J Pharm Innov (2008) 3:258–270 DOI 10.1007/s12247-008-9048-9
RESEARCH ARTICLE
Quality by Design Methodology for Development and Scale-up of Batch Mixing Processes Patricia M. Portillo & Marianthi Ierapetritou & Silvina Tomassone & Christine Mc Dade & Donald Clancy & Petrus P. C. Avontuur & Fernando J. Muzzio
Published online: 2 December 2008 # International Society for Pharmaceutical Engineering 2008
Abstract In this study, a quality by design approach was applied to the design and scale-up of a batch mixing process. Mixtures of acetaminophen and lactose were sampled at different mixing times using a groove sampler. Samples were subsequently analyzed using NIR reflection spectroscopy. The effects of four processing parameters on the empirical mixing rate in a bin blender were examined. Blender rotation rate (two levels), powder fill level (two levels), powder cohesion (two levels), and blender size (three levels) represent the four parameters studied. Blender geometry and blender loading method were treated as constant parameters. Statistical analysis was used to assess the impact each parameter had on the mixing rate. Blender size (p=0.02), powder cohesion (p=0.05), and rotation rate (p=0.07) all significantly affected the mixing rate. The least significant parameter was the vessel fill level (p=0.18), indicating mixing performance is not strongly affected by fill level, given the range studied. Keywords Quality by design . Batch powder mixing . Bin blender . Statistical analysis . Mixing rate P. M. Portillo : M. Ierapetritou : S. Tomassone : F. J. Muzzio (*) Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ 08854, USA e-mail:
[email protected] C. Mc Dade : D. Clancy Process Technologies, Glaxo Smith Kline Company, 709 Swedeland Road, King of Prussia, PA 19406, USA P. P. C. Avontuur GlaxoSmithKline R&D, New Frontiers Science Park, Third Avenue, Harlow, Essex CM19 5AW, UK
Introduction Powder mixing has been the subject of substantial research. This is motivated by applications in a variety of industrial sectors, which include pharmaceuticals, food, ceramics, catalysts, metals, and polymer manufacturing. Understanding mixing mechanisms and identifying critical process and material parameters is often a crucial step during process development. Content uniformity problems have four main root causes: (a) powder stream flow properties [1], (b) poor equipment design or inadequate operation [2], (c) particle segregation due to differences in particle properties, and (d) particle agglomeration, driven by electrostatics, moisture, softening of low melting point components, as well as other factors. Scale-up of mixing operations continues to present a concern to the pharmaceutical development process. The reliable scaling of a process requires an understanding of the effects that processing parameters may illicit on intermediate- and finished-product properties. Generally, processing conditions are thoroughly examined at small scales during process development of powder formulations. The design and scale-up of blending operations is a multivariate issue; the relative magnitudes of shear, dispersion, and convective forces may be altered as the process is transferred to larger scales [3]. A problem with the current scale-up philosophy is a failure in addressing several critical variables. Shear rate and total strain have been shown to affect blend microstructure [4], which may consequently affect the degree of ingredient agglomeration, blend flow properties, tablet hardness and final product dissolution, which may ultimately result in failures during the scale-up process. An example of this includes blend over-lubrication resulting from the increase in shear (per revolution of the blender)
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intensity as a function of increasing scale [5]. In a separate study, blender rotation rates were found to affect the relative standard deviation (RSD) plateau of a given system [6]. Powder cohesion properties also affect the velocity gradient, where interpaticulate forces dilate the powder bed density. This may have further implications on downstream processing. Optimization of the blending process requires an understanding of blending mechanisms and critical variables. Although modifications to powder cohesion, blender size, and geometry may not be feasible due to other constraints, operating conditions such as rotation rate and fill level are easier to alter. An understanding of the interactions among these variables is essential. V-blenders, tote blenders, and double-cone blenders are examples of batch blenders that vary in geometric design. For these systems, variables such as blender size and fill level may affect mixing behavior [7–9]. Mixing in tumbling blenders is limited in the ability to improve upon component segregation, typically attributable to variations in particle characteristics (e.g., size and shape), once it occurs [10]. Further, initial load configuration (top/bottom and left/right) of the active pharmaceutical ingredient (API) and excipients has been shown to affect the mixing rate [11]. Brone and coworkers [12] examined the effect of changing the rotation rate from 8 to 24 rpm for glass beads in a V-blender. This study illustrated that the mixing mechanism of free flowing materials was not affected by rotation rate; however, the total mixing time was ultimately reduced. Sudah and coworkers [13] varied the rotation rate from 5 to 15 rpm for art sand in a rectangular tote blender. This study showed rotation rate did not affect mixing rate (per revolution) in earlier stages of the mixing process (up to 64 revolutions of the blender) but did affect the asymptotic variance plateau (total achievable homogenization). The studies also showed that for a cohesive blend, rotating the vessel at 10 rpm resulted in the smallest asymptotic variance, which suggested the presence of competing mechanisms. Later on, Arratia and coworkers [6] examined the effects of blender fill level (40–85%) on mixing rate. The study showed a decrease in mixing rate with increasing fill level for Bohle-Bin blenders. Alexander and Muzzio [3] generalized some simple guidelines to help the scale-up process. Some of these may be applicable for the formulations used in the present case study. 1. When altering blender size, the dominant mixing mechanism ratio (i.e., gravitational, shear, convective), order of material addition, and powder arrangement should be kept constant. 2. The number of blender revolutions is a key parameter for free flowing powders. Rotation rates, however, are largely unimportant.
