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AAPS PharmSciTech. Sep 2012; 13(3): 928–933.
Published online Jun 26, 2012. doi:  10.1208/s12249-012-9818-z
PMCID: PMC3429663
The Stokes Number Approach to Support Scale-Up and Technology Transfer of a Mixing Process
Tofan A. Willemsz, Ricardo Hooijmaijers, Carina M. Rubingh, Henderik W. Frijlink, Herman Vromans, and Kees van der Voort Maarschalkcorresponding author
Department of Pharmaceutical Technology and Biopharmacy, University of Groningen, A. Deusinglaan 1, 9713 AV Groningen, The Netherlands
Pharmaceutical Sciences and Clinical Supply, Merck MSD, PO Box 20, 5340 BH Oss, The Netherlands
Quality of Life, TNO, PO Box 360, 3700 AJ Zeist, The Netherlands
Department of Pharmaceutics, Utrecht Institute for Pharmaceutical Sciences (UIPS) Utrecht University, PO Box 80082, 3508 TB Utrecht, The Netherlands
Competence Center Powders and Formulations, Purac Biochem, PO Box 21, 4200 AA Gorinchem, The Netherlands
Kees van der Voort Maarschalk, Phone: +31-412-662342, Fax: +31-412-662617, tofan.willemsz/at/
corresponding authorCorresponding author.
Received February 8, 2012; Accepted June 8, 2012.
Transferring processes between different scales and types of mixers is a common operation in industry. Challenges within this operation include the existence of considerable differences in blending conditions between mixer scales and types. Obtaining the correct blending conditions is crucial for the ability to break up agglomerates in order to achieve the desired blend uniformity. Agglomerate break up is often an abrasion process. In this study, the abrasion rate potential of agglomerates is described by the Stokes abrasion (StAbr) number of the system. The StAbr number equals the ratio between the kinetic energy density of the moving powder bed and the work of fracture of the agglomerate. In this study, the StAbr approach demonstrates to be a useful tool to predict the abrasion of agglomerates during blending when technology is transferred between mixer scales/types. Applying the StAbr approach revealed a transition point between parameters that determined agglomerate abrasion. This study gave evidence that (1) below this transition point, agglomerate abrasion is determined by a combination of impeller effects and by the kinetic energy density of the powder blend, whereas (2) above this transition point, agglomerate abrasion is mainly determined by the kinetic energy density of the powder blend.
Key words: dry mixing, scale-up, stokes number
One of the challenges during scale-up and technology transfer of a mixing process is that there usually are considerable differences in blending conditions between different mixer scales and types (1). Finding the blending conditions that lead to the desired blend uniformity is not a trivial operation (2,3). For this reason fill volume, impeller rotational speeds and blender geometry are preferably kept constant as much as possible during such a technology transfer (4,5). In practice this is not always possible. Moreover, such an approach does not necessarily mean that the blend conditions are always similar (6). Still, obtaining the correct blend conditions is crucial because only this safeguards formation of a sufficiently uniform blend. A specific, but frequently occurring case is a blend that contains cohesive components that tend to form agglomerates. Removal of these agglomerates and prevention of the formation of new agglomerates is often the critical step in the assessment of the uniform blend (7,8).
Removal of agglomerates in a dry mixing system predominantly occurs via abrasion (8,9). The abrasion process is typically characterized by a high frequency of impacts by filler particles on the surfaces of the agglomerates. Mechanical properties of the agglomerates and product and process-related parameters like filler particle size and the rotational rate of the impeller were found to affect the size reduction rate of the agglomerates (8). It appeared to be possible to describe the abrasion process via definition of a Stokes number, the Stokes abrasion number (StAbr). This number is the ratio of the kinetic energy density of the powder bed to the work of fracture of the agglomerate (9). Results so far showed that it is possible to predict effects of filler particle size and impeller rotation rate on abrasion rate with reasonable accuracy. The purpose of this study is to check the validity of the StAbr approach and apply it to technology transfer situations where mixers of the same working mechanisms, but different production scales and different geometries are applied. Additionally, this paper identifies limits of applicability of the Stabr approach.
The materials used were microcrystalline cellulose (Avicel PH-101, FMC, Philadelphia, USA) and α-lactose monohydrate (Pharmatose® 100M from DMV Fonterra Excipients, Goch, Germany, with a bulk density of 750 kg/m3).
Model Agglomerates (Brittle Calibrated Test Particles)
The model agglomerates or spherical brittle calibrated test particles (bCTPs) were prepared as described before by Willemsz et al. (8). The porosities of all bCTPs produced were measured from the diameters and the weights of the bCTPs. The true density of the MCC was determined using a pycnometer (AccuPyc 1330, Micromeritics, Norcross, U.S.A.) using nitrogen as test gas and was found to be 1,600 kg/m3. The mechanical properties of the bCTPs have been described in Willemsz et al. (9).
