Powder Technology 194 (2009) Contents lists available at ScienceDirect. Powder Technology. journal homepage:

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1 Powder Technology 194 (2009) Contents lists available at ScienceDirect Powder Technology journal homepage: Effects of rotation rate, mixing angle, and cohesion in two continuous powder mixers A statistical approach Patricia M. Portillo, Marianthi G. Ierapetritou, Fernando J. Muzzio Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ 08854, United States article info abstract Article history: Received 6 May 2008 Received in revised form 8 March 2009 Accepted 25 April 2009 Available online 3 May 2009 Keywords: Continuous powder mixing Statistical analysis ANOVA Homogeneity Residence time In this paper we examine the effect of rotation rate, mixing angle, and cohesion on the powder residence time and the content uniformity of the blend exiting from two continuous powder mixers. In addition, differences in mixing performance between the two blenders are examined. Analysis of variance is used to determine significance of main effects and their interactions. The results show that the effect of powder cohesion is scale-dependent, having a significant effect in the larger mixer. The overall rotation rate was the least influential parameter in terms of content uniformity. The residence time is significantly affected by both rotation rate and mixing angle Elsevier B.V. All rights reserved. 1. Introduction As part of their product development process, pharmaceutical companies carry out intensive research efforts focused on examining and optimizing the production of homogeneous solid mixtures. Minimizing variability in powder blends is critical to pharmaceutical (and many other) manufacturing operations because blend uniformity has direct impact on product quality and performance. Deviations from desired mixing performance, which often lead to batch failures, usually trigger costly process investigations and corrective actions required to maintain regulatory compliance [1]. Unfortunately, powder flow and powder mixing are topics that are far from being well understood. Often, powder mixing processes are designed ad-hoc, based on a limited set of experimental information. Not surprisingly, the need to understand blending has been a central focus of regulatory interest in the past 15 years, and remains a key target of QbD and PAT efforts. In the recently issued Q8(R1) guidance [2], the FDA has recently published their current thinking on using QbD methods to identify critical quality attributes (CQAs), stating that product quality should be studied and controlled by systematically identifying the material attributes and process parameters that can affect the products CQA. Among emerging technologies for improving the performance of blending operations, continuous mixing (and continuous processing in general) currently commands enormous interest at pharmaceutical companies. Continuous processing has numerous known Corresponding author. Tel.: ; fax: address: muzzio@sol.rutgers.edu (F.J. Muzzio). advantages, including reduced cost, increased capacity, facilitated scale up, mitigated segregation, and more easily applied and controlled shear. However, development of a continuous powder blending process requires venturing into a process that has a large and unfamiliar parametric space. While continuous blending processes have been used in other industries, in general such applications operate at much larger flow rates and have less demanding homogeneity requirements than typical pharmaceutical applications. Experimental work published so far has focused on operating conditions such as rotation rate, mixer inclination angle, and flow rate. While several types of continuous mixers have been built, and many more can easily be conceived, only a few geometric designs have been examined in the literature. In our previous work [3] we examined a continuous mixing process and examined a set of operating and design parameters that were found to affect the content uniformity of the final product. The case studies illustrated in previous publications demonstrated that the powder's residence time and content uniformity were affected by operating conditions (rotation rate and mixing angle). A second continuous blender was examined for a broader set of operating conditions. However, many more conditions remain to be examined, and for many interesting designs, performance has never been quantitatively examined in the literature. Thus, substantial work is necessary in order to develop the prior knowledge needed to enable companies to design continuous processes with confidence and economy. Given the magnitude of the task ahead, some consideration should be paid up front to the design of the methodology used to gather shareable information, and the statistical methods to be used to quantify performance and establish significance of various parameters /$ see front matter 2009 Elsevier B.V. All rights reserved. doi: /j.powtec

2 218 P.M. Portillo et al. / Powder Technology 194 (2009) Due to the large experimental data set that arises from the various parameters, we propose systematic application of design of experiments and statistical analysis (specifically, analysis of variance ANOVA) to examine the significance of main factors and their interactions. A reasonable starting point is to consider the system response that is of most interest. A natural approach would be to extend to continuous mixers the methods typically used for batch processes, where a mixing index (typically, a Relative Standard Deviation, also known as the Coefficient of Variability) is computed at the end of the blending process based on samples extracted with a thief. Several other indexes have been used to quantify the mixing performance of particle processes, for example, Lacey (1943) [26] developed a mixing index that considers several variances. Approximately thirty-five other mixing indices can be found in the excellent review by Fan and coworkers [4], which outlines the criteria for selecting an index based on the different degrees of content uniformity that can be achieved. These measurements have been applied to many systems, including various rotating horizontal cylinders [5], V-blenders [6 10], double cones [11], bin blenders [12 14]), ribbon