Chemical Engineering Science

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1 Chemical Engineering Science 69 (2012) Contents lists available at SciVerse ScienceDirect Chemical Engineering Science journal homepage: DEM simulation of continuous tablet coating: Effects of tablet shape and fill level on inter-tablet coating variability Daniele Suzzi a, Gregor Toschkoff a, Stefan Radl a,b, Daniel Machold a, Simon D. Fraser a, Benjamin J. Glasser c, Johannes G. Khinast a,b,n a Research Center Pharmaceutical Engineering GmbH, Graz, Austria b Institute for Process and Particle Engineering, Graz University of Technology, Graz, Austria c Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ, USA article info Article history: Received 7 April 2011 Received in revised form 9 August 2011 Accepted 5 October 2011 Available online 28 October 2011 Keywords: Continuous manufacturing Tablet coating Discrete Element Method Simulation Pharmaceuticals Tablet shape abstract Tablet coating is a common pharmaceutical technique of applying a thin polymer-based film to a tablet or a granule containing active pharmaceutical ingredients (APIs). Inter- and intra-tablet variability of film coating is a critical issue in the production of solid oral dosage forms. In fact, inhomogeneity in the coating thickness can lead to significant variations in the delivery rate of active pharmaceutical ingredients and compromise the functional attributes of the tablet film. Although attempts have been made to use numerical approaches to analyze this complex problem, at present the uniformity of coating thickness is difficult to predict without expensive experimental work. The aim of this work is to analyze and understand the effects of tablet form and fill volume on the intra-tablet coating variability in a semi-continuous coating device. To this end, the Discrete Element Method was used to numerically reproduce the tablet motion inside a chamber of the coating pan. First, the material attributes of a sample placebo tablet were experimentally quantified in detail. Thereafter, three different tablet shapes, namely bi-convex, oval, and round, were modeled by means of the glued spheres method. The effect of three different fill volumes was then analyzed in terms of RT of the tablets under the coating spray, leading to a quantification of the intra-tablet coating variability for each particle shape. A detailed analysis of the tablets velocities, both translational and rotational, on top of the tablet bed is presented. These results help to understand the dynamical behavior of the tablets under a spray gun that is essential for a satisfactory intra-tablet coating homogeneity. Finally, the various behaviors observed during the numerical simulations were addressed through a detailed analysis of the tablets flow on the bed in terms of mean velocities and granular temperatures. The aim of this work is to demonstrate how a numerical simulation may be used for the development and design of continuous pharmaceutical tablet coating processes. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. Batch vs. continuous pharmaceutical manufacturing Conventional pharmaceutical manufacturing is described in FDA s Guidance for Industry: PAT A Framework for Innovative Pharmaceutical Development, Manufacturing, and Quality Assurance as being generally accomplished using batch processing with laboratory testing conducted on collected samples to evaluate quality (FDA, 2004). Although this statement is a simplification and is generally not applicable to all pharmaceutical unit operations or n Corresponding author at: Graz University of Technology, Institute for Process and Particle Engineering, Graz, Austria. Tel.: þ ; fax: þ address: (J.G. Khinast). the associated process analysis, it is nevertheless an apt description of the state of current pharmaceutical production technology. One reason for this is that a batch-based approach offers advantages in terms of quality assurance, as a batch can be controlled, and thus, accepted or rejected (Leuenberger, 2001). Nevertheless, batch production presents many disadvantages that can be listed as follows: defined batch size (output quantity driven by batch size), long throughput times from start to finish, large raw material and intermediate inventories, extensive validation and scale-up activities needed, and quality measured by in-process sampling and end-product testing. Due to these severe drawbacks, pharmaceutical industry and the regulatory bodies now actively encourage the development /$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi: /j.ces

2 108 D. Suzzi et al. / Chemical Engineering Science 69 (2012) and implementation of innovative pharmaceutical development, and, most important, continuous manufacturing. Although a general trend towards continuous manufacturing is being proposed in the literature (Thakral and Thakral, 2009; Reklaitis et al., 2010; Teunou and Poncelet, 2002), literature on continuous processing in the pharmaceutical industry is still scarce. In a recent paper by Vanarase et al. (2010), the authors presented an experimental analysis of continuous blending for the manufacturing of powder-based products via NIR spectroscopy, and Portillo et al. (2010) reported the investigation of a similar process using Positron Emission Particle Tracking. An analysis of continuous blending using the Discrete Element Method was presented by Sarkar and Wassgren (2010), highlighting the influence of cohesion under different process conditions. Fundamental studies on continuous tablet coating processes are absent from literature, except for the basic evaluation study of Cunningham et al. (2009) Continuous tablet coating Coating is a process to generate a thin layer or film on the surface of the tablet cores. In most cases, the coating is introduced in a liquid form (often an aqueous polymer dispersion) and the solvent is evaporated. Depending on the tablet s dimension and coating functionality, the film thickness varies between 5 mm and 