Blending Tests
The blending experiments reported in this study were performed using convective mixers with bowl volumes of 25 l (Fukae Powtec model FS-GS-25J, Japan, bottom-driven impeller) and 50 l (Glatt model VG50, Germany equipped with a top-driven impeller). The chopper was never installed. Table I lists the parameters that were varied. A test was started by adding selected test particles to a powder sample of lactose 100 M. This mixture was placed in the blender. After a given blending time, the blend was sieved over a 500-μm sieve to collect the test particles. The weights and dimensions of the bCTPs were determined as a function of blending time as mentioned in the previous communication (8).
Table I
Table I
Geometry of the High Shear Mixers and Experimental Set-Up for the blending Tests
The Froude number (Fr) was calculated as follows:
equation M1
With N the impeller rotational rate, D bowl diameter, and g is the acceleration of gravity.
Powder Surface Velocimetry
To collect data for powder surface velocimetry analysis, a plexiglass lid was placed on the 25-L granulator. The powder surface velocimetry data from the 50-L high-shear mixer were collected by recording through the watch glass of the apparatus. The powder flow was recorded using a high-speed video camera (Casio-EX-F1, Casio computer co., LTD, Tokyo, Japan) operating at a speed of 600 frames per second. The data were analyzed according to Willemsz et al. (10). The camera was placed perpendicular to the bowl and such that about 50% of the total powder surface was visible for the 25-L high-shear mixer and 25% of the surface in the 50-L high-shear mixer.
Statistical Analyses
The outlier diagnostics, standard deviation (SD) and 95% confidence interval calculations described in this paper were performed using SAS V9.1 software (SAS institute Inc., North Carolina, USA).
Abrasion Rate Constant (ξm) Measurements in the 25- and 50-L High Shear-Mixer
In this study, two vertical axis high-shear mixers of different geometries (as described in Table II) were used to assess how the abrasion rate constants (ξm) of brittle agglomerates scale with process variables in high-shear mixers. The bCTPs mass reduction (Mrel) over time was determined. It obeys apparent first order kinetics, with mass reduction rate constant as described by Willemsz et al. (8):
equation M2
with M(t) as the mass after blending time t and M0 as the initial mass.
Table II
Table II
Fit Parameters of Mechanical Properties Using equation M3 with X = Y or X = σc and X0.55 = σc or Y at ε = 0.55 (The Data Indicate the Average ± 95% Confidence (more ...)
The purpose of the current experiments was to investigate the effects of abrasion rate constants of agglomerates with different porosities when process variables are varied. The results are depicted in Fig. 1.
Fig. 1
Fig. 1
The effect of process settings on the mass based abrasion rate constant for the 25-L (black square) and 50-L (white square) high-shear mixers. Fr represents the Froude number, [var phi] the degree of fill of the equipment, ξm the abrasion rate (more ...)
Figure 1 shows that the abrasion rate constants (ξm) of the agglomerates in the 50-L mixer are always lower than those obtained in the 25-L mixer when Froude numbers are identical. Abrasion rates increase with Froude number but decrease with increasing fill levels. These results are in line with findings discussed in previous papers (e.g. [8, 1113]).
It is reasonable to assume that a reduction in fill volume implies that the contribution of the impeller to the total rate of agglomerate abrasion will increase. To visualize this effect additional tests have been performed where the powder just covers the impeller. This corresponds with a relative fill level of 8% in the 25-L mixer. Figure 2 shows the abrasion rates (ξm) of the bCTPs at different fill levels for two different Fr numbers. Figure 2 clearly shows a considerable additional effect of the impeller at low fill levels on the abrasion rates of the particles. Moreover, there seems to be a step change in behavior: abrasions rates at fill levels above 16% are more or less in line, a low fill level gives much higher abrasion rates.
Fig. 2
Fig. 2
The mass based abrasion rate constants (ξm) of agglomerates for the 25-L high-shear mixer at a [var phi] (v/v) of 8% (white circle), 16% (black circle), 27% (black square), and 37% (black diamond)
Powder Surface Velocity and Abrasion
The powder surface velocity has been measured as previously described (10). The powder velocities (vp) were determined at the conditions described in Table I, and Fig. 3 depicts the results.
Fig. 3
Fig. 3
Powder surface velocities (vp) at different fill volumes and Froude numbers (black diamond, white diamond: Fr = 0.12; black square, white square: Fr = 0.46; black triangle, white triangle: Fr = 1.04) for (more ...)
Figure 3 shows decreasing powder surface velocity at increasing relative fill volume. This was observed in both mixers. The figure also shows that the powder velocities measured in the 50-L mixer are significantly lower compared to those in the 25-L mixer scale at comparable Fr numbers. Filler particle velocity is an important parameter in relation to the rate of abrasion of the agglomerates (8,9). The effects were correlated using the Stokes abrasion number (StAbr). Applying StAbr numbers gives the possibility to assess how the abrasion rate constant m) scales with process variables in different types/scale of high-shear mixers.
The Stokes abrasion number (StAbr) concept has been discussed in more detail earlier in our previous paper (9). StAbr compares the energy density during blending (equation M4) with the work of fracture of an agglomerate (equation M5):
equation M6
With ρb bulk density of the filler, vp powder surface velocity, Y elastic moduli, and σc fracture stress.