blenders [15], and continuous blenders [16,17]. Although indices can be used to quantify whether design and operating parameters and/or material properties affect mixing performance, by themselves they are poor tools when it comes to revealing which effects are more influential. For the typical number of samples used to characterize batch processes, RSDs are very noisy, and statistically significant differences between process responses for different parametric settings can be established only rarely. Rollins and coworker [18] presented a theoretical discussion on the advantage of the ANOVA technique for Monte Carlo simulations. ANOVAs have also been used for particle processing such as nanoparticle wet milling [19]. Walker and Rollins [20] examined how well ANOVAs perform for detecting mixture in-homogeneity with several non-normal distributions. They found that the Kruskal Wallis test was not superior to the ANOVA technique even when the assumption of normality was broken. Given that ANOVA is the essential tool used in design of experiments, which is one of the essential toolkit components of a modern QbD approach, it seems fitting to introduce the ANOVA technique for the characterization of developing technologies that are intended to be used in modern pharmaceutical manufacturing processes. The basic structure of the paper is as follows. Next, the experimental setup used to examine the content uniformity within a continuous mixer is outlined (Section 2). Section 3 describes the homogeneity measurements and the residence time method is described in Section 4. The statistical analysis method used in this paper is described in Section 5. In Section 6, the results from the first continuous mixer are statistically examined. The effects of mixing angle, rotation rate, and cohesion are explored independently, and then a statistical analysis on all the effects and their interactions is considered. The same type of analysis is then carried out for results obtained for the second mixer. Once both mixers have been examined independently, a 4-way ANOVA is used to determine whether differences between the two mixers are statistically significant. The paper concludes in Section 7 with a summary and conclusions. 2. Materials and processing methods 2.1. Materials Model blends have been formulated using Milled Acetaminophen (30 µm), Lactose 100M (130 µm), and Lactose 125M (55 µm). The average bulk density of Acetaminophen (Mallinckrodt) is 0.297± 1.57E 02 g/ml, for Lactose 100 it is ± g/ml, and for Lactose 125 it is 0.785±0.009 g/ml. A technique for analyzing the effect of interparticle forces, which can be correlated to the flow behavior of powder systems under the influence of gravity includes the measurement of the Hausner Ratio. The Hausner Ratio, which is the ratio of the tapped density to the apparent (or poured) density of the powder, is often used as a preliminary quantifier of powder cohesion (the apparent density tends to decrease as the interparticle friction and adhesion in a powder system increases). The tapped density tends to decrease as well, though at a lesser rate. Therefore, a more cohesive powder (such as Lactose 125M) will have a higher Hausner Ratio than another less cohesive powder (i.e. Lactose 100M). The supplier [21] stated that Lactose 100M has a Hausner 1.21 ratio and Lactose 125M has been reported to have a 1.28 ratio (De Melkindustrie Veghel product specifications Overview) Feeding units After the selection of materials, the powder is fed directly into the mixer inlet using two vibratory powder feeders manufactured by Eriez. Built-in dams and powder funnels are used to further control the feed rate of each feeder. The feed rate for Lactose 100 is 15.5 g/s with a standard deviation of 2.53 g/s and Lactose 125 has the feed rate of g/s with a 2.46 g/s. Samples are taken approximately every 3 s, that means for the shortest average residence time of about 6 s at least 2 samples can be captured Mixing units The two mixing systems examined in this article are both continuous blenders manufactured by GEA Buck Systems. One of the blenders, shown in Fig. 1a, has been discussed in a previous publication Fig. 1. a 1st Continuous Mixer. b 2nd Continuous Mixer.

3 P.M. Portillo et al. / Powder Technology 194 (2009) Table 1 Continuous mixing geometrical descriptions. Mixer Diameter (m) Length (m) No. of blades Blade Blade type length (m) [3]. Previously obtained results will be summarized and used in this article to compare to results obtained for the second mixer, shown in Fig. 1b. The blenders vary in diameter and length as well as the design of the blades within the vessel. The first blender (Fig. 1a) has a diameter that is 3 fold that of the second blender (Fig. 1b). Moreover, the first blender has an axial vessel that is 2.4 times longer than the second blender. Geometric parameters of each blender are shown in Table 1. Fig. 2a and b shows the blade design for each of the continuous mixers. Other than geometrical differences, the systems work similarly, except that the smaller mixer is capable of much higher impeller speeds. The blenders have three main adjustable parameters that determine the degree of operational flexibility (the operational space): the vessel angle, impeller rotation rate, and the blade pattern. For both mixers, the process is as follows: as material enters the mixer, the powder crosses the pathway of several impeller blades attached to a rotating shaft placed along the axial length of the horizontal cylinder. Convective flow is the primary source of cross-sectional mixing, driven by the impeller blades. As the blades rotate, shear stress is applied, powders experience extensive strain, and agglomerates are broken up. Finally, particles collide with each other, or experience micro-avalanches, leading to dispersive mixing in all directions. One primary objective of this (and any) continuous mixer is to minimize the variability that exists in the feeding rate of ingredients by axial and cross-sectional dispersion so that the exiting stream is as homogeneous as possible. The other function of the convective motion is to axially transport the powder along the vessel (from the entrance to the discharge). The effectiveness of the mixer is particularly affected by the design of the convective system (the impeller and