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3. Mixing is a function of shear rate for cohesive powders. In summary, the main variables known to affect mixing performance are: (1) the design of the mixing system (e.g., geometry and blend mechanism), (2) blender size, (3) the fill level, (4) the blender loading mode, (5) the speed of rotation of the blender, and (6) the material properties of the ingredients being mixed (particle size, shape, and density, etc.). Historical practices in pharmaceutical process development have largely involved univariate (OVAT, “one variable at a time”) approaches, where the effects of a single variable are examined for a few conditions selected based on prior experience from a “safe” subset of the permissible design space. A value of the first variable is then selected and kept constant as a second variable is examined, and so forth. However, as suggested in the Process Analytical Technology (PAT) Guidance [14], the OVAT approach does not effectively address the effect of interactions between multiple process variables. As a result, unless the effects of all variables are nearly independent of one another, the optimal conditions for operating the process will not be determined. The pharmaceutical industry has recently focused substantial effort on improving its understanding of key unit operations and developing statistical, instrumental, and fundamental methods for characterizing and controlling sources of variability in product performance. Beginning with the introduction of the PAT Guidance in 2003, and continuing with the quality by design (QbD) initiative (for which draft guidance exists in ICH Q8 [15], Q9 [16], and Q10 [17]), the industry is transitioning from OVAT approaches to a more multivariate statistical method for assessing the effects of process variables on product quality. The “process understanding” that is considered a keystone of the PAT and QbD initiatives enables the process control that facilitates the manufacture of quality products meeting desired performance specifications.. Clearly, application of QbD methods is not a temporally discrete activity to be completed at an early stage of product/process development. Rather, QbD is a longitudinal component of the product life cycle, which, early in the development process serves as a risk assessment and formulation screening methodology, later, as a product/ process optimization approach, and finally as a continuous improvement method during commercial manufacturing. While the philosophy of QbD methodologies is straightforward, with the necessary toolbox having been well developed and long used in other industries, the actual implementation, however, represents a significant task due to the fact that (1) the mechanical and physicochemical properties of many pharmaceutical APIs and excipients are only partially understood, thus limiting identification of
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Experimental Method Blender Specifications
Fig. 1 The three tote blenders used in this study. From left to right: 10, 0.5, and 2 ft3 blender
critical material variables, and (2) there is an incomplete knowledge of critical process variables for many pharmaceutical operations. As a result, prioritization (early screening) of factors is difficult, and studies need to address the large comprehensive parametric space of all conceivably relevant variables. Because of this incomplete knowledge of what is truly critical, naive attempts at application of QbD methodologies are likely to be suboptimal due to a poorly constructed design space. In this paper, we attempt to introduce some prioritization guidelines for batch blending in tumbling blenders, where a knowledge base exists. The scale-up of blending and assurance of homogeneity may benefit substantially from the development and incorporation of a realistic QbD strategy. QbD has already begun to be capitalized where new methods for quantitatively assessing product quality are being developed. A risk-based strategy for quality assessment which uses model-based simulation to link variation in drug product parameters and clinical performance has been recently presented [18]. As mentioned, this paper outlines a QbD strategy for the design of batch blending operations. In the next section, we discuss the experimental method. This provides the scope of experimental conditions investigated and the details behind the fixed parameters, such as blender specifications, loading pattern, and materials. This section covers all necessary details concerning the experimental and analytical methods used in obtaining the data. This includes the sampling method, analysis technique, and the quantification methods used to measure mixing performance. The “Effects and Characterization of Cohesion” section describes cohesion, its effect on mixing, and the methods used to quantify different levels of cohesion. The “Results” section is devoted to a statistical analysis of the factorial batch-blending experiments. Finally, the “Outlook and Conclusions” section provides closing comments and conclusions.