100 mm. A modern pan coater typically has a fully perforated cylindrical drum to allow efficient air flow through the tablet bed. In a batch process, batches ranging from 500 g to 2000 kg are placed in the rotating drum (Porter, 2006). The coating liquid is sprayed onto the tablet bed by two-component nozzles that are tailored to the liquid dispersion and that allow the generation of sprays with well-defined droplet size distributions. The underlying principle of continuous pan coating is similar for all large-scale systems that are commercially available nowadays. In a nutshell, the tablet cores are continuously fed into a rotating drum at one end, and are coated using spray guns while being transported to the other end, where the finished product emerges. The axial dimension of the coating drum has to be large enough so that the time it takes for the tablet to traverse from one side to the other is sufficiently long to apply the coating. Differences between systems arise in the choice of the mechanisms of transportation along the axial direction. While the tablet cores reside inside the coating drum, the coating solution is applied by spray guns, where a greater number of spray nozzles compared with the batch process can be used. Thus, also multi-layer films may be applied. The necessary evaporation of the water content is achieved by introducing heated drying air, either in dedicated drying zones or in the same place where the spraying process occurs. Switching from batch production to continuous manufacturing has many advantages. Typically, the uniformity of the film on the tablet is improved, mainly due to the reduced depth of the tablet bed and increased number of tablets on the bed surface and due to a greater number of spray guns. The time required for loading, warming up, drying, and unloading of the tablets is minimized, allowing an increased number of tablets to be coated per time unit. Continuous coating also offers advantages in the areas of design, control and automation of processes. For example, all various stages of coated tablets are available simultaneously in the corresponding locations inside the drum, making the in-line measurement of process parameters and automated regulation easier. In addition, the first finished tablets are available for at-line or off-line examination after a short period of time. If irregularities are detected at this point, only a relatively small number of tablets are affected, in contrast to discarding the entire batch Characterization of the coating process A wide range of investigations, experimentally- and simulationbased, has been performed to characterize the tablet flow inside various devices, especially in pan coaters. Using a digital imaging system together with appropriate post-processing, either manually or by computational image analysis, has proven to be well-suited for a tablet flow investigation. One option is to use a differentcolored tracer particle to examine velocities and residence times (RTs). To eliminate the misinterpretation of the hues, all tablets except for the tracer may be colored black. Pandey et al. (2006a,b) recorded the tablet position, as well as the exposed area of the tracer particle in the spray zone, using this method and found a linear relation between the average cascading velocity and the pan speed. Discrete Element Method (DEM) simulations confirmed the velocity profiles along the top cascading layer of the particle bed. As a result, the characteristic velocity at the granular bed was expressed as a function of pan radius, pan rotation rate, gravitational acceleration, particle size and fractional fill volume, defined as the ratio between the volume occupied by the bed and the total pan volume. Similarly, Alexander et al. (2002) proposed an expression of the dimensionless maximal velocity as a function of pan geometry, process parameters and particle characteristics. An investigation of the RT of tablets in the spray zone experimentally and via a DEM simulation was performed by Kalbag et al. (2008). The RT was expressed as a dimensionless appearance frequency, defined as the number of appearances of a tablet in the spray zone during one pan revolution. In this work, more metrics were introduced to characterize the mixing behavior on the bed, i.e., the circulation and the fractional RTs. Theoretical models for predicting the surface renewal rates of the tablet bed in a rotary coating drum were reported by Denis et al. (2003). They found an excellent agreement between the prediction of their model and the experimental results for spherical particles and bifluid pneumatic nozzles. Freireich and Wassgren (2010) recently examined both analytically and numerically the influence of the orientation on the coating uniformity, leading to a deeper understanding of intra-tablet film variability. An interesting alternative approach was proposed by Tobiska and Kleinebudde (2001), who showed that the mixing behavior of a Bohle BLC pan coater can be characterized by measuring the temperature difference between the spatially separated spraying and drying zones. For the investigation of the coating uniformity in a Bohle lab-coater, a more conventional method of determining mass variance was used (Tobiska and Kleinebudde, 2003). With regard to a numerical simulation of continuous coating, no publications have been found in the literature to date. While most experimental studies focus on a single tablet shape for the analysis of inter- and intra-tablet coating uniformity, e.g., spherical (Chang and Leonzio, 1995), oval (Tobiska and Kleinebudde, 2003a) or standard round concave (SRC) (Sandadi et al., 2004). Wilson and Crossman (1997) presented the effects of the pan speed and four tablet shapes, namely round, capsule, small, and large oval, on intra-tablet coating variability. The best uniformity was found for round tablets and the worst for large oval ones. Furthermore, the edge of the land and the tablet band appeared to have approximately half of the coating thickness of the tablet face. The pan speed considerably affected the film thickness on the tablet band, while having little effect on the tablets face and edge. Also most numerical simulation studies of the particle flow in coaters (e.g., Dubey et al., 2008; Pandey et al., 2006a; Yamane et al., 1995) generally assumed a spherical tablet shape, in order