blades). As shown in our previous work [3], a design parameter that affects mixing performance is the blade angle relative to the shaft. Axial transport is also affected by the vessel angle relative to the direction of gravity, because gravitational forces also affect axial transport (and powder residence time distribution) as a function of inclination. This factor will be discussed further in later sections of this paper Near Infrared (NIR) Analysis of sample composition Speed (RPM) Rectangular with a circular tip Triangular with a circular tip Powder samples are retrieved from the mixers outflow and characterized using Near Infrared Spectroscopy (NIR). This method is commonly and conveniently used to assay the content of powder samples [22]. The NIR System used to analyze the experimental data presented in this paper is the Nicolet Antaris, Near-IR Analyzer from Thermo Electron Corp. The samples are analyzed to calculate the amount of Acetaminophen present in the sample using Near Infrared (NIR) Spectroscopy. In the calibration set, a total of 90 samples is used, each sample composed of a different ratio of APAP and Lactose. The range we used in this study consists of APAP blends from 0 to 9%. Each sample has a total mass of approximately 5 g. These samples are then scanned using the NIR reflectance spectroscopy; and their absorbance spectrum is determined for a wavelength range of nm using OMNIC. Within this range we examine two spectrum regions: and nm. Using TQ Analyst mathematical regression is applied to all the calibration spectra, and a resulting model is built using partial-least squares of the 2nd order derivative of the spectrum using a constant path length, no correction, no smoothing, and normalizing with a mean centering technique. The performance of the model is then assessed using a set of validation samples (samples of known concentration not used in the calibration set). The validation samples are scanned and their predicted content is obtained from the NIR model. These values are then compared to the known component concentration. The degree of accuracy in predicting the composition of the validation samples provides a quantitative method for validating the NIR model. The closer the plot of the measured versus predicted concentrations are to a linear function, the better the models performance. In this study, a regression value of R 2 =0.99 was obtained. Once a model is developed, the function of the model is to examine the spectrum of samples of unknown concentration and measure their components concentration. 3. Homogeneity measurements The homogeneity of samples retrieved from the outflow is measured by calculating the variability in the samples Acetaminophen concentration. The Relative Standard Deviation (RSD) of Acetaminophen concentration shown in Eq. (1) measures the degree of homogeneity of the mixture relative to the average concentration of the samples: RSD = sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P n ðx i X 2 Þ i =1 X n 1 where X i is the sample Acetaminophen concentration retrieved at time point t i ; n is the number of samples taken; and X is the average concentration over all samples retrieved. Lower RSD values mean less variability between samples, which implies better mixing. The standard definition of the relative variance, σ 2, is shown in Eq. (2) ð1þ Fig. 2. Convective design of a) Continuous Mixer 1. b) Continuous Mixer 2.

4 220 P.M. Portillo et al. / Powder Technology 194 (2009) where n is the number of samples, and x is the mean composition (Eq. (2)). = P n i =1 X 2 ðx i XÞ 2 n 4. Residence time The residence time distribution is an allocation of the time different elements of the powder flow remain within the mixer. In this study the residence time measurements are found as follows: A quantity of a tracer substance (which in our case is Acetaminophen) is injected into the input stream; instantaneously samples are then taken at various times from the outflow. After the injection, the concentrations of the injected material in the exit stream samples are analyzed using Near Infrared (NIR) Spectroscopy. This will provide the residence time distribution, which is used to obtain an average residence time. 5. Statistical analysis A randomized experimental design was used to examine the four main variables (mixer type, mixing angle, rotation rate, and powder cohesion), as well as their interactions. For each mixer, we initially examine a three-way ANOVA considering mixing angle, speed, and type of powder. Initially, all factors and interactions are considered, subsequently reducing the statistical model to remove the non-significant effects. It is important to mention that we examine some of these variables in more detail in order to illustrate the effect of mixing performance and residence time. On the first mixer, a full factorial design is used, for the second a fractional factorial design, and when we examine both mixers a fractional factorial design is built from the data. The levels examined for the factorial design consider 3 mixing angles and 2 rotation rates (16 RPM and 76 RPM) for the first mixer, reflecting speed limitations in the device. A broader set of conditions is considered for the second mixer, including 5 mixing angles and 9 rotation rates up to 300 RPM. The section on rotation rate illustrates the effect of increasing the speed further for the second continuous mixer. For both systems, 2 different Lactose powders, Lactose 100M and Lactose 125M, a slightly more cohesive powder, are examined. The methodology used in this study begins with the full statistical model for the three-way ANOVA of each mixer: y jkl = μ + α j + β k + αβ jk + γ l + αγ jl + βγ kl + αβγ jkl + e jkl In the above equation, the single-symbol terms in the model refer to the overall average α and the main effects; α for mixing angle, β for rotation rate, and γ for powder cohesion which are estimated based on the sum of squares error. Their subscripts j, k, l refer to the number of levels of each variable: mixing angle, rotation rate, and cohesion, respectively. The bilinear terms represent the interactions between main factors and the error term is represented by ε. The p-value is an indication of significance. A p-value lower than 0.05 usually means that the effect is significant, because the probability that