatively, a driving factor in whether or not a particle will collide is thought to be its inertia, whereby particles with a larger inertia have a much stronger tendency to penetrate the squeeze film boundary layer. However, a direct link to a measure of particle inertia such as the Stokes number is difficult to quantify as the characteristic flow length, l0, and particle relaxation time, τ, in

Figure 3. Image inversion process; two captured particles become light intensities after subtracting a reference image. The inverted image is searched for pixels that match a global lightintensity threshold; for example, it might only consider a pixel to be part of a particle if its intensity is above 50% of the minimum intensity of the whole image. Figure 4 outlines this global threshold for a first pass in identifying all possible particles. However, factors such as imperfections in target surfaces, pixel noise, background image noise, and out-of-focus particles can lead to spurious or unwanted particle representations due to the 1 μm resolution scale of the technique. Therefore, it is imperative that images are thoroughly processed in order to eliminate any such error as derived velocities can be affected by misrepresented particles. Filtering of out-of-focus particles is controlled via a series of userdefined limits associated with maximum and minimum light intensities and their respective spatial distributions. Figure 5 shows an example of how a specific particle can be filtered using high- and low-pass filters.

Stk =

V0τ l0

(2)

needs to be appropriately defined in order to accurately represent the ultra-Stokesian flow regime here where Re ≫ 1. C

DOI: 10.1021/acs.cgd.7b00125 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 6. Effect of particle size on velocity profile near the boundary wall for particle sizes of 100−400 μm.

Figure 7. Particle velocity profiles for 300 and 400 μm particle sizes across the full range of nominal inlet velocities.

Figure 8. Detail of profiles exhibiting a squeeze-film limiting behavior for 100, 200, and 300 μm particles.

Furthermore, particle geometry likely plays a large role in determining if surface collision will result. Particles with similar

masses yet different geometries will present different areas to the target surface, thereby increasing or decreasing the D

DOI: 10.1021/acs.cgd.7b00125 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 9. Reynolds Numbers at particle inlet plotted against the particle’s distance to the target surface as its velocity approaches zero, i.e., δ ≥ 0 implies no collision.

distance from the target at which the particle’s normal velocity component approaches zero. It is evident now that particle’s with Reynolds numbers above 250 can be expected to contact the target surface with a finite residual velocity. Those particles below this threshold are then observed to arrest and redirect with the flow as they approach the target plane. Following this, the formal definition of a critical Reynolds number can then be given as

magnitude of the retardant force with area. Therefore, a more readily available method for discriminating between particle collision or arrest is the freestream particle Reynolds number. A threshold between contact and noncontact particles could then be defined through an associated critical freestream particle Reynolds number. Particle Trajectories. Now, in order to determine a critical Reynolds number outlining the threshold between surface contact and particle arrest, nominal particle sizes of 100, 200, 300, and 400 μm were used in conjunction with those velocities representative of blade tip-speeds (1 → 10 m/s). Starting with the 300 and 400 μm particle sizes in Figure 7, collision was evident in all cases, with particles seen to retain approximately 10% of their initial velocity upon collision. However, with such small impact velocities there was no observable crystal fragmentation, suggesting that the squeeze film can effectively prevent direct mechanical breakage in these cases. Furthermore, this then lends credit to a particle fatiguing mechanism suggested in ref 7 for extremely long time-scale processes as these low-velocity collisions may build up stress over time in the crystal structure and cause microattrition over time. However, the data in Figure 7 is unable to identify the threshold between contact and arrest as all particles are seen to impact the target surface (y = 0) with some small residual velocity. Therefore, in order to determine a critical Reynolds number for arrest, particle sizes were reduced to the effect of reducing their associated Reynolds number. Thus, at this lower spectrum of Reynolds numbers, the point at which particle arrest will occur can be more easily determined. Furthermore, a formal definition for cases of complete particle arrest is now required. A sensible definition for this point is the freestream particle Reynolds number for which a particle only just collides with the surface, i.e., those freestream particle Reynolds numbers for which V0 ≈ 0 at h = 0. Following this, the velocity profiles of 100, 200, and 300 μm particle sizes shown in Figure 8 are indicative of the limiting behavior of a squeeze film effect near the target surface. It is evident that the particles’ normal velocities are approaching zero at some finite distance, δ, from the target surface. The 300 μm particle is seen to collide some small residual velocity, while the 200 μm particle is arrested before collision; indicating a threshold has been crossed whereby collision is no longer probable. From here, the freestream Reynolds numbers of each case can then be seen in Figure 9 plotted alongside δ, the

Rec =

ρVNcdc = 250 μ

(3)

where VNc and dc represent the critical freestream velocity and particle diameter, above which contact is likely to occur. Therefore, at some given freestream velocity there will be an associated critical particle diameter, below which particles will be fully arrested by the squeeze film boundary layer. Conversely, the same is true that for a given PSD there exists some critical freestream velocity, or tip-speed, below which particle arrest will occur.

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CONCLUSIONS

Arising from concerns of particle breakage in the stirred batch crystallization of paracetamol, the subject surrounding particle− impeller interactions has been investigated in detail. It was found that squeeze film boundary layer effects play a leading role in the effective stagnation and/or redirection of particles near a boundary surface. Furthermore, while some particles were found to collide with the target surface, none were seen to have enough residual velocity to prompt any measurable degree of breakage or fragmentation. It was seen that particles below a critical Reynolds number, represented by eq 3, were likely to be arrested entirely as their inertia is not enough to penetrate the existing boundary layer. In this way, the fundamental fluid dynamics of a moving impeller surface effectively protects crystals to a great extent, the magnitude of this effect being dependent on particle size and shape in addition to the fluid density and viscosity. Therefore, it has become difficult to argue in favor of the traditional concept of hard-surface collisions and crystal breakage being directly responsible for the production of secondary nuclei during a typical crystallization process. E

DOI: 10.1021/acs.cgd.7b00125 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Rory Tyrrell: 0000-0002-9761-1638 Brian De Souza: 0000-0002-4469-7802 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research has been conducted within the Synthesis and Solid State Pharmaceutical Centre (SSPC) with financial support provided by Science Foundation Ireland (SFI) through Grant 12/RC/2275.

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REFERENCES

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DOI: 10.1021/acs.cgd.7b00125 Cryst. Growth Des. XXXX, XXX, XXX−XXX