3 D. Suzzi et al. / Chemical Engineering Science 69 (2012) to limit the computational demand of the DEM approach. Indeed, very few computational works address the effects of the tablet shape on film coating uniformity. Conceptually, two different approaches have been reported that integrate the behavior of non-spherical particle shapes into a DEM solver: Direct mathematical description of the particle shape, for example, via ellipsoids or superquadrics (Hogue, 1998; Dziugys and Peters, 2001). Even if this method is the most accurate for reproducing the exact particle shape, the complex algorithms used for contact detection drastically reduce the computational speed. The glued sphere approach, where singular spheres are rigidly connected to reproduce a specific shape (Kodam et al., 2009). In the current work we use the glued sphere approach to reproduce various tablet shapes. In our work the amount of multiple spheres is deliberately kept low, e.g., 8 elements or less, not only to allow a reasonable simulation time, but to avoid the over-damping effects in presence of multiple constituent spheres reported by Kruggel-Emden et al. (2008). 2. Goals A sound understanding of the critical parameters affecting the performance of each unit operation can provide a considerable reduction of experimental effort, material and time consumption and offer advantages with regard to troubleshooting and redesign. Thus, the aim of this study is to numerically analyze the tablet flow inside a continuous pharmaceutical coater and to understand the effects of a tablet shape and fill height on the intratablet coating variability. State-of-the-art computational approaches based on the DEM were used to characterize a real-life production device. An experimental characterization of the tablet s material properties was performed in order to provide correct input data for the numerical solver. Three tablet shapes, i.e., bi-convex, oval, and spherical, as well as three fill volumes, were considered in this work. The intra-tablet coating variability was quantified in terms of RT in the spray zone, leading to a quantification of the time needed to obtain a sufficient film thickness for the continuous coating device. Furthermore, surface velocities, both translational and rotational, on top of the tablet bed were examined in order to define the best spray gun position to obtain a homogeneous film around the tablet. Also, the local mixing effects connected to the different tablet shapes and fill volumes were analyzed in terms of the tablets mean velocity and its fluctuation, quantified by the granular temperature value. This offers a deep understanding of the surface renewal and mixing processes inside the tablet bed. In summary, the main objectives of this work are as follows: to experimentally characterize the material properties of a pharmaceutical tablet, to model the tablet flow inside a continuous coater by means of the DEM, to analyze the effects of the different tablet shapes and fill volumes on the inter-tablet coating variability, to optimize the location of the spray gun inside the coater chamber in terms of surface velocities on the tablet bed and thus to reduce the inter-tablet coating variability, and to predict the outcome of continuous coating operations. The final results demonstrate how numerical modeling can play a decisive role in the development and the design of continuous pharmaceutical processes, such as tablet coating. 3. Numerical approach In recent years, DEM has been increasingly applied for the investigation of particulate flow. The underlying principle is relatively simple. In one time step, for each particle the forces that are exerted by neighboring particles or boundaries are examined. In general, the forces that are considered are the body force F b,i, the normal contact forces F c,n,ij, and the tangential contact forces F c,t,ij between particles i and j. After that, Newton s equation of motion is solved to calculate the velocity of the particle. Following the same principle, a rotational momentum balance is solved to track the rotation rate of the particle. Then, together with the length of the time step, a new position of the particle is calculated. This is carried out for every particle in a single time step and repeated for each time step. However, the main issue with the DEM is that the number of possible inter-particle and particle wall contacts greatly increases as the number of the particles increases. Therefore, efficient algorithms are needed for contact detection. In addition, a considerable amount of information is generated and has to be stored efficiently. A great number of contact calculations for each time step limits the time that the evaluation of a single contact can take, calling for simple yet sufficiently accurate models. Hydrodynamic forces are typically not considered under the DEM approach and were not included in our work. This is generally true for tablets being mixed in a coating device. Inter-particle cohesive forces have also been excluded from the numerical model, as we assumed a bed of free-flowing materials. This is duly justified in the case of particles 41 mm. Friction between tablets has, however, been included by an appropriate model for the tangential contact forces. The basic principles of the DEM simulations can be found in detail in the review paper of Zhu et al. (2008). Inour work we modeled the collision between particles by means of the so-called soft-sphere approach or time-driven method (TDM). The collisions were represented as contacts of deforming particles that last over few time steps, where new values of particle positions and