observed differences corresponding to different levels of the independent variable (or, for interactions, the combinations of levels of two or more variables) be due to chance are lower than p. Thus, it is concluded that groups of observations for different levels of independent variables are significantly different from each other, and that the variable therefore has a statistically significant effect, and as a result, the null hypothesis (that results for different levels are not different from each ð2þ ð3þ other) can be rejected with a high probability (great than 95%) of correctness. An example of a null hypothesis in this study would be that the mean variability of the content uniformity for different levels of cohesion be the same, i.e. that the levels of cohesion of the powder considered in the study do not have a statistically significant effect on the homogeneity of samples. The terms that are found to be nonsignificant (pn0.2) for the initial model, are eliminated in subsequent models in order to form a new ANOVA. This step is repeated until all the effects left are considered significant (pb0.05). The same analysis is performed for the 4-way ANOVA, where the additional parameter h represents the effect of the mixer y ijkl = μ + η i + α j + ηα ij + β k + ηβ ik + αβ jk + γ l + ηγ il + αγ jl + βγ kl + ηαβ ijk + ηβγ ikl + αβγ jkl + αβγη ijkl + e ijkl ð4þ Analysis of Variance (ANOVA) is a standard statistical procedure where the variability in a data set is properly calculated for each main effect and for each interaction retained for a given statistical model. An ANOVA table includes the different treatments examined. The degrees of freedom, DF, for each treatment reflects the number of different levels. If the different number of levels for each treatment is equal to g, the degrees of freedom is found by, DF=g 1. The sum of squares, SS, and the Mean Sum of Squares, MS for each treatment and error are found using SAS version 9.1 (SAS Institute Inc., Cary N.C.). Many equivalent commercial software packages exist for conducting ANOVA analysis of data sets. In this paper, the sum of squares was determined by inputting the relative variance of powder streams for each experiment in SAS. An appropriately formed F-statistic (or F-ratio) is computed for each effect and interaction, and the value obtained is compared to a critical value corresponding to a certain (pre-selected) probability that the observed effects be in fact due to chance. Results can be used for comparing models and, during post-anova processing, to establish which groups within a data set typically represent the response of the system for a given set of treatment conditions. Moreover, the p-value is defined as the probability of obtaining a result at least as extreme as a given data point, under the null hypothesis. The p-value was calculated using M.S. Excel's p-dist function. The smaller the p-value, the larger the component has a significant contribution to the main effect. Values of p greater than 0.05 do not mean that the null hypothesis is true, they simply mean that given the amount of data available, we cannot assert with sufficient confidence that they are actually different from each other (i.e., that an effect actually exists). Moreover, given a certain data set, p values are customarily used to rank the relative significance of the multiple variables and their interactions. This practice is somewhat misleading, since the relative values of p can (and do) depend on the number of levels of a given variable that are explored, the number of replications, etc, and therefore, comparisons (and statistically based conclusions in general) should always be considered under the caveat given available data. 6. Results The results presented in our previous work [3] described the mixing performance and residence time of the first continuous mixer. In this study we supplement the previously published results with new results obtained for the second continuous mixer. A summary of results for both systems is presented in Table 9. In the next section we compare the performance of both mixers and examine the significance of the various model parameters and their interactions. Moreover, another advantage to applying statistical analysis to multivariate factorial experimental design in comparison to onefactor-at-a-time experiments is that the interactions between variables are also considered.

5 P.M. Portillo et al. / Powder Technology 194 (2009) Statistical analysis for Continuous Mixer 1 As mentioned before, the three parameters specifically examined for the first mixing vessel (Fig. 1) are vessel angle, impeller rotation rate, and blend cohesion. The three mixing angles that were examined were an upward (+15 ), horizontal, and downward inclination ( 15 ). Two impeller rotation rates (16 and 76 RPM) were examined, and two different grades of lactose; Lactose 100M and Lactose 125M. The Hausner ratio illustrated that Lactose 100M was less cohesive than Lactose 125M. The results are summarized in Table 2 using the compositional relative variance of powder samples taken at the discharge of the mixer data as the main response. For each treatment combination, about 20 samples approximately 3 g in weight were examined. The samples were taken at the outflow approximately every 2 3 s. Results readily showed that all the parameters play an important role on the mixing performance. In what follows, the statistical analysis will be split into two parts one considers three main effects (mixing angle, rotation rate, and cohesion) on homogeneity and the effects of mixing angle and rotation rate on residence time Homogeneity Here we briefly recount three previously published observations: (1) between the two different rotation rates, on average, lower compositional relative variances are found for the lower rotation rate; (2) a more cohesive powder did show different results than the less cohesive powder. Interestingly, performance did not seem to improve when cohesion was reduced; (3) the inclination of the vessel played a critical role in the content uniformity. In order to establish the statistical significance of these observations, the results were analyzed using ANOVA. Initially, the statistical model used is: y jkl = μ + α j + β k + αβ jk + γ l + αγ jl + βγ kl + αβγ jkl + e jkl For n=1 this