Modeling the breakage stage in spheronization of cylindrical paste extrudates

Funding information The University of Queensland Abstract Spheronization of cylindrical extrudates on a rotating friction plate involves breakage and rounding. Little attention has been given to the breakage stage and quantitative modeling of this process is scarce. Two simple models are compared with experimental data obtained for the early stages of spheronization of microcrystalline cellulose/water extrudates. Tests were conducted for different times (t), rotational speeds (ω), initial loadings, and on pyramidal friction plates with different dimensions. The first model, describing the number of pellets, validated ωt as a characteristic time scale for the breakage stage. The kinetic parameters obtained by fitting showed a systematic dependence on plate dimensions expressed as a scaled gap width. The second model, a simple population balance, described the evolution of the number and length of pellets. The pseudo rate constants provided insights into the kinetics: extrudates tended to break near the middle, while breakage of smaller pellets was slowed down by more pellet–pellet collisions.


| INTRODUCTION
Spheronization (also known as marumerization) is a widely used granulation technique in the pharmaceutical sector, 1 which can produce smooth, relatively spherical pellets with a narrow size distribution from a fine powder. It is a two-stage process: in the first stage, the material is mixed with a binder to form a wet mass (a soft solid termed the "dough" or "paste" in different communities) and extruded through a mesh or die plate to generate extrudates of approximately equal diameter. 2 These are then fed into a cylindrical bowl with its axis vertical whose base (the friction plate) rotates at high speed ( Figure 1A). The plate motion throws the extrudates against the wall. Collisions with the wall and with other extrudates cause them to break into shorter sections, which travel around the edge of the plate in a "rope" (a toroidal bed: see References 3 and 4), dragged by the protuberances on the plate.
Detailed studies of spheronization dynamics, such as References 5 and 6, have shown that breakage and rounding are effectively sequential processes, with the number of pellets changing little after the initial, short, breakage stage. The time taken to obtain pellets of acceptable sphericity is dominated by the later rounding stage, and this has attracted most attention to date, ranging from dimensional analysis 7 and discrete element modeling. [8][9][10] The literature indicates that the friction plate rotational speed, ω, spheronization time, t, and the rheology of the paste are the primary factors governing the rounding process while the amount of extrudates loaded, the friction plate pattern, and extrudate dimensions also play significant roles.
The breakage stage is nevertheless important as it determines the number of pellets and thus their average size, as well as the formation of fines, which may either be retained or lost from the process. 11 Fines play an important role in rounding as they re-attach to the pellets. 12,13 The tendency to generate fines is governed by the energy involved in collisions (and thus operating conditions), the rheology of the material (and thus formulation), and drying (changing the binder content and hence affecting the rheology, driven by operating conditions such as humidity, temperature, and rotational speed).
Relatively little attention has been given to the breakage stage in spheronization and the authors are not aware of any quantitative modeling of this process. Population balance models are widely applied in other granulation technologies. 14 In these, breakage and agglomeration kernels act in parallel to evolve the pellet number and size distributions: in spheronization, the number distribution is established early and is followed by evolution of shape. The current article presents a detailed investigation of breakage kinetics for a simplified spheronization operation, employing the approach reported by Lau et al, 6 where notionally identical experiments are performed in which a set number of extrudates of equal length are spheronized for different times and the pellets analyzed, yielding insight into the kinetics of breakage. The approach was adapted here to improve the amount of data that could be obtained from each test.
The analysis focuses on the yield of pellets from extrudates of given length and the timescale involved. The extrudate diameter is D. Wilson and Rough 2 reported that spheronized pellets often have diameters consistent with an initial cylindrical length of 1-1.5D. This insight is used here in a simple kinetic scheme describing pellet length, which is compared with experimental results for spheronization using different extrudate loadings and rotational speeds.
A second characteristic length scale in spheronization is that associated with the features on the friction plate. Zhang and coworkers 11,15 investigated the influence of protuberance geometry on spheronization behavior. For the pyramidal cross-hatched patterns employed in this study (see Figure 1B) they identified a critical extrudate diameter, D c , below which cylindrical fragments are expected to sit in the cavities between the protuberances: Giving a scaled extrudate diameter, D*: By conducting experiments with different extrudate diameters, they investigated how the size of extrudates relative to the protuberance geometry affected extrudate attrition and subsequent rounding of pellets. They found that sharp protuberances, quantified by the angle θ in Figure 1B, gave more fines when D* > 1, which was attributed to a greater amount of attrition as the extrudates moved across the plates rather than sitting in furrows. On the contrary, blunter protuberances (larger θ), similar to those investigated here, gave unimodal pellet size distributions when D* > 1 and bimodal distributions when D* < 1, indicating an effect of D* on breakage. They did not investigate the effect of protuberance shape on breakage explicitly.
A second, simpler, metric for quantifying the tendency for cylindrical fragments to sit in the cavities between protuberances, considered here, is a dimensionless gap width, w*, defined as.
The effect of the rotational speed of the friction plate, ω, on the timescale for extrudate breakage has not been investigated. The time taken for complete spheronization, t s , has been reported to decrease with an increase in ω, and with an increase in the friction plate radius, where N 0 is the initial number of pellets (i.e., extrudates) loaded into the spheronizer. The experimental data were found to follow the following relationship between N* and scaled time, ω 3 t: where k N is a pseudo rate constant and β is a parameter related to the final value of N*. By inspection, β can be interpreted as the average number of fragments broken off from each extrudate. Since ω 3 t (and R 2 ω 3 t) captures the effect of process parameters R and ω on the number of collisions and kinetic energy involved in collisions, k N can be interpreted as an efficiency, which is expected to be influenced by several factors. In this work, the effect of the spheronizer plate geometry on both terms is considered.
This result can be obtained by modeling breakage as the batch reaction A ! (1 + β)B, where species A is an initial extrudate, which breaks once to give (1+ β) fragments, labeled B, and the rate is first order in A (see Appendix S1). B does not undergo further breakage (but may undergo rounding). Wilson and Rough 2 reported that the final diameter of the spherical pellets obtained at the end of the rounding stage is $1-1.5 times that of the diameter of the cylindrical extrudates fed to the spheronizer. For the extrudates used in these tests, featuring an initial length of 20 mm and diameter 2 mm, each extrudate would be expected eventually to yield $6 or 7 fragments. The asymptotic value for N* was found to lie between 5 and 6 under the experimental conditions employed here (see Figure 3).