velocities were computed in fixed time-intervals. The deformations of impacting particles were modeled by overlaps of colliding spheres. Finally, the contact forces were computed as a function of these overlaps. As presented by Dziugys and Peters (2001), the soft-sphere method offers an accurate reproduction of particle elasticity, as well as sliding and damping effects due to friction. The Linear-Spring-Dashpot model was used in our study. The main advantage is that analytic solutions are available for a direct verification of the numerical schemes. This model is still widely used in the area of DEM simulations, as more sophisticated non-linear interaction models appear to provide minor benefits compared to the increased computational effort (Di Renzo and Di Maio, 2004). In the Linear-Spring-Dashpot model the normal force is calculated adding an elastic term modeled by a spring to a second term representing the dissipation modeled by a dashpot: F c,n,ij ¼ K n d n,ij þc n _ d n,ij The term k n is the normal stiffness coefficient, c n is the normal damping coefficient and d n is the normal overlap between the particles. The normal stiffness coefficient is evaluated based on the material and geometrical properties of the particles and a characteristic collision velocity. The forces acting in the tangential direction are similarly represented by a linear spring and dashpot model with frictional slider: 8 < k t d t,ij þc t d _ t,ij F c,t,ij ¼ d : mf t,ij c,n,ij 9d t,ij 9 for F c,t,ij rmf c,n,ij for F c,t,ij 4mF c,n,ij ð1þ ð2þ

4 110 D. Suzzi et al. / Chemical Engineering Science 69 (2012) In analogy to the normal force model, the term k t d t,ij represents the force of the spring in the tangential direction, while c t _ d t,ij describes the contribution of the damping element, i.e., the dashpot. The friction coefficient m between the two materials in contact characterizes the frictional slider. Furthermore, rolling friction is accounted for by h i M r ¼ m r 9F c,n,ij 9r i ð3þ 9h i 9 The simulations presented in our work were performed using the commercial DEM software EDEM TM from DEM Solutions Ltd. 4. Case definition 4.1. Geometry The continuous tablet coater considered in this work was the DRIACONTI-T s Pharma coater from DRIAM Anlagenbau GmbH. The functional principle of this device is shown in Fig. 1. Compared to the traditional batch coating, this design allows a semi-continuous cycled application of film coating solutions. In this coater a cylindrical pan is divided into several chambers or sections, in which selected processing steps are performed according to the final product requirements (position film coating ). As soon as an individual process operation is finished, the contents of each section are moved to the next chamber by a flap (position product transfer ). As a result, a cycled-continuous application of film coating is achieved. Conceptually, the device combines the advantages of small-scale batch production and a continuous product supply chain. In our study we considered a single chamber of the DRIA- CONTI-T s Pharma coater, aiming primarily at obtaining a quantification of the tablet s mean RT per pass in the spray zone. This information was necessary to predict the film thickness of the tablets at the end of the coating process. Moreover, the film variability between the tablets in the same chamber needed to be controlled to match the quality requirements in terms of Relative Standard Deviation (RSD) of the film thickness and the required dissolution specifications. The modeled geometry in position of flap film coating is presented in Fig. 2. Eleven couples of baffles with 0.03 m height and 451 inclination related to the coater axis are mounted inside the chamber. The chamber diameter and width were 1 m and 0.25 m, respectively Simulation details The tablets used for the experimental characterization were standard pharmaceutical bi-convex tablets consisting of 570 mg of placebo blend previously coated with a polymer-based film. The tablets had a diameter of 10 mm and a thickness of 5 mm. The materials constituting the film and the tablet core were deliberately unknown in order to provide the detailed characterization described in the next section and to give our approach a universal applicability (e.g., for various tablets provided by manufacturers). The tablets we numerically analyzed had the same mass and volume (and thus density) and material and surface properties as the tablet experimentally characterized in this work. The three tablet shapes considered, i.e., round, oval, and biconvex tablets, are also shown in Fig. 2. The tablet shapes were approximated by means of the glued-spheres method, under which the constituting spherical particles were chosen in order to obtain the same volume (and thus mass) for each tablet. This approach allows for a representation of the complex shapes by a relatively low number of spheres, which decreases simulation time and avoids over-damping effects (Kruggel-Emden et al., 2008). While a limited amount of spheres does not allow modeling the real form of the tablet in every detail, the overall tablet flow behavior is well reproduced, as properties like the moments of inertia are described accurately. When two glued-sphere particles collide, a tangential overlap is detected for each sphere of the particles. From this, the forces are calculated as described above, but taking into account that the single sphere is part of the multi-sphere particle. The properties of the three tablets are summarized in Table 1, where L, W, and T represent the tablet length, width, and thickness, respectively. As previously stated, three chamber fill levels have been considered, i.e., 15 kg, 18 kg, and 21 kg. As shown in Table 2, the fill cases were characterized in terms of volume fill ratios, defined as the total volume occupied by the tablets divided by the volume of the coater chamber. The whole chamber is simulated. Fig. 1. Functional principle of the DRIACONTI-T s Pharma coater from DRIAM.