model is not fully solvable; in particular, the threeway interaction is confounded with the error. Since n=1 for the first mixer, not all interactions can be examined simultaneously. Multivariate analysis requires assuming that some interactions do not exist in order to release degrees of freedom to construct an error term ε. Since the three-way interaction is the least likely to be significant, we neglect this term (i.e., we assume that the three-way interaction is not significant) and use the degrees of freedom of the three-way interaction to form an error term, which results in the following model: ð5þ denoted M for mixing angle, R for rotation rate, and C for cohesion. This yields the following mean square (MS) equations: MS M = + / MR + / MC + / M MS R = + / MR +2/ RC +2/ R MS C = + / MC +2/ RC +2/ C MS MR = + / MR MS MC = + / MC MS RC = +2/ RC MS E = ð7þ ð8þ ð9þ ð10þ ð11þ ð12þ ð13þ The solutions to these equations for the error terms can be found as: =MS E ð14þ / MR =MS MR MS E ð15þ / MC =MS MC MS E ð16þ / RC = MS RC MS E 2 Fig. 3. Normality plot of data shown in Table 2. ð17þ y jkl = μ + α j + β k + αβ jk + γ l + αγ jl + βγ kl + e jkl ð6þ / M =MS M MS MR MS MC +MS MRC ð18þ Next we compute the expected mean squares (EMS) terms. Fixed effects are represented by the letter ϕ, with the appropriate subscript Table 2 Continuous Mixer 1 experimental relative variance results obtained from varying materials, mixing inclination, and rotation rate. Observation Mixing angle Speed Cohesion Relative variance 1 Upward 16 Lactose Horizontal 16 Lactose Downward 16 Lactose Upward 75 Lactose Horizontal 75 Lactose Downward 75 Lactose Upward 16 Lactose Horizontal 16 Lactose Downward 16 Lactose Upward 75 Lactose Horizontal 75 Lactose Downward 75 Lactose / R = MS R MS MR MS RC +MS MRC 2 / C = MS C MS MC MS RC +MS MRC 2 Using the error terms, the F-statistical ratio can be found by F M = + / MR + / MC + / M F R = + / MR +2/ RC +2/ R F C = + / MC +2/ RC +2/ C F MR = + / MR ð19þ ð20þ ð21þ ð22þ ð23þ ð24þ

6 222 P.M. Portillo et al. / Powder Technology 194 (2009) F MC = + / MC ð25þ Table 5 Continuous Mixer 1 residence time as a function of rotation rate and processing inclination for Lactose 100. F RC = +2/ RC ð26þ The experimental data was analyzed under the usual assumptions of normality and independence. Model check for residuals is shown in the normality plot in Fig. 3. For this model, the standard ANOVA table is shown in Table 3,where the sources are vessel angle, impeller rotation rate, and powder cohesion grades. Three angles, two rotation rates, and two different powders that vary in cohesion were studied. As mentioned in the statistical analysis section, main effects are listed in order of increasing p-values, where the lowest p-value is the (statistically) most significant factor affecting the relative variance for the data set at hand. In this case, the impeller rotation rate is the most significant factor, followed by powder cohesion; the least significant being vessel angle. The interactions are fairly insignificant with p-values greater than 0.2. Thus, we re-examine the main effects using a 3-way ANOVA neglecting the interactions. The resulting model is shown below: y jkl = μ + α j + β k + γ l + e jkl ð27þ The ANOVA for this model is shown in Table 4. Clearly, all the main effects remain significant, displaying very small values of p. The two most significant factors are rotation rate and cohesion based on the MS. The least significant factor, although still clearly significant, is the mixing angle Residence time In our previous work [3], we showed that the residence time of powder in the blender was affected by rotation rate and vessel angle. Here we examine the effect of rotation rate and processing angle on the residence time. The 12 observations used are shown in Table 5, the resulting statistical model is as follows: y jk = μ + α j + β k + αβ jk + e jk ð28þ The ANOVA results are shown in Table 6. Clearly both main effects are significant, whereas the interaction can be considered insignificant with a p-value of 0.3. Table 3 3-way ANOVA on the blend uniformity relative variance for Continuous Mixer 1 considering the treatments as: mixing angle, rotation rate, cohesion, and their interactions. Mixing angle E E Rotation rate E E Cohesion E E Mixing angle rotation rate E E Mixing angle cohesion E E Rotation rate cohesion E E Error E E 06 Table 4 3-way ANOVA on the blend uniformity relative variance for Continuous Mixer 1 considering the treatments as: mixing angle, rotation rate, cohesion. Mixing angle E E Rotation rate E E Cohesion E E Error E E 06 Observation Mixing angle Rotation rate (RPM) Residence time (s) 1 Upward Upward Horizontal Horizontal Downward Downward Upward Upward Horizontal Horizontal Downward Downward Table 6 2-way ANOVA for residence time of the first continuous mixer examining mixing angle, rotation rate, and their interactions. Mixing angle Rotation rate 1 26, , Mix. angle Rot. rate , Error In order to further examine the significance of the two main effects, the interaction term is eliminated, and the resulting model is as follows: y jk = μ + α j + β k + e jk ð29þ The ANOVA shown in Table 7 for this model clearly shows that both process parameters are significant where rotation rate is partly more influential than mixing angle. As expected, lower shear rates and vessel inclinations resulted in longer residence times, which have also been noticed in rotary calciners [23] Second continuous mixer The preceding section illustrated that the mixing inclination was the least significant parameter among variations in rotation rate and cohesion. In this section, the second, smaller continuous blender with a different geometric and blade design (Fig. 1b) is examined for a broader set of operating conditions. We first provide an individual discussion of the observed effects of the main parameters, followed by a full statistical analysis of the data set Second continuous mixer: effect of vessel angle The effects of vessel angle on the content uniformity of the outgoing powder are shown in Fig. 4a for experiments using 3% APAP and the rest consisting of Lactose 125M at a rate of 50 RPM, at a total flow rate of 16 g/s. This figure illustrates the results from 5 different mixing angles. Results indicate that the higher the vessel angle from the horizontal position, the better the content uniformity. This can be an effect of the larger residence time the powder experiences at higher inclinations. Residence times at each vessel angle are shown in Table 7 2-way ANOVA for residence time of the first continuous mixer examining mixing angle, and rotation rate. Mixing angle Rotation rate 1 26, , Error