The mechanical properties Y (elastic modulus) and σc (fracture stress) of the bCTPs have been calculated as previously described (9) and are based on the porosity (ε) values of the agglomerates. Table II summarizes the fit parameters for elastic moduli and fracture stresses after performing a least square fit analysis assuming exponential relationships (14,15).
Figure 4 shows the relationship between the abrasion rates and the Stokes abrasion numbers in the blending experiments at different working conditions. Visually, three distinct relationships can be seen: with the largest group of tests at fill levels larger than 16% and two groups that both describe relationships when fill level is low.
Fig. 4
Fig. 4
The relationship between the abrasion rate constants (ξm) and the Stokes abrasion number (StAbr) of various bCTPs at defined conditions. The two solid lines indicate the abrasion data deviating from the proposed regression model (dashed line) (more ...)
Model diagnostic plots of the data-set indicate that both variables (ξm and StAbr) should be log-transformed before analysis to fulfill the statistical requirements for normal distribution of the values to identify outliers. From these data sets several outlier diagnostics (studentized residuals, DFFITTS, leverage, and DFbetas) were used to identify outliers in the data-set of Fig. 4.
From the five curves depicted in Fig. 4, the analyses marked three observations as real outliers. These outliers correspond with bCTPs collected during tests using the 50-L high-shear mixer. This mixer is larger which implicates that larger amounts of filler had to be sieved to collect the model agglomerates. It is likely that this introduces additional errors. This was the rationale to remove the outliers from the data set. These data points are not shown in Fig. 4. After removing these three outliers, different regression models correlating ξm and StAbr have been produced:
equation M7
Table III lists the models produced.
Table III
Table III
Regression Models Between ξm and StAbr at Various Relative Fill Volumes for the Curves Depicted in Fig. 4
The results demonstrate a relationship between abrasion rate of agglomerates and the value of StAbr. The R2 presented in Table III indicates the extent that the values of StAbr explain abrasion at various process conditions. Here, R2 approaching 100% indicates that abrasion is fully explained by the parameters that describe the Stokes abrasion (StAbr) number of the system. The R2 presented in Table III shows that the StAbr number is a reasonable way to predict agglomerate abrasion while there is no clear difference between the fits of the results between the different blenders. This makes it possible to combine these results into one model. This model includes 78% of the variance when the fill level exceeds 16%. The regression analysis in our previous study (9) included 84% of the variance using a smaller data set. The data-set in this study also covers the abrasion data for the 50 L high-shear mixer scale.
It is clear that a low fill level leads to much faster abrasion of the test particles (Fig. 4 and Table III). There is apparently a transition where the impeller starts to dominate the abrasion. To study the impact of fill level, regression analysis has been performed separately for all fill levels. These results are depicted in Table IV.
Table IV
Table IV
Regression Models Between ξm and StAbr at Various Fill Degree for Two Different High-Shear Mixer Scales Depicted in Fig. 4
To study the effect of the impeller, the fill degree of the blender has been defined relative to the impeller height, the relative fill height (Δhpowder):
equation M8
With h0,powder height of the stationary powder and himpeller the impeller height (Table I). Figure 5 shows the relationship between the fit constants in Table III and the relative fill height of the powder in the blenders.
Fig. 5
Fig. 5
Relationships between the variables slope (α, upper figure) and intercept (β, lower figure) with the relative distance between impeller and powder height ([increment]hpowder) for the 25 L (black circle) and 50 L (letter x (more ...)
The slope (αi) of the fits is almost constant and has a value of around 1. This implicates that the relationships between abrasion rate and StAbr are almost linear relationships. As a consequence, the intercept β describes the slope of the (almost) linear relationships in Fig. 4. The value of β increases drastically when the relative fill height is low.
The intercept between the dotted and solid lines shown in Fig. 5 has been calculated and gives a transition point at a [increment]hpowder value of 3. This result shows that agglomerate abrasion is predominantly determined by the powder bed movements when the [increment]hpowder value is larger than 3. Obviously, the presence of enough powder is a prerequisite for the applicability of the Stokes number approach. When insufficient powder is present, the impeller starts to dominate the process. Logically, direct contact between impeller and the bCTP’s yields a deviating abrasive phenomenon than the shear forces occurring when there is plenty of powder present.
The abrasion of agglomerates during dry mixing at different fill volumes, impeller rotational speeds, and two different high-shear mixer scales and types has been investigated. This study reveals that the StAbr number is able to predict the abrasion potential of agglomerates at variable process conditions. This includes high-shear mixers that are geometrically different.
The study reveals a transition point between agglomerate abrasion completely dominated by the powder blend and where a combination of impeller and powder blend effects play a significant role.
The StAbr number concept described in this study demonstrates to be a useful tool to predict the abrasion of agglomerates at conditions during process variation exercises in dry mixing such as transferring the same mixture composition (filler) to a different type and scale of mixer.
This study was performed within the framework of Top Institute Pharma project number D6-203. The authors would like to thank Clinton Rambanapasi and Jan van Dinther for their experimental assistance in this study.
Open Access
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