| Rate constants for the sub-processes
For modeling purposes, each extrudate was assumed to consist of 6 units of equal length (see Figure 2). Breakage was assumed to occur at one point at any given time and yield two fragments, each having a length of integral multiples of the unit length. Consider the initial extrudate, which comprises 6 units: in one breakage step, it could break into either (i) a 1-unit and a 5-unit fragment; (ii) a 2-unit and a 4-unit fragment; or (iii) two 3-unit fragments. Following the same logic, a 5-unit fragment could break into either a 1-unit and 4-unit fragments, or a 2-unit and a 3-unit fragment, and so on. This discretization scheme is a simplification, and reflects practice in many areas of particle technology whereby size distributions are quantified in terms of size intervals.
Breakage is assumed to be a first-order process in terms of the mother fragment: in effect, collisions with other fragments are not considered to be as important as collisions with the spheronizer wall or the friction plate. Setting n i to be the number of i-unit fragments and scaled time τ = ω 3 t, the corresponding differential equations are: dn 5 dτ = −k 5,1 n 5 −k 5,2 n 5 + k 6,1 n 6 ð7Þ dn 4 dτ = −k 4,1 n 4 −k 4,2 n 4 + k 6,2 n 6 + k 5,1 n 5 ð8Þ dn 3 dτ = − k 3,1 n 3 + 2k 6,3 n 6 + k 5,2 n 5 + k 4,1 n 4 ð9Þ dn 2 dτ = − k 2,1 n 2 + k 6,2 n 6 + k 5,2 n 5 + 2k 4,2 n 4 + k 3,1 n 3 ð10Þ Solutions were obtained using the fourth order Runge-Kutta method (employing Microsoft Excel user-defined functions) with an integration step size of 0.05 × 10 7 s −2 . This gave good agreement between the analytical and numerical solutions for n 6 . Identification of the optimal values of the pseudo rate constants was carried out using the Microsoft Excel Solver. The parameter-fitting algorithm minimized the sum of squared residuals between the experimental and predicted values of n i (τ) for i = 1, 2, …, 6, in line with the least squares method for the solution of population balance problems. 16 The goodness of fit is quantified using the coefficient of determination, R 2 , where R 2 = 1 − (sum of squares of residuals)/(total sum of squares).

| Materials
Microcrystalline cellulose (MCC) powder (Avicel ® PH-101) was purchased from Sigma Aldrich and used as received. Deionized water was used to prepare the MCC paste.