7 P.M. Portillo et al. / Powder Technology 194 (2009) Fig. 6. Number of blade passes Lactose 125M experiences as a function of rotation (RPM). Fig. 4. a. RSD versus mixing angles at 50 RPM using Lactose 125M. b. Residence time versus mixing angles at 50 RPM using Lactose 125M. Fig. 4b. Clearly both residence time and content uniformity are affected by the vessel angle; the data suggests that more effective mixing occurs at the upward angle, which, as shown in Fig. 4b corresponds to the highest residence time Effect of rotation rate As discussed above, the rotation rate of the blades determines the rate of shear and the intensity of material dispersion throughout the mixer, potentially affecting mixing performance. For the second mixer we examine six different levels of impeller speed (or process shear rate) at the horizontal vessel position for a Lactose 125M blend. The RSD results are shown in Fig. 5a and indicate that, once again, better content uniformity is observed at the lower shear rates. This might be a result of the effect of rotation rate on residence time, shown in Fig. 5b, which illustrates to be higher at lower rotation rates (since the total strain the powder experiences is proportional to the total number of blade passes). However the total number of blade passes is actually larger for the highest rotation rate. Fig. 6 shows the number of passes as a function of RPM, confirming that at higher shear rates the powder experiences a greater total amount of strain. In fact, the relationship between the total number of blade passes and rotation rate can be considered a fairly linear function with a regression coefficient of Both total strain (total blade passes) and shear rate (RPM) affect the content uniformity in a similar manner Effect of powder cohesion In addition to operating conditions such as rotation rate and mixing inclination, material properties have shown to affect the blending performance of batch mixing systems [24]. For a continuous convective system, Harwood et al. [17] examined the same formulation composed of sand and sugar for several convective continuous mixing systems, varying cohesion by sifting the materials into different particle size ranges, but failed to observe a significant effect. Bridgwater and coworkers [25] for a closed convective mixing system found that the motion of varying size of tracer particles from 2 to 4 mm, processing at 4 Hz showed no discernible effect in terms of particle trajectories. The case studies presented in this work examine the mixing performance between two different Lactose materials that vary in cohesion. Fig. 7 illustrates the results obtained from mixing Fig. 5. a. RSD versus rotation rate (RPM) at a horizontal mixing angle for Lactose 125M. b. Residence time (s) versus rotation rate (RPM). Fig. 7. Continuous mixing RSD results from Lactose 100 and Lactose 125.

8 224 P.M. Portillo et al. / Powder Technology 194 (2009) Milled Acetaminophen with Lactose 100 and Lactose 125, at the horizontal mixing inclination. The new results presented here reveal that an effect indeed exists, although it is not very significant. In fact, the effects of cohesion can be system-dependent. Since cohesion can affect the degree of variability in the flow rate delivered by a powder feeder, it should be expected that cohesion could have impacted on the performance of the integrated system, including feeders, mixers, and downstream finishing equipment. However, the differences in relative standard deviation between the two powders are small. The lack of a large observed effect could be due to the fact that shear rates are typically higher in convective systems than in tumblers (in fact convective blenders are often used for cohesive materials because they impart more shear), and it is possible that for Table 9 Three-way ANOVA on the blend uniformity relative variance for the second Continuous Mixer considering the treatments as: mixing angle, rotation rate, cohesion as well as 2- way and 3-way interactions. Mixing angle E E Rotation rate E E Cohesion E E Mixing angle rotation rate E E Mixing angle cohesion E E Rotation rate cohesion E E Mixing angle rotation cohesion E E Error E E 05 Table 8 Continuous Mixer 2 experimental relative variance results obtained from varying materials, mixing inclination, and rotation rate. Observation Mixing angle Speed (RPM) Cohesion Relative variance 1 Upward 16 Lactose Horizontal 16 Lactose Downward 16 Lactose Upward 75 Lactose Horizontal 75 Lactose Downward 75 Lactose Upward 16 Lactose Horizontal 16 Lactose Downward 16 Lactose Upward 75 Lactose Horizontal 75 Lactose Downward 75 Lactose Upward 50 Lactose Upward 50 Lactose Upward horizontal 50 Lactose Upward horizontal 50 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal down 50 Lactose Horizontal down 50 Lactose Downward 50 Lactose Downward 50 Lactose Horizontal 25 Lactose Horizontal 25 Lactose Horizontal 25 Lactose Horizontal 25 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal 100 Lactose Horizontal 100 Lactose Horizontal 100 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 175 Lactose Horizontal 175 Lactose Horizontal 175 Lactose Horizontal 175 Lactose Horizontal 275 Lactose Horizontal 275 Lactose Horizontal 300 Lactose Horizontal 300 Lactose Horizontal 25 Lactose Horizontal 25 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal 75 Lactose Horizontal 75 Lactose Horizontal 125 Lactose Horizontal 125 Lactose both materials considered here, cohesion is simply too small to affect the outcome of the convective mixing process to a large degree. However, an ANOVA can be helpful in order to determine whether or not the small observed effect of cohesion is statistically significant and the application of statistical analysis is the focus of the following section Statistical analysis (second continuous mixer) In this section, an ANOVA is conducted taking into account the effects of processing inclination, rotation rate, and cohesion on the homogeneity