5 D. Suzzi et al. / Chemical Engineering Science 69 (2012) Fig. 2. (a) Simulated geometry of the coater chamber at flap position coating and (b) simplified shapes of round, oval, and bi-convex tablets. Table 1 Tablets material and geometrical properties. Tablet form Mass (g) Therefore, no additional boundary conditions (e.g., periodic boundaries) are needed. All simulations were run at a constant pan speed of 10 RPM for 10 revolutions of the coating chamber, thus 60 s of real time. The rotational velocity of the coater corresponded to a Froude number of In coating operations the Froude number is defined as Fr ¼ o2 r ð4þ g with o and r being the rotational speed and the coater radius, respectively. As the Froude number was lower than 0.1, the tablet flow remained in the so-called cascading regime, where a homogeneous coating process is to be expected (Mellmann, 2001). 5. Tablet properties 5.1. Coefficient of friction Density (kg/m 3 ) Amount of single glued spheres Dimensions (L/W/T) (mm) Round /8.46/8.46 Oval /7.00/7.00 Bi-convex /10.00/7.00 In order to estimate the coefficient of friction between two tablets, and between the tablets and the wall of the coater, experiments were performed using a rheometer (AntonPaar MCR 300). The experimental setup is presented in Fig. 3. The test object (a normal round tablet) was glued to one side of a glass sample holder. On the other side a rectangular foam buffer was mounted. The glass sample holder was positioned on the stationary temperature plate (TEK 150P-CF/C) of the rheometer such that the foam buffer is between sample holder and bottom plate, in this way ensuring elastic bearing as denoted by the spring in Fig. 3. The surface plate tool (type PP50, diameter 50 mm) was Table 2 Definition of the test cases. Fill case Total tablet mass (kg) Coater volume fill ratio (dimensionless) Fill ,362/ 26,362 Fill ,634/ 31,634 Fill ,906/ 36,906 Amount of tablets/ single spheres Round Oval Bi-convex 26,362/ 79,086 31,634/ ,906/ 110,718 26,362/ 210,896 31,634/ 253,072 39,906/ 295,248 then lowered until it applied a defined normal force N onto the tablet. For each measurement, the distance r n of the contact point from the center of the plate is determined. When measuring the coefficient of friction, the rheometer plate rotated at a certain speed. The torque T that was necessary to maintain constant rotation speed and the normal force F N were constantly monitored. As expected, torque and normal force oscillated periodically due to a stick slip transition motion. Different normal forces were used, and the actual values were recorded every 0.1 s for a period of 100 s, giving a total of 1000 measured points. From this, the coefficient of friction was calculated according to m ¼ T ð5þ F N r n An acrylic glass disk covered with the coating material was used to determine the coefficient of friction between tablets and steel. While the results were inconclusive, the friction coefficient seemed to be similar to the coefficient for tablet/steel. Therefore, the same coefficient was used for tablet wall and tablet tablet friction. Six separate measurements to determine the coefficient of friction (i.e., 3 different tablets at 2 friction speeds) were undertaken. In each measurement, four different normal forces were applied, resulting in a total of 4000 data points per parameter set. Due to the stick slip transitions during measurement, the major part of these

6 112 D. Suzzi et al. / Chemical Engineering Science 69 (2012) Friction coefficient Sample 0 Sample a Sample b Bi-convex tablet v = (m/s) Normal force (N) Fig. 4. Results for the coefficient of friction, m/s friction speed. Fig. 3. Pin-on-disk setup for the measurement of the friction coefficient between a particle and a rotating disk Sample 0 data points resembles the static friction, while a minor part was collected while the tablet was showing slipping behavior. Therefore, the static friction measurements were selected manually, and an average static friction coefficient was calculated. The results are shown in Figs. 4 and 5. Sample 0 was excluded from the calculation of the average coefficient of friction, as it showed signs of wear on the tablet surface and the coefficient of friction increased markedly (see Fig. 5). The average coefficient of friction for both speeds is equal to m¼ This value was used for the numerical simulations Coefficient of normal restitution (COR n ) To determine the COR n, normal tablets were dropped on a marble plate, where the impacting and the rebounding velocities were measured. The speed measurement was performed by a high speed camera MotionScope M3 at a frame rate of 1 khz (see Fig. 6). From the image data the position of the tablet was determined in each frame and based on it the speed was calculated. To obtain a statistically significant statement, this process was repeated 20 times using five different tablets. The resulting mean value for the CoR n was 0.74 with a standard deviation of Results Initially, tablets were dropped in the mixer and the tablets were marked half black and half red. By initializing the tablets in two horizontal layers, complete segregation was obtained initially. A comparison between the tablet beds for the three shapes and fill case 3 after 10 coater revolutions is presented in Fig. 7. Optically, the tablet bed appears slightly wider for the round tablets. This may be due to the different interaction between the particle shapes, which determines the final bed angle. In order to quantify the coater performance for various tablet forms and loads, the following parameters were analyzed: the relative standard deviation (RSD) of a binary mixture as a measure of mixing, the residence time (RT) of the tablets in a selected spray zone, the mean velocities and the granular temperatures in a section of the tablet bed, and the average cascading translational and angular velocities on top of the tablet bed. Friction coefficient Sample a Sample b Bi-convex tablet v = (m/s) Mixing performance Normal force (N) Fig. 5. Results for the coefficient of friction, m/s friction speed. The mixing performance of the coater was analyzed in terms of the standard deviation s of the mixture composition. During the simulations, multiple