The blenders used in this study are shown in Fig. 1. They have a fixed geometry comprised of a rectangular bin blender and a pyramidal hopper that forms the tote. This design was selected for several reasons, including: (1) it is common, (2) it is available in our lab in three sizes, (3) it has been thoroughly examined in previous studies, and (4) a good working knowledge of the critical-to-performance variables is available. The two larger blenders were manufactured by the GEA group (Birmingham, UK) and the smallest blender is a custom-made vessel run under a step motor control. The rectangular bin blenders used in this study have been previously employed in the assessment of blender performance [9, 13, 19]. A schematic of the blender geometry is illustrated in Fig. 2. The corresponding dimensions for the three different blenders are shown in Table 2. Baffles were used since they have been shown to improve mixing performance [20] by increasing axial flow. Powder Materials A binary blend system was investigated. The two blends examined contained acetaminophen (Mallinkcrodt, milled to 30 μm) and one of two grades of lactose (De Melkindustrie Veghel): lactose 125 (55 μm) or lactose 100 (130 μm). The bulk densities of the three powders used were measured by taking the weight of a finite portion of powder and dividing it by the volume the powder sample occupied. The procedure was repeated ten times for each powder. Experimental densities for lactose 100M, Lactose 125M and acetaminophen are reported as 0.785±9.02E−03, 0.765±1.33E−02, and 0.297±1.57E−02 g/ml. Powder Loading The method by which materials are initially loaded into the blender vessel is a parameter that has been shown to affect the mixing performance of tumbling blenders. Two particular loading patterns previously examined are the top-to-bottom and left-to-right starting configurations. In the top-to-bottom Fig. 2 Bin blender schematic
L
D
Axis of rotation
H1 θ V
H2
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Table 1 Experimental conditions examined Tote size (ft3) 0.5 0.5 0.5 0.5 2 2 2 2 10 10 10 10 0.5 0.5 0.5 0.5 2 2 2 2 10 10 10 10
Fill level 50 70 50 70 50 70 50 70 50 70 50 70 50 70 50 70 50 70 50 70 50 70 50 70
Speed (rpm)
Cohesion
Fr no.
Low (10) Low (10) Low (10) Low (10) Low (10) Low (10) Low (10) Low (10) Low (8) Low (8) Low (8) Low (8) High (14) High (14) High (14) High (14) High (14) High (14) High (14) High (14) High (11) High (11) High (11) High (11)
Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose Lactose
4.11E−04 4.11E−04 4.11E−04 4.11E−04 4.29E−04 4.29E−04 4.29E−04 4.29E−04 4.22E−04 4.22E−04 4.22E−04 4.22E−04 8.06E−04 8.06E−04 8.06E−04 8.06E−04 8.42E−04 8.42E−04 8.42E−04 8.42E−04 7.97E−04 7.97E−04 7.97E−04 7.97E−04
100 100 125 125 100 100 125 125 100 100 125 125 100 100 125 125 100 100 125 125 100 100 125 125
configuration, one powder is initially loaded into the vessel, above this powder bed another powder is layered. In the leftto-right configuration, a separator is initially inserted into the vessel where one side of the mixer is loaded with one powder and the other side with another. In previous experimental studies [11], the axial variance, defined as the variability within the axial length of the vessel (axial length is perpendicular to the axis of rotation) of a powder blend, was examined in a 56-L tote blender for both loading patterns. The top-to-bottom loading resulted in significantly faster mixing rates than left-to-right loading. Thus, the topto-bottom loading was used for this study. Experimental Design A randomized full factorial design was used to determine the effect of each parameter and their interactions on the rate of the mixing process. The full list of experimental conditions from the combined variable levels is shown in Table 1. Experiments are conducted for three tote sizes (0.5, 2, 10 ft3) and two volumetric fill levels (50% and 70%). Each tumbler gyrates at two speeds (low and high) as shown in Table 1. The speeds are dependent on tumbler size and are adjusted to keep the Froude number constant, as illustrated in Table 1. The Froude number is a
nondimensional parameter comparing inertial and gravitational forces. In theory, if you keep this number the same for the varying blender sizes, the powder blends within the mixers are maintaining a constant ratio of inertial and gravitational forces [3]. No first principle approaches currently exist for the design of a dry blend process scaleup, except for the application of the Froude number. The Froude number can be justified from a generalized momentum balance under fairly drastic assumptions. The Froude number for tumbler mixers is given by: Fr ¼
Ω2 R g
ð1Þ