| Preparation of paste
Paste with 47 wt% MCC was prepared in batches of 250 g. A planetary mixer (Kenwood Chef KM200, Kenwood Ltd) was used to mix the MCC powder and deionized water based on the procedure in Reference 11.
Briefly, the mixer was run at speed settings "min," 1, 2, 3, and 4 for 1, 2, 3, 3, and 2 min, respectively. Deionized water was added over the first minute. A wooden spatula was used to scrape off any paste stuck to the mixing element or bowl between each mixing step. The prepared paste was then transferred to a polyethylene bag and allowed to rest for at least 2 h in the sealed bag. The paste was used for spheronization on the same day, and unused paste was discarded.

| Compaction and extrusion
Approximately 80 g of paste was loaded into a cylindrical stainlesssteel extrusion barrel with a chamber diameter of 25 mm. The paste was compacted by hand for every 10 g of paste loaded to help remove air trapped in the paste. The paste was then compacted to about 1 MPa using a strain frame (Zwick/Roell Z050, Zwick Testing Machines) set up to operate as a ram extruder. 17 The maximum force (i.e., 491 N) was held for 5 s before being released. The compacted paste was subsequently extruded through a concentric single-holed cylindrical die of diameter D and die land length L using a steady ram velocity v ram . The extrudate diameter was set by the die land diameter. Table 1 gives the values of v ram and L, which produced smooth extrudates without surface fractures while minimizing liquid phase migration. 18 The majority of tests employed a die land with D = 2.0 mm.
All extrusions were performed at room temperature and humidity.
Extrudates were stored in a sealed plastic container immediately after extrusion to prevent water loss.

| Cutting of extrudates
After extrusion, the extrudates were immediately cut into equal lengths of 10D (e.g. 20 mm for 2 mm diameter extrudates) using a scalpel with the aid of graticule stickers, similar to the procedure followed by Bryan et al. 5 The cut extrudates were stored in covered petri dishes to minimize evaporation of water.

| Spheronization
A set number of cut extrudates (N 0 = 20 or 80) were loaded into the spheronizer (Caleva Spheronizer 120, Caleva Process Solutions Ltd). Figure 1B shows a schematic diagram of the friction plate, which featured a cross-hatched pattern of square pyramidal protuberances. Table 2 summarizes the dimensions of the stainless steel 316 friction plates employed in this work (photographs provided in Figure S1). The majority of the tests employed a plate with dimensions W = 0.6 mm, H = 0.8 mm, and S = 2.6 mm (labeled in Table 2).
The spheronizer was operated for a set time t at constant rotational speed, ω. The rotational speed was measured using a tachometer. For tests with N 0 = 20, the pellets were imaged in situ (see below) and the T A B L E 2 Dimensions of friction plates (see Figure 1B) Note: F is a flat plate. Pyramid sharpness (see Figure 1B)

| Imaging of pellets and image processing
The pellets generated in the spheronizer were imaged using a digital camera immediately after the friction plate had come to rest. The pellets, which were white in color (see Figure 1C), were placed on a black background to enhance the contrast in the images. A box enclosure was used to block ambient light.
The ImageJ software tool (National Institutes of Health) was used to analyze the images to obtain the number and dimensions of pellets at a given time. The original image was first cropped to remove unwanted outer areas, the distance in pixels for a known length identified, and the number of pixels per unit length was determined using the function "Set Scale" in ImageJ. The image type was changed into 8-bit greyscale, and an optimal threshold was chosen for each image. The "Analyze Particles" function in ImageJ was used to determine the maximum caliper length (i.e., the longest distance between any two points along the outline of the pellet), which was reported as the pellet length. They found that higher loadings led to lower pellet velocities, which was attributed to higher energy dissipation within the deeper pellet bed.

| Effect of friction plate geometry
A brief study was conducted to quantify the influence of friction plate protuberance dimensions on breakage behavior. Fewer tests were conducted so the data are subject to greater uncertainty. Figure 5 shows the impact of protuberance size on breakage dynamics for the plates in Table 2, with 2 mm diameter extrudates and two plate rotational speeds. Little breakage occurred with the flat plate (labeled F), with the extrudates tending to roll on the plate and bounce off the spheronizer wall. All the plates with pyramidal geometry promoted breakage, with profiles similar in form to those displayed in Figure 3.
All the profiles fitted the scaled relationship (Equation (5)), with noticeably slower breakage on plate S1, for which D* = 2.2 and w* = 0.55 (see Equation (3)). Extrudates would not be expected to reside or be trapped within the furrows between protuberances in this case. Figure 6A shows the effect of protuberance dimensions on the breakage model parameters obtained by fitting the data in Figure 5 to Equation (5). The parameter β increases with increasing w*, indicating that such geometries promote breakage of 3-unit and 2-unit fragments. The values of k N are similar for w* ≥ 1, and noticeably smaller for w* < 1. Figure 5 also shows that the initial rate of breakage, when expressed in scaled terms, that is, dN * /d(ω 3 t), is similar for plates with w* ≥ 1. Equation (5) indicates that the initial scaled rate is proportional to βk N : the values of the product βk N are reported in the figure legend and are similar for w* ≥ 1, and lower for w* < 1 (see also The scaled initial breakage rates (βk N ) for different diameters were similar to those obtained for different plates with w* > 1 (Figure ).