measurements of the second continuous mixer, followed by an investigation on the effects of mixing angle and rotation rate on the residence time. The approach is essentially the same as the one used for the first mixer Homogeneity. In this section, we examine the effects on blend homogeneity of the three parameters previously mentioned: processing inclination, rotation rate, and cohesion. As shown in Figs. 4a and 5a, we have obtained a larger number of experimental results for the second mixer than for the first mixer for one grade of lactose. Five mixing angles and seven rotation rates were considered where the mixing experiment was duplicated 2 5 times, the result was a total of 55 experimental observations. Table 8 lists all the observations from the main effects (mixing angle, rotation rate, and powder cohesion). Initially, the full model is used: y jkl = μ + α j + β k + αβ jk + γ l + αγ jl + βγ kl + αβγ jkl + e jkl ð30þ As previously discussed, blend relative variance appears to change as a function of all these parameters. However, the question that remains is whether the observed effects are indeed significant. Table 9 illustrates the three-way ANOVA for the fractional factorial design, which since nn1, it can be solved for all interactions. Since the observations result in a fractional factorial design, it is important to point out that the degrees of freedom for the interactions are not multiples of the main sources. Results show that mixing angle is the most significant contributor to the observed differences in blend relative variance. The following significant parameter is rotation rate, followed by cohesion, which is not significant for the available data, and is characterized by a very high p-value of 0.7. Only the interaction between angle and rate is significant; all interactions involving Table 10 Two-way ANOVA for relative variance of the second continuous mixer examining mixing angle, rotation rate, and a 2-way interaction. Mixing angle E E Rotation rate E E Mixing angle rotation rate E E Error E E 05

9 P.M. Portillo et al. / Powder Technology 194 (2009) cohesion are also clearly non-significant. Using this information we simplify the model as follows: y jkl = μ + α j + β k + αβ jk + e jkl ð31þ The error terms for the second mixer are found in the same manner as for the first mixer discussed in Section 6.1. The results of this statistical model are shown in Table 10. All three terms remain significant, showing a lower value of p than in the full model. One remaining question is whether differences between the mixers are significant. Which is important considering one of the main variables between the mixers is blade design, which was shown in our previous experimental study to have an impact on product performance. Later in this paper, a 4-way ANOVA will consider the results from both mixers, and reassesses the significance of other parameters when considering both datasets. Prior to that, in the next section we examine the behavior of the powder residence time in the second mixer Residence time. In our previous work [3] we found a direct correlation between improved mixing and higher residence times. As shown in Figs. 4b and 5b, both angle and rotation rate affect the residence time. In the experiments reported here, five mixing angles and seven rotation rates where considered, each experiment was duplicated, resulting in a total of 24 observations. Clearly from Fig. 4a and b the average residence times are influenced by these operating parameters. However, what is not obvious is which one of these parameters is the most dominant and whether the variability between the duplicated experiments lessens the impact of this results. Details are shown in Table 11. Above, we considered whether the low significance of rotation rate on mixing is a result of rotation rate not statistically affecting residence time. Not enough data exists to determine the interaction of rotation rate and mixing angle but the main effects can be examined using the following statistical model: y jk = μ + α j + β k + e jk ð32þ The 2-way ANOVA for this model is shown in Table 12, where we consider the sources of mixing angle and rotation rate on residence time. After examining the results using statistical analysis the factors can be prioritized, it is evident that mixing angle has a significant Table 11 Continuous Mixer 2 experimental residence time results obtained from varying materials, mixing inclination, and rotation rate. Observation Mixing angle Speed (RPM) Residence time (s) 1 Upward Upward Upward hori Upward hori Horizontal Horizontal Horizont down Horizont down Downward Downward Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Table 12 2-way ANOVA for residence time of the second continuous mixer examining mixing angle and rotation rate. Mixing angle 4 14, E 10 Rotation rate Error effect on residence time, with a p-valueb0.0001, followed by the effect of rotation rate whose effect has a lower significance, exhibiting a p-value of The MS is a good indicator of relative significance among factors because of its incorporation of degrees of freedom, where the MS for mixing angle was 3519, suggesting a more significant effect than for rotation rate at 66. It is important to mention that the analysis suggests that both mixing angle and rotation rate affect blend uniformity as well as residence time. Although, the data may suggest that higher residence time does result in better blend uniformity there is no direct linear correlation, primarily because residence time is an indicator of the amount of time spent with the mixer and not the magnitude of shear or radial mixing applied on a powder bed Four-way ANOVA After we examine the mixing inclination, rotation rate, and cohesion for each individual mixer, we examine the effect of the different mixers. This approach addresses design space studies across scales, since blender size is now treated as an independent variable. For batch rotating mixing systems, the scale of a mixer affects the shear rate; the larger the mixer, the greater the shear rate. For free flowing powders this effect may be dismissed since shear is not required to achieve homogenization; however for cohesive mixtures, a reduction in shear can lead to a decrease of the achievable degree of homogeneity [24]. As previously mentioned, convective