where Ω is the rotation rate (revolutions per minute), R is the radius (mm), and g is the acceleration from gravity (millimeter per square minute). Conversely, semi-empirical approaches are based on the Rayleigh method to develop similarity criteria. This yields a resulting equation that is a function of particle velocity, vessel rotation rate, radius, particle diameter, and gravitational acceleration [3]. Sampling Method For each treatment condition, powder samples were taken after 5, 25, 50, and 100 revolutions using a groove sampler. The groove sampler consists of a hollow sleeve (1 in. in diameter) surrounding a solid inner steel rod possessing a groove along most of the length of the rod. The inner pipe has a sampling cavity that is 1/2 in. deep and 1/2 in. wide along the middle 80% of the rod. Rotating the inner pipe relative to the outer pipe opens and closes the groove sampler. The sampler (in its open position) was inserted into the powder bed and subsequently rotated to trap material within the sampling cavity. After being removed from the powder bin, the sampler was then placed horizontally on a stand while open, and the entire device was rotated to discharge the collected material into a series of small trays. Sample size can vary with size or width of the sampler [10, 18]. Sample size and sampling location were constant for all experiments. The axial sampling locations lie on the axis of rotation, and the vertical sampling locations lie perpendicular to the axis of rotation. Samples were retrieved from five radial positions for all three mixing vessels. Ten axial positions were examined for the two larger mixers (10 and 2 ft3) and five axial positions were examined for the smaller (0.5 ft3) mixer due to the smaller axial bed. The analysis and limitations of accuracy and precision for the sampling device used here have been discussed in detail by Muzzio and coworkers [19, 21].
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NIR Analysis on Homogeneity Effects Near-infrared spectroscopy (NIR) was used in this study due to its rapid real-time analysis, high-throughput capability, and nondestructive nature. NIR technique details may be found elsewhere [6, 20, 22]. Following extraction, samples were collected into glass vials (Fisher, Pittsburgh, PA, USA) and analyzed using single-point near-infrared spectroscopy (FOSS NIR Systems, Silver Spring, MD, USA). The composition of each sample was examined using a Rapid Content Analyzer (NIR 5082) manufactured by FOSS NIR Systems, Inc. Empirical modeling of the full NIR (1,100–2,500 nm) portion of the spectra (second derivative pretreatment) was performed using partial least squares regression. The amounts of acetaminophen and lactose varied in the calibration and validation samples. Samples ranged from 0% to 5% w/w acetaminophen (0.1% increments) and 5–10% acetaminophen (1% increments). Each sample was scanned 32 times without repositioning the vial to obtain an NIR spectrum. The performance of the calibration model was validated using 2-g samples with known acetaminophen concentrations. The NIR performance method was assessed by the root mean square error of calibration (RMSEC) and the root mean square error of prediction (RMSEP). RMSEC and RMSEP values obtained in this study were 0.997 and 0.976, respectively. The resulting model was use to predict the concentration of acetaminophen in each sample obtained from the groove sampler. Powder samples were collected in the same glass vials (28 mm diameter, 61 mm long, 20 mL volume capacity) used to analyze the calibration and validation samples. Sampling volume and size may substantially affect the estimate of variability between sample concentrations. Due to the increase in scale of scrutiny, larger samples exhibit smaller variability between acetaminophen concentrations. When the analytical method interrogates the same surface area of the powder, however, the measurement sample size is constant. The depth of powder in the vial should exceed 4 mm for reflectance measurements to ensure the effective beam penetration depth does not exceed the powder depth bed. Reflectance spectroscopy may assay a small fraction of the entire sample, making it relatively more vulnerable to inhomogeneities within the sample. To mitigate such problems, multiple cycles of sample agitation followed by sample analysis may be employed; however, this technique may result in sample segregation. When the particle size distribution is broad, larger particles will segregate by levitating to the top of the powder bed. To check for such effects, we evaluated the effect of agitation and repeated assaying. Figure 2 illustrates the RSD profile of all 50 samples (ten samples along the axial bed at 5 radial positions) scanned a single time. The second RSD profile resulted from agitating and subsequently rescanning all the