| Population balance model
Each data point in Figures 3 and 4 represents a time instant where spheronization was halted and the fragments photographed. The number of fragments in each size range at that instant, that is, n i (τ), was identified and the data sets for each run fitted to the population balance model. The initial dynamics can be seen in Figure , where the data are presented on log-linear axes.  Table and show that the agreement is less good at the lower rotational speeds: drying is expected to be more significant under these conditions as the tests last longer.

| Effect of rotational speed
The R 2 values for the n 5 and n 4 profiles were noticeably lower than those of the other size fractions and were negative in some cases, indicating greater uncertainty in the model in these cases. This is partly a result of the number of these fragments being small and their lifespan short, as mentioned above: the parameter fitting calculation then tends to weight their contribution less strongly. It also means that there is lower confidence in the values of the pseudo rate constants.
The pseudo rate constants obtained for each rotational speed are summarized in Figure 8. Increasing ω from 287 to 1150 rpm leads to noticeable increases in k 6,2 and k 6,3 , whereas k 6,1 and k 5,2 are almost constant. Both k 3,1 and k 2,1 decrease with increasing ω: although small in absolute terms, the trends represent the 3-unit and 2-unit fragments breaking less rapidly than the longer fragments.
For all four rotational speeds tested, the pseudo rate constants for end-breakage for a given i-unit fragment, that is, k i,1 , are smaller than those for mid-breakage, k i,2 and k i, 3 . This indicates that breakage occurs The mid-span breakage pseudo rate constants for the initial extrudate, k 6,2 and k 6,3 are, in most cases, larger than k 5,2 and k 4,2 , implying that a longer extrudate has a higher probability of breakage than a shorter extrudate. Both k 6,2 and k 6,3 increase with an increase in ω, whereas k 5,2 and k 4,2 do not, suggesting that the simple kinetic rate law used here, where only one breakage event occurs per fragment at any given time, does not capture the physics for the 6-unit fragments completely. The effect of extrudate length on breakage behavior is considered further in the next section. at the same rotational speed ( Figure 7C). The differences in the fitted curves for n 2 to n 6 are small, which is consistent with Figure 4, where the pseudo rate constants (k N ) for the two loadings are similar. There is, however, a noticeable difference in n 1 profiles between the two loadings, with the appearance of 1-unit fragments being slower for the larger loading. The initial dynamics can be seen in Figure , where the data are presented on log-linear axes.

| Effect of loading
The fit of the model to the data for N 0 = 80 is excellent and the R 2 value for each profile is reported in Table . The R 2 values are all higher than those obtained with N 0 = 20, particularly for n 5 and n 4 , indicating greater confidence in the model parameters. The pseudo rate constants obtained for each initial loading are summarized in Figure 10 and show the same pattern, of breakage occurring preferentially at the middle of longer fragments (k 6,2 and k 6,3 » k 6,1 ; k 5,2 » k 5,1 ; k 4,2 » k 4,1 ). Increasing N 0 from 20 to 80 does not affect k 6,2 and k 6,3 strongly, but k 6,1 , k 3,1 and k 2,1 are all noticeably smaller. Comparing the k i,j values in Figure 10 allows the effect of extrudate length to be considered further. The similarity in k 6,2 and k 6,3 values is consistent with these steps involving a collision between the initial extrudate and the walls, independent of the number of pellets in the bed: the 6-unit fragments tend to tumble and even become airborne (evident in the videos provided in Reference 7). Smaller fragments tended to accumulate in the rope of material at the friction plate edge (see Figure 1C) and are involved in collisions with other fragments as well as with the wall. The decrease in k 5,2 , k 4,2, and k 3,1 values are consistent with lower collision speeds, making it harder to break shorter fragments. This is also consistent with the observation that the larger loading gave a smaller asymptotic value of N* (and β, see Figure 4) and larger final pellet size. i and a lower velocity is required for a longer rod to reach the material's breaking limit. The pellet velocity is, however, likely to be affected by pellet length so this is an incomplete description. Flexural strength considerations can, however, explain the consistently small values obtained for k 2,1 : the flexural strength of short, stubby rods is known to be high (three-point bending tests such as ASTM C1684-13 recommend that the span length to specimen diameter ratio shall be not less than 3) so short pellets are more likely to undergo plastic deformation (and rounding) rather than breaking to give shorter lengths.
There is considerable scope for further investigation of the impact of loading on breakage, as a longer breakage stage will extend the spheronization time via the additional time required to generate shorter fragments. Higher loadings are known to lead to overmassing, which is consistent with many low-speed collisions leading to fusion of fragments rather than breakage.