tablets samples i with a constant sampling size of M¼150 tablets were taken from the bed, and the standard deviation was computed. For sampling, the domain of the coater was divided into a grid containing cells corresponding to width, height and depth, respectively. For computing the statistics, only cells filled with more than M¼150 tablets were used. More details of the post-processing method can be found by Adam et al. (2011). In order to compare cases with different initial mixtures, the results were normalized in terms of the RSD of the particle mixture, defined as the ratio between the standard deviation s and the mean mass fraction W: RSD ¼ s ð6þ W The RSD results obtained for the three tablet shapes and fill levels are shown in Fig. 8. The radial mixing in the coating device was quite good for each tablet shape in question, except for the round tablets at a higher fill ratio. This means that at a fill mass of 21 kg the round tablets cannot guarantee the same mixing performance as the other shapes after 10 revolutions of the coater pan. In other words, a fill limit seems to be reached for the round tablets at fill ratio. In order to numerically quantify the mixing performance inside the coater chamber, the mixing constant k is used. As presented by other authors, e.g., Brone and Muzzio (2000) for a double cone blender, the time evolution of the RSD of a binary

7 D. Suzzi et al. / Chemical Engineering Science 69 (2012) Fig. 6. (a) Setup for the determination of the coefficient of restitution and (b) image sequence recorded with a high-speed camera to establish the coefficient of restitution. Fig. 7. Tablet bed after 10 revolutions for the fill case 3. From left to right: round, oval, and bi-convex tablets. mixture can be modeled using an exponential law as follows: RSD 2 ¼ RSD r 2 þe kn The term N represent the revolutions of the coater, the exponent k is the so-called mixing constant and RSD r is the relative standard deviation of a random mixture, defined for a certain composition of particles and a given sample size as a minimum theoretical value of standard deviation that can be achieved by random mixing. This theoretical lower limit of RSD (randomly mixed mixture) is RSD r ¼ s r ð8þ W where rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pð1 pþ s r ¼ ð9þ M Here, p is the mass fraction of one component in the mixture (in our case 0.5 for the binary color tracer initialization) and M is the total number of particles in the sample (Lacey, 1954). The mixing constants k for the different tablet shapes and fill ratios are presented in Fig. 9. The higher the value of k is, the faster the radial mixing of the tablets inside the coater is. As expected, an increase in the fill ratio of the coating chamber leads to a slower mixing process for all tablet shapes. As can be seen, the dispersive mixing of the bi-convex tablets was in all cases faster than for the oval shapes. The round tablets showed a significantly better performance at the lowest fill ratio. However, the mixing quality deteriorated drastically as the bed mass increased. ð7þ The analysis of the tablets flow patterns inside the coater can underline this behavior. In Fig. 10 the trajectories of 10 randomly chosen tablets are presented. For fill level 1 the round tablets appear to be transported from the core towards the outer regions of the bed quickly, as can be seen by the erratic trajectories. Once the fill level increases to level 3, the trajectories become smoother, implying that particles do not move in the direction perpendicular to the flow (i.e., the definition of diffusive mixing). In all figures it can be seen that this effect (i.e., the erratic trajectories) occurs mostly at the lower right part of the particle bed, i.e., were particles impact with the coater wall after sliding down the slope. Similar effects can be seen at the left top part, where particles start to slide down the slope. Thus, these parts of the bed are responsible for radial diffusive mixing. Once the bed height (or fill level) increases this effect is dampened, perhaps because of the higher hydrostatic pressure in the bottom region. For spherical tablets this dampening is most pronounced, and thus, the decrease in k is more significant for these tablets. Interestingly, bi-convex tablets have a tendency to follow spiral-shaped trajectories even for tablets in the center of the bed and even for fill level 3. Instead, oval and round tablets seem to recirculate longer in the middle of the bed. It must be emphasized that the mixing constants only quantify radial diffusive mixing, not the recirculation behavior of the tablets under the spray zone. This aspect will be analyzed in the following sections Residence time In order to quantify the inter-tablet coating variability, the elapsed time in a defined spray zone was calculated for each

8 114 D. Suzzi et al. / Chemical Engineering Science 69 (2012) Fig. 8. RSD of binary mixture for round, oval, and bi-convex tablets. Fig. 9. Mixing constants for the binary mixture of round, oval and bi-convex tablets for the three considered coater fill ratios. tablet in the coating device. As illustrated in Fig. 2, a circular region of effective spraying with a diameter of 200 mm was chosen at one-third of the tablet bed length. The diagrams in Figs. 11 and 12 show the average fractional RT f R (defined as the ratio between the time spent by a tablet in the spray zone located at the top of the surface and the total coating time) and its relative standard deviation RSD f R for all cases considered in this work. The diagrams in Fig. 11 show that in all cases an increase in the coater fill volume leads to a decrease of the average fractional RT, and thus, to a decline of the coating speed. For example at fill case 1 the spherical tablets spend 3% of the coating time in the spray zone and for fill case 3 only about 2%. This is a well-known fact. Interestingly, the bi-convex tablets seemed to be less affected by the fill ratio, reflected by a weaker decline of the f R value. This behavior may be explained by the tablets trajectories inside the tablet bed (see Fig. 10). The spiraling flow patterns of the bi-convex tablets for the higher fill level lead to a greater average