blenders impart high shear conditions particularly beneficial for cohesive materials, which may otherwise agglomerate. More intense shear can break and disperse agglomerates, enhancing homogeneity on a finer scale. The entire set of results used for 4-way analysis is shown in Table 13. Initially the model is: y ijkl = μ + η i + α j + ηα ij + β k + ηβ ik + αβ jk + γ l + ηγ il + αγ jl + βγ kl + ηαβ ijk + ηβγ ikl + αβγ jkl + αβγη ijkl + e ijkl ð33þ The Four-way ANOVA for this model is shown in Table 14; the sources are the mixer, processing inclination, rotation rate, and cohesion. The ANOVA showed that for the range of cohesions studied, cohesion is not a significant factor. Mixing angle and mixer, followed by rotation rate, are the most significant parameters. The interaction between the three effects (cohesion, mixing angle, and mixer) was also the most influential among the interactions. The least influential main effect was rotation rate. All other interactions with the exception of the three-way interaction, were also fairly insignificant with p- values greater than Further examining the effects of the three most significant factors we neglect the main effect of cohesion and all interactions, which results in the following model: y ijkl = μ + η i + α j + β k + ηα ij + αβ jk + e ijkl ð34þ The ANOVA for this statistical model is shown in Table 15. The ANOVA illustrates that mixer, processing angle, and rotation rate are significant. Harwood et al. (1975) [27] observed that the mixing performance of several convective continuous mixers was sometimes independent of the formulation primarily because blade designs differ and play an important role in blending. This might lead to an

10 226 P.M. Portillo et al. / Powder Technology 194 (2009) Table 13 Relative variance observations as a function of mixer, processing angle, speed, and cohesion. Observation Mixer Mixing angle Speed Cohesion Relative variance 1 1 Upward 16 Lactose Horizontal 16 Lactose Downward 16 Lactose Upward 75 Lactose Horizontal 75 Lactose Downward 75 Lactose Upward 16 Lactose Horizontal 16 Lactose Downward 16 Lactose Upward 75 Lactose Horizontal 75 Lactose Downward 75 Lactose Upward 16 Lactose Horizontal 16 Lactose Downward 16 Lactose Upward 75 Lactose Horizontal 75 Lactose Downward 75 Lactose Upward 16 Lactose Horizontal 16 Lactose Downward 16 Lactose Upward 75 Lactose Horizontal 75 Lactose Downward 75 Lactose Upward 50 Lactose Upward 50 Lactose Upward horizontal 50 Lactose Upward horizontal 50 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal down 50 Lactose Horizontal down 50 Lactose Downward 50 Lactose Downward 50 Lactose Horizontal 25 Lactose Horizontal 25 Lactose Horizontal 25 Lactose Horizontal 25 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal 100 Lactose Horizontal 100 Lactose Horizontal 100 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 125 Lactose Horizontal 175 Lactose Horizontal 175 Lactose Horizontal 175 Lactose Horizontal 175 Lactose Horizontal 275 Lactose Horizontal 275 Lactose Horizontal 300 Lactose Horizontal 300 Lactose Horizontal 25 Lactose Horizontal 25 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal 50 Lactose Horizontal 75 Lactose Horizontal 75 Lactose Horizontal 125 Lactose Horizontal 125 Lactose assumption that convective continuous mixers may not be affected by material properties, whereas the convective design and blender geometry may be important parameters to define. Previously in the 3-way ANOVA of the second mixer we found that cohesion was not an Table 14 Four-way ANOVA considering the treatments as: mixer, mixing angle, rotation rate, cohesion, and their interactions. Mixer E E Mixing angle E E Rotation rate E E Cohesion E E Mixer mixing angle E E Mixer rotation rate E E Mixer cohesion E E Mixing angle rotation rate E E Mixing angle cohesion E E Rotation rate cohesion E E Mixer mix. angle rotation r E E Mixer mix. angle coh E E Mixer rotation r. coh E E Mix. angle rotation r. coh E E Mixer mix. angle rot coh E E Error E E 05 important parameter that statistically affected the mixing performance. Clearly in this work we found that cohesion did not affect blend performance. 7. Summary and conclusion A majority of the existing continuous mixing work examines the effect of the convective system and rotation rate on the mixing behavior and residence time. In this work we extend our investigation of rotation rate, cohesion, and mixer inclination using statistical analysis. Several ANOVAs were presented; a 3-way ANOVA for the first mixer illustrating that all processing and material parameters did influence performance. In the 3-way ANOVA for the second mixer the mixing angle played a more significant role on mixing than the rotation rate. Cohesion did not have a significant effect on homogeneity when we examined two different cohesion levels. Given the difference in size and convective design of the blenders presented, a mixer effect was to be expected. A 4-way ANOVA examined the main effects of processing conditions, material parameters, and the mixers. The result indicated that the mixer angle was a significant parameter and the more influential parameters were the rotation rate and mixer variability, followed by cohesion. Within the range examined, cohesion was the least significant factor, with a p- value of 0.43 in the 4-way ANOVA. Neglecting cohesion and its interactions as a source of error in the statistical model resulted with a clear indication that the significant parameters were the mixer angle, mixing device, and rotation rate based on MS. Residence time was also examined and clearly illustrated to be influenced by rotation rate and mixing angle for both mixers. For the first continuous mixer we examined two different speeds and 3 mixing angles, where the most significant factor was the rotation rate. On the other hand for the smaller mixer, 5 mixing angles and 7 rotation rates were examined and mixing angle showed to be the more influential parameter. The objective of this work was to apply a statistical method to characterize the significance of design, operation, and material Table 15 Three-way ANOVA considering the treatments as: mixer, mixing angle, and cohesion. Mixer E E E E 04 Mixing angle E E E 20 Rotation rate E E E 05 Mixer mixing angle E E E E 05 Mixing angle rotation rate E E E 12 Error E E 05