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samples. The results indicated no real advantage from agitating and scanning the sample multiple times, for the system under study. Further, some potential segregation was detected. Therefore, samples were assayed a single time. Quantification of Mixing Performance Homogeneity Measurements In order to determine powder homogeneity, the sample-tosample variability was quantified in terms of the RSD. The standard definition of RSD (also known as coefficient of variance (CoV)) is given by: RSD ¼ CoV ¼
s x
ð2Þ
where s represents the sampling estimate of the standard deviation and x the average of all the samples. As mentioned, samples were retrieved from the vessel using a sampler and subsequently measured via NIR. For each radial core position (denoted as j), xij is a sample concentration, xj is the mean concentration, and Nj is the number of samples in that core [23, 24]. The standard definition of variance (s2) is given by Eq. 3: X X xij x 2 s ¼ Ni j i 2
ð3Þ
P xj ¼
i xij Ni
ð4Þ
where N is the number of samples and x is the mean composition found using Eq. 4. The total variance is decomposed into two components for axial and radial variability (Eq. 5): s2 ¼
2 1 X X 2 1 X Nj xj x þ xij xj N j N j i
ð5Þ
The first term is an estimate of axial variance (s2A ) and the second term, radial variance (s2R ) [11]. Axial variance measures the differences in concentrations between the top and bottom of the powder bed. Statistically, if random samples are taken from a mixture of average composition q, given the fraction of the first component is P and second component is (1−P), and the mixture has a random structure, the composition of the samples will be normally distributed. The theoretical variance can be calculated for completely random
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mixtures using Eq. 6 and for nonrandom mixtures using Eq. 7:
Effects and Characterization of Cohesion
P 2 s ¼P 1 N
Cohesion ð6Þ
ð P ð 1 P Þ LÞ 2 s2 ¼ L þ L N
ð7Þ
where L represents a constant for a given mixture or state of mixedness and may be determined experimentally when the value of σ is known for a given value of N. For a system where the two components are completely unmixed, the initial variance (s 20 ) of the sample composition may be calculated using Eq. 8 [21, 25]: s 20 ¼ Pð1 PÞ
ð8Þ
However if Eq. 8 was followed for a mass ratio of 97% lactose and 3% acetaminophen, the initial RSD would be ∼3%. This value should represent the largest obtainable variance for this system. The initial RSD (RSD0) for these experiments was calculated from a statistical approach published elsewhere [22, 26]. The RSD0 is 2.45% for the larger and medium tote (50 samples per time point) and 2.10% for the smaller tote (25 samples per time point). The discrepancies in RSD values may be due to the differences in the number of samples retrieved relative to the total powder mass in each vessel. Mixing Rate Process performance monitoring for each parameter combination was evaluated by the mixing rate of acetaminophen in lactose. The mixing rate was computed by retrieving powder samples from the blender as a function of revolutions. Sample variance and relative standard deviation as a function of vessel revolutions were determined from NIR-predicted concentrations. In the absence of segregation, the variance in a blender typically decays to its asymptotic value as an exponential of time. Therefore, mixing rate is measured as the slope of the logarithm of the variance. The slope, m, is determined from Eq. 9: P revolutionsi revolutions log s2i logðs2 Þ m¼ 2 P revolutionsi revolutions ð9Þ where revolutions is the revolution average and logðs2 Þ is the logarithmic variance average.
Powder cohesion is one of the most important properties affecting flow, and by extension, powder mixing. Cohesion is caused by Van der Waals, capillary, and electrostatic attraction forces. Cohesion of a bulk solid is defined as its resistance to shear (shear strength) under null normal stress on the plane of failure [24, 27]. Cohesion of powders, although poorly understood is known to depend on powder moisture content, presence/absence of glidants, and particle size. As the size of a particle decreases, the ratio of its surface area to mass increases. A cohesive powder can be defined as a material where the interparticle adhesive forces exceed the particle weight by at least an order of magnitude. In such systems, particles no longer flow independently; rather, they move in “chunks” where the size is dependent upon the intensity of the