value of the fractional residence time, as well as to a reduction of its standard deviation. In contrast to the fractional RT, the RSD of the fractional RT in the spray zone increased with fill level, as shown in Fig. 11. In fact, the RSD f R increased from about 4% to about 5.5% for round and oval tablets. Again, the behavior of bi-convex shapes was different, and the increase was less pronounced. Interestingly, apart from the bi-convex tablets the increase in the RSD values did not seem to follow a linear trend, which means that the coater fill ratio plays an important role in the inter-tablet coating variability. In other words, if the objective is to maintain the RSD of the film thickness between tablets within the range of 470.5%, for example, the round and oval tablets should not be coated in a chamber filled with more than fill case 2. The average RTs per pass in the spray zone obtained in our study match the range of the experimental and numerical data reported by Kalbag et al. (2008) for spherical particles. Although the pan geometry is not identical, this underlines the validity of our simulations. Some coating solution is transferred to the tablet surface every time a tablet passes through the spray zone. In a first-order approximation back-splashing of satellitedropletsandthetransfer of coating solution from a tablet to neighboring tablets may be neglected. Thus, the mean film thickness and its inter-tablet standard deviation are directly correlated to the value and the relative standard deviation of the RT per pass. Thus, assuming a certain coating efficiency z of the impacting spray droplets, defined as the mass remaining on the tablet over the mass impinging on the tablet, and _m spray the impinging mass on a tablet per second, the overall coating performance in a continuous coater chamber can be quantitatively assessed. This way, the average film mass per tablet after a number N of pan revolutions can be written as m Coat ðnþ¼f R 2p o Nz _m spray ð10þ

9 D. Suzzi et al. / Chemical Engineering Science 69 (2012) Fig. 10. Trajectories of 10 randomly chosen round, oval and bi-convex tablets at the different coater fill levels. Fig. 11. Average fractional RT in the spray zone for round, oval and bi-convex tablets at the coater fill ratios. Fig. 12. Relative standard deviation of the RT per pass in the spray zone for round, oval, and bi-convex tablets at the coater fill ratios. while the relative standard deviation of the inter-tablet coating variability RSD Inter can be assumed equal to RSD f R. These results are crucial for the design and the optimization of continuous coating devices, as they provide an estimation of the number of pan revolutions needed to obtain a target film mass in each chamber of the coater. Moreover, the RSD Inter provides the expected variability in terms of film mass between the coated tablets representing the final product. Eq. (10) can be extended to configure the continuous coater in terms of throughput and number of required chambers. In fact, if we define a target film mass per tablet M Coat obtained at the end of the process, this can be expressed in terms of the process time T C, thus number of revolutions N C, in each chamber of the coater, as well as the number of chambers n C : M Coat ¼ f R ðn Tabs,Ch ÞT C z _m spray n C ¼ f R ðn Tabs,Ch Þ 2p o N C _m sprayzn C ð11þ It has to be emphasized that according to Eq. (11) the fractional residence time per pass f R is a function of the number of tablets per chamber N Tabs,Ch. The number of processed tablets per time unit is _N ¼ N Tabs,Ch ð12þ T C Considering a constant rotational velocity o, the throughput may be maximized if we reduce the process time or increase the

10 116 D. Suzzi et al. / Chemical Engineering Science 69 (2012) number of tablets per chamber. On the other hand, if we want to obtain a defined film mass per tablet M Coat, the product f R ðn Tabs,Ch ÞT C n C must remain constant as well. This means that the production rate can be enhanced by increasing the number of chambers n C. This solution is nevertheless limited by the costs of the device. In our case, increasing the number of tablets per chamber appears to be a possible solution to increase the throughput of the continuous coater for biconvex tablets, as in this case, the fractional residence time is not a strong function of fill level. For the round and oval tablets the strong decrease in f R with the fill level would increase the necessary coating time per zone such that an overall reduction of throughput would occur. For example, the 16.7% increase in tablets between levels 2 and 3 leads to a reduction of f R of less than 10% for the bi-convex tablets, while the decrease is more than 20% for round and oval shapes. Thus, increasing the fill level is only an option for biconvex tablets. The coating efficiency and the intra-tablet coating variability due to the spraying process of a single pharmaceutical tablet have already been numerically analyzed by Suzzi et al. (2010). Further work will include a coupling of these methods in order to assess both inter- and intra-coating variability in an industrial tablet coater Tablet flow Velocity fluctuations are a key quantity of any particle mixing process, as diffusive particle mixing is related to the fluctuating velocity profile in the tablet bed. Velocity fluctuations, as well as time and locally averaged velocities, must be analyzed on a Eulerian grid. In order to transfer the velocity information on the Eulerian grid (on the contrary to the Lagrangian grid defined by individual particles), the locally averaged velocity in a grid cell must be calculated using the surrounding particle information. To reduce boundary effects, a vertical cut through the middle of the coater perpendicular to the rotational axis was used for the evaluations. Due to the flat cylindrical shape of the geometry, the resulting grid has a depth of one cell in axial direction. Therefore, in the following, only indices i and j for the two in-plane directions are given, and the axial index is omitted. In each time step, the velocity value of a particle is counted in the grid cell in which the particle is currently located. Thus, we incorporated the particle velocity information into a continuous function on the Eulerian grid to ensure that a meaningful locally averaged velocity u i,j was calculated even when there are only a few (or no) tablets in the volume characterized by the indices i and j. A similar calculation is performed for the pan-relative velocity u rel. In sum, the magnitude of the three-dimensional particle velocity is mapped onto a stationary two-dimensional spatial grid. Not those for most of the analysis in these work only pan-relative velocities in a pan-fixed coordinate system were used. Details for this type of calculation are provided by Radl et al. (2010). To identify the main direction of the velocity fluctuations, we analyzed the individual radial, circumferential, and axial velocity fluctuations u circ, u rad,andu z, respectively. This was achieved by a simple transformation of the coordinate system. In order to compare the fluctuation levels at various pan speeds, the calculated mean and fluctuating quantities were normalized by the circumferential pan speed and the circumferential pan speed squared, respectively. In our investigation we also introduced a metric (namely the granular temperature) used in many studies to quantify granular flows but to date not used for analyzing tablet coating problems. In order to compute the granular temperature, first the variance s 2 i,j of the velocity in each spatial direction was taken as a metric for tablet velocity fluctuations. This quantity was calculated from the locally averaged pan-relative velocity u rel,i,j and the pan-relative particle velocity v Rel,i,j in the pan-fixed coordinate system. The x component is given as s 2 x,i,j ¼ 1 X ðu N rel,x,i,j v rel,x,i,j Þ 2 i,j P A p i,j ð13þ where N i,j and p i,j denote the total number of particles, thus tablets, as well as the list of particles in the grid cell, respectively. The y-and z-components are calculated accordingly. Further details of similar calculations performed for a four-blade mixer can be found by Radl (2010). The variance s 2 i,j characterizes the degree of uncoordinated tablets motion in a certain grid cell at a certain point in time. Similarly to the mean velocity fluctuation, we defined a scalar quantity S 2 that quantifies the mean level of (time-averaged) particle velocity fluctuations as S 2 i,j ¼ðs2 x,i,j þs2 y,i,j þs2 z,i,j Þ=3 ð14þ Note thats 2 x,i,j, s2 y,i,j, and s2 z,i,j represent the Cartesian components of the time-averaged tablet velocity fluctuations as per Eq. (13). The quantity defined in Eq. (14) is often referred to as granular temperature in the literature (Goldhirsch, 2008) and can be used to quantify diffusive mixing (Rosato et al., 2008). Fig. 13a illustrates the local averaging process for obtaining locally averaged velocity information on the Eulerian grid for both the time-averaged velocity fluctuation and the granular temperature. Fig. 13b highlights the various metrics. The granular temperature S 2 is the time-average of the variance of the tablet velocity, while the time-averaged velocity fluctuation is the time average of the difference between locally averaged relative velocities and their time-averaged values squared. The average velocity fields for all tablet shapes and fill ratios are presented in Fig. 14. It shows 2D cross-sectional views normal to the pan axis in the middle of the chamber width with the velocity fields normalized by the pan motion. In this Figure we displayed the results on a Eulerian grid. Time averaging was performed over 600 time samples and it was started after one full revolution of the coater to avoid transient effects influencing our results. Interestingly, all velocity fields appear quite similar, with high velocities on the surface of the tablet bed and a slower motion at the contact with the rotating pan wall. This can be explained by the cascading behavior of the tablets on top of the bed and by the transport of the immersed tablets caused by the attrition with the pan wall and by the action of the mixing baffles. In between these zones, there is a relatively stagnant zone, exhibiting very low velocities. Differences were insignificant with respect to fill level and to tablet shape. The only difference was detected for the roundshaped tablets, which had a slightly higher velocity on top of the bed. Fig. 15 shows a comparison between the granular temperatures S 2 for all considered shapes and fill ratios. In general, the mean granular temperature profiles show a maximum on the surface of the tablet bed, and decrease towards the core region. The tablet shape appears to affect strongly the velocity fluctuations and thus the granular mixing. The round shape has the strongest velocity fluctuations, with a decreasing trend for higher fill ratios and a peak in the upper edge of the bed. On the other hand, bi-convex tablets appear to dissipate less energy for granular fluctuations in the particle bed, probably due to better packing characteristic obtainable for this shape, leading to a more coordinated flow of the individual tablets inside the bed. This behavior is also evident in the trajectories as shown in Fig Surface velocities During post-processing we analyzed the tablet flow over the tablet bed in terms of translational and rotational velocities. Both values represent an important metric to optimize the coating

11 D. Suzzi et al. / Chemical Engineering Science 69 (2012) v P, Rel u av, rel s 2 u av, rel u av, rel s 2 u 2 p i, j s 2 Fig. 13. (a) Sketch of the averaging process and (b) time profiles of the locally averaged and time-averaged quantities (vertical lines indicate the norm of a vector, horizontal lines indicate time-averaged quantities; the spatial indices i and j have been omitted for clarity) (Radl et al., 2010). t Fig. 14. Normalized averaged tablets velocity fields for round, oval and bi-convex tablets at various coater fill ratios (vertical cut in the middle of the bed). process, as they affect the interaction between the tablets and the coating spray. In fact: Higher cascading velocities lead to a lower RT of the tablets under the spray gun, and thus, to a longer processing time to obtain a target film thickness. Higher rotational velocities lead to a more homogeneous wetting of the tablet surface, e.g