| DISCUSSION
Extrudate breakage in spheronization is known to be a random process 2 so it is challenging to predict the evolution of pellet sizes. This information is needed as this behavior ultimately determines the size distribution of the products. The population balance model presented here proved to be quite effective and provides some insight into the breakage stage of the spheronization process. It gave a good description of both the total number of pellets formed and their length distribution, which gives an approximate indicator of pellet volume. It does not, however, capture the evolution of shape: this is the subject of ongoing work.
The tendency for the initial extrudates and longer pellets to break near their center has been reported in attrition studies but has not, to the authors' knowledge, been reported for spheronization applications. Only one initial extrudate length was considered in this work and there is a need for other lengths to be considered, as industrial operations feature a mixture of extrudate lengths in the initial batch.
Extrudates are typically generated by screen and basket devices and the length is often determined by the location of the die hole on the die plate or screen. The effect of extrudate length on k i,j values has been determined for one initial length and studies with different lengths would provide insight into dynamics in the rope. If breakage behavior (and thus rounding) could be controlled via extrudate length this would offer a way of improving process reproducibility. Studies of other initial extrudate lengths (e.g., 16.7 and 13.3 mm, representing the n 5 and n 4 size fractions) would also allow confirmation of the finding that pellets tend to break at the center.
Breakage has been investigated in other applications, particularly comminution, by discrete element method (DEM) simulation (e.g., Delaney et al 23 ). In the field of spheronization this technique has been used to investigate the rounding of pellets 8,9 and convective mixing within the rope, 10 for spherical or near-spherical pellets. DEM is well suited to describing the dynamics of extrudates on a rotating friction plate and pellets within a toroidal bed: adding a breakage step to the simulations appears a logical development in the field.
The brief study of friction plate characteristics shows that certain geometric combinations promote breakage. These do not, however, necessarily promote rounding and this offers insights into why investigations of friction plate geometry do not show simple relationships.
Industrial practice is to use higher initial loadings than those investigated here. While the initial step of extrudate breakage was found to be influenced more by interactions between extrudates and the equipment surfaces, pellet-pellet interactions affected the later stages of breakage. It is, therefore, expected that the time for breakage for industrial loading levels will extend beyond those reported here. Since the timescales for breakage and rounding both scale with ω 3 t, the overall dependency on time is expected to scale in a similar manner for different speeds but the dependency on loading remains to be established. Extending the approach used here to such larger loadings will increase the image processing task. Identifying individual pellets for sizing (and shape analysis) can be time-consuming and is well suited to machine-learning approaches, which is the subject of ongoing work.
While the focus on this work has been on breakage as an initial step in spheronization, where it is followed by rounding, it is expected that these results will apply to other operations such as pelletization, where extrudates are broken into shorter lengths but not rounded.

| CONCLUSIONS
Modeling and experimental studies were conducted to determine the sequence of events involved in the early stages of spheronization of cylindrical extrudates. ω 3 t has been shown previously to be a characteristic time scale for the overall spheronization process and this work has demonstrated that it also applies to the short, initial, breakage stage. Comparing experimental data using ω 3 t as the scaled time showed that breakage followed a similar characteristic behavior for the range of rotational speeds tested. The range is representative of those employed in pharmaceutical manufacturing applications, and this result can be utilized as the characteristic time scale when planning experiments and analyzing results.
The evolution of pellet numbers was modeled using two approaches. The first, an overall measure, described the dynamics in terms of an overall gain and a breakage pseudo rate constant. The influence of rotational speed was captured by the ω 3 t scaling, and the gain was not strongly dependent on the speed. Increasing the initial number of extrudates reduced the gain, which was attributed to more frequent pellet-pellet collisions.
The overall model allowed the impact of friction plate dimensions on breakage to be quantified. The gain and pseudo rate constant were found to be related to the plate dimensions and extrudate diameter in a simple manner when these were expressed as the scaled gap, w*.
The second model, a simple population balance, gave a good description of the evolution of pellet lengths. Extrudates and long pellets were found to break preferentially near their center, while higher loadings reduced the rate of breakage of shorter pellets.   (2)