cohesive stresses [25, 28]. The effective magnitude of cohesive effects depends primarily on two factors: (1) the intensity and nature of the cohesive forces and (2) the number of interparticle contacts per unit area (packing density). The effect of cohesion on mixing behavior is not always obvious. Slightly cohesive powders have been observed to mix faster than free flowing materials. Strongly cohesive powders, however, blend much more slowly and often require externally applied shear, which may be supplied by an impeller [3]. Chaudhuri and coworkers [26, 29] showed that material possessing a low intensity of cohesion (defined as a bond number of 0.1) enhanced mixing relative to no cohesion (bond number equal to 0) in a rotating drum. Conversely, high values of cohesion (bond numbers greater than 60) reduced the mixing rate. Slight cohesion was shown to improve mixing rate in a rotating drum blending process [27, 30]. In a separate report, slight cohesion may also result in agglomerates [28, 29, 31, 32] that ultimately result in segregation due to the variability in particle diffusion in the vessel [26, 29]. Depending on the blending process, size, and design conditions of the equipment, the effect of cohesion varies as shown by several references in the “Introduction” section. The following sections discuss two methods for quantifying cohesion. Hausner Ratio Interparticle surface forces such as friction and cohesion are dependent on the total surface area. Since mass is proportional to the volume, the surface area to volume ratio is a good general indication of the “flowability” of a powder system [30, 33]. The Hall flowmeter and Hausner ratio are two common techniques for analyzing the effect of interparticle forces on the flow behavior of powder systems
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Table 2 Bin blender and baffle dimensions Mixer (ft3) 0.5 2 10
D (mm)
H1 (mm)
H2 (mm)
L (mm)
V (mm)
θ
Baffle width (mm)
Baffle height (mm)
279.4 457.2 762
153 318.8 516
150 240 500
228.6 381 609.6
88.9 152.4 203.2
35 35 35
31.75 50.8 152.4
50.8 82.55 266.7
under the influence of gravity. The Hausner ratio is the ratio of the tapped density to the apparent (poured) density of the powder. The apparent density tends to decrease as the interparticle friction in a powder system increases. The tapped density tends to decrease as well, albeit a lesser extent due to the additional energy imparted from tapping. The cohesive behavior of a powder is a qualitative description of how powder moves. Yield strength increases with powder cohesion because a larger stress is required to deform the powder [25, 28]. A cohesive powder will have a higher Hausner ratio relative to one that is free flowing. The US Pharmacopeia [34] defines ranges of the Hausner ratio which describe powder flowability. Hausner ratio values between 1 and 1.11 are considered to reflect excellent flow properties. Values greater than 1.6 typically suggest very poor flow, a characteristic of cohesive powders. The larger the surface area to volume ratio, the greater the probability a particle will cling to another. DMV International reports Hausner ratios of 1.21 and 1.28 for lactose 100M and lactose 125M, respectively. Gravitational Displacement Rheometer Many studies measure the magnitude of cohesive forces indirectly using “flow testers.” A common approach is to use a “shear cell” to measure cohesion in the incipient failure regime [24, 27]. A different approach to characterizing cohesion of powder in the dilated state was adopted here. A method using a gravitational displacement rheometer (GDR) to characterize powder flowability, originally developed by Faqih and coworkers [32, 35], is employed in this study. This device produces a “flow index” that is proportional to the yield strength of the dilated powder. Higher flow index values indicate a more cohesive powder and consequently decreased flowability. In the GDR, a cylinder containing the powder sample is mounted on a pivoted table supported by a load cell. As the cylinder rotates, the powder avalanches down the cascading surface, thereby resulting in a change to the center of mass. This shift is measured by the force registered by the load cell. The size and frequency of avalanches are analyzed. As the cohesive nature of the material increases, the resulting avalanches become larger and the frequency of avalanche tumbling decreases. The RSD of the force signal is calculated at several rotation rates and averaged to give an accurate characterization of avalanche size.
Results from this method were used to select grades of lactose with different cohesiveness. The measured flow indices of lactose 100M and lactose 125M were 17.3 and 20.26, respectively.
Results In this section, we discuss the effects of four parameters (tote size, cohesion, rotation rate, and fill level) on the mixing rate of typical pharmaceutical materials in a tote blender. The experiments were performed using acetaminophen, which is typically regarded as a difficult-to-mix API. Two lactose grades were used to simulate formulations of varying cohesion (based on the Hausner ratio). The main effects and interactions were examined. Statistical analysis was used to: (1) identify the critical parameters and (2) develop proper analytical methodology. The variance at each experimental condition is listed in Table 2 for the 0.5-, 2-, and 10-ft3 blenders. The remainder of this section presents the effects of the four experimental parameters on mixing rate. Statistical Analysis Methodology Analysis of variance (ANOVA) is a mathematical procedure for partitioning the variability of a data set into components associated with different main and interaction effects. The information provided by ANOVA is used to construct statistical tests to determine the statistical significance of main effects and their interactions. An F-statistic is computed for each effect (including main and interactions), which is used to test hypotheses about the existence of the effects of variables [33, 36]. In this work, a fully randomized factorial design of the four processing parameters (n=1) was examined. All four variables were treated as fixed-level variables (tote size 0.5, 2, and 10 ft3; speed: H, L; cohesion: lactose 100, lactose 125; fill level 50% and 70%) resulting in a total of 24 treatment conditions (Table 3). Data were analyzed under the usual assumptions of normality and independence. Given the large number of variables, which prevented replications, it was necessary to assume that higher order interactions did not exist in order to release degrees of freedom to estimate an error term. Two models were examined: (1) a model where
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Table 3 Variance results for the three tote blenders 0.5, 2, and 10 ft3 Tote 0.5 ft3 Rev
Tote 2 ft3 Var
Log(var)
Details: low rpm, 50% fill, lactose 100 5 1.353 0.131 25 0.015 −1.825 50 0.014 −1.866 100 0.011 −1.948 Slope= Mixing rate= −0.017 Details: low rpm, 70% fill, lactose 100 5 1.210 0.083 25 0.343 −0.464 50 0.172 −0.765 100 0.076 −1.120 Slope= Mixing rate= −0.012 Details: low rpm, 50% fill, lactose 125 5 1.011 0.005 25 0.112 −0.952 50 0.042 −1.377 100 0.013 −1.881 Slope= Mixing rate= −0.018 Details: low rpm, 70% fill, lactose 125 5 1.472 0.168 25 0.123 −0.910 50 0.072 −1.144 100 0.014 −1.867 Slope= Mixing rate= −0.019 Details: high rpm, 50% fill, lactose 100 5 0.912 −0.040 25 0.194 −0.712 50 0.037 −1.434 100 0.005 −2.314 Slope= Mixing rate= −0.023 Details: high rpm, 70% fill, lactose 100 5 1.668 0.222 25 0.103 −0.988 50 0.020 −1.705 100 0.009 −2.024 Slope= Mixing rate= −0.022 Details: high rpm, 50% fill, lactose 125 5 0.275 −0.561 25 0.045 −1.349 50 0.035 −1.456 100 0.002 −2.737 Slope= Mixing rate= −0.021 Details: high rpm, 70% fill, lactose 125 5 1.117 0.048 25 0.105 −0.977 50 0.023 −1.634 100 0.013 −1.890 Slope= Mixing rate= −0.019
Tote 10 ft3
Rev
Var
Rev
Var
5 25 50 100 Slope=
0.468 0.159 0.032 0.011 Mixing rate=
−0.330 −0.800 −1.490 −1.976 −0.017
5 25 50 100 Slope=
0.187 0.048 0.020 0.012 Mixing rate=
−0.727 −1.322 −1.692 −1.932 −0.012
5 25 50 100 Slope=
0.652 0.286 0.038 0.015 Mixing rate=
−0.186 −0.544 −1.425 −1.816 −0.018
5 25 50 100 Slope=
0.124 0.064 0.024 0.016 Mixing rate=
−0.906 −1.192 −1.621 −1.789 −0.009
5 25 50 100 Slope=
0.065 0.016 0.009 0.005 Mixing rate=
−1.190 −1.792 −2.067 −2.302 −0.011
5 25 50 100 Slope=
0.067 0.050 0.023 0.021 Mixing rate=
−1.175 −1.303 −1.646 −1.670 −0.005
5 25 50 100 Slope=
0.520 0.053 0.059 0.025 Mixing rate=
−0.284 −1.275 −1.232 −1.609 −0.011
5 25 50 100 Slope=
0.138 0.049 0.025 0.023 Mixing rate=
−0.859 −1.310 −1.610 −1.644 −0.008
5 25 50 100 Slope=
0.173 0.035 0.002 0.002 Mixing rate=
−0.762 −1.454 −2.786 −2.754 −0.021
5 25 50 100 Slope=
0.114 0.029 0.024 0.004 Mixing rate=
−0.942 −1.545 −1.626 −2.433 −0.015
5 25 50 100 Slope=
0.439 0.091 0.019 0.009 Mixing rate=
−0.357 −1.039 −1.728 −2.047 −0.017
5 25 50 100 Slope=
0.177 0.018 0.015 0.015 Mixing rate=
−0.752 −1.748 −1.825 −1.832 −0.009
5 25 50 100 Slope=
0.226 0.016 0.007 0.006 Mixing rate=
−0.645 −1.783 −2.156 −2.245 −0.014
5 25 50 100 Slope=
0.156 0.048 0.035 0.023 Mixing rate=
−0.807 −1.320 −1.453 −1.629 −0.008
5 25 50 100 Slope=
0.260 0.083 0.039 0.032 Mixing rate=
−0.584 −1.081 −1.406 −1.498 −0.009
5 25 50 100 Slope=
0.184 0.029 0.015 0.012 Mixing rate=
−0.734 −1.534 −1.832 −1.914 −0.011
all two-way and three-way interactions are considered where 2 degrees of freedom remain for the error term (from assuming a four-way interaction did not exist), and (2) a model where only the two-way interactions are considered
Log(var)
Log(var)
where 9 degrees of freedom remain for the error term. The results are summarized in Tables 4 and 5. The sums of squares, SS, were calculated using SAS version 9.1 (SAS Institute Inc., Cary NC, USA). The p
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Table 4 Four-way ANOVA Source
DF
Rotation rate Fill level Cohesion Tote Fill × tote size Fill × cohesion Fill × rotation rate Rotation rate × tote Rotation rate × cohesion Tote size × cohesion Fill × tote × rotation Fill × cohesion × rotation Fill × cohesion × tote Tote × cohesion × rotation Error
1 1 1 2 2 1 1 2 1 2 2 1 2 2 2
SS
MS
F
p
4.27E−05 1.35E−05 6.02E−05 3.44E−04 1.75E−06 1.35E−05 6.00E−06 1.46E−05 6.00E−06 6.01E−05 7.75E−06 6.70E−07 1.83E−05 1.68E−05 6.58E−06
4.27E−05 1.35E−05 6.02E−05 1.72E−04 8.75E−07 1.35E−05 6.00E−06 7.29E−06 6.00E−06 3.00E−05 3.88E−06 6.70E−07 9.13E−06 8.38E−06 3.29E−06
12.97 4.10 18.29 52.22 0.27 4.10 1.82 2.22 1.82 9.13 1.18 0.20 2.77 2.55
0.07 0.18 0.05 0.02 0.79 0.18 0.31 0.31 0.31 0.10 0.46 0.70 0.27 0.28
value was calculated using Microsoft® Excel’s pdist function. A value of p≤0.05 was selected as the threshold for considering an effect to be significant. The first model (Table 4) indicates only tote size to be significant. The calculated p values for the first model are as follows: tote size (p=0.02), cohesion (p=0.05), rotation rate (p=0.07), and fill level (p=0.18). The error estimate, once again, was obtained from neglecting a four-way interaction. The results obtained from the second model are given in Table 5. This model assumed all three-way interactions to be negligible, a reasonable assumption considering the range of p values (0.27–0.70). The second model, therefore, focuses on the contribution of the main and two-way effects. This model resulted in p values lower than 0.05 for three main effects (tote size, speed, and cohesion), while fill level was not significant. Only one of the two-way interactions (tote size × cohesion) resulted in a low p value. This is consistent with the fact that both tote size and cohesion were the most significant main effects. The error
term, again, was estimated through degrees of freedom obtained by neglecting three-way interactions. Further consolidation of the model does not change the significance of factors mentioned above. A model (not shown) where only the tote size × cohesion and the fill level × cohesion interactions were retained gave nearly identical results. The same three main effects, again, were significant (tote size (p< 0.0001), speed (p=0.016), cohesion (p=0.006)), while fill level was not significant (p=0.15). The tote size × cohesion interaction was significant (p=0.02) and fill level × cohesion interaction was not significant (p=0.15). It must be stressed that failure to prove significance for a given set of experiments is not proof of statistical nonsignificance, especially when a borderline p value is obtained. Effect of Tote Size The effects of tote size have been examined previously [13], where it has been shown that the magnitude of the
Table 5 Four-way ANOVA with no three-way interactions Source Rotation rate Fill level Cohesion Tote Fill × tote size Fill × cohesion Fill × rotation rate Rotation rate × tote Rotation rate × cohesion Tote size × cohesion Error
DF 1 1 1 2 2 1 1 2 1 2 9
SS
MS
F
p
4.27E−05 1.35E−05 6.02E−05 3.44E−04 1.75E−06 1.35E−05 6.00E−06 1.46E−05 6.00E−06 6.01E−05 5.00E−05
4.27E−05 1.35E−05 6.02E−05 1.72E−04 8.75E−07 1.35E−05 6.00E−06 7.29E−06 6.00E−06 3.00E−05 5.56E−06
7.68 2.43 10.83 30.92 0.16 2.43 1.08 1.31 1.08 5.41
0.02 0.15 0.01 0.00 0.86 0.15 0.33 0.32 0.33 0.03
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1.4 1st RSD
1.2
2nd RSD
RSD
1.0 0.8 0.6 0.4 0.2 0.0 0
20
40
60
80
100
120
Revolutions
Fig. 3 The results of a blending experiment with acetaminophen and lactose (highly cohesive) in the 2-ft3 mixer filled to 60% capacity. The blending speed was set to 12 rpm
scale-up effect on mixing performance is dependent upon blend flow properties. A number of process problems are caused by powder cohesion. This is illustrated by interparticle forces resulting in API agglomeration. Figure 3 illustrates the effect of tote size on mixing rates. As expected, the smaller tote had the fastest mixing rate, followed by the medium tote and large tote, respectively. On average, the smallest tote had a mixing rate that was ∼2 times greater than the largest tote and 1.32 times greater than the medium-sized tote. The ANOVA indicated that this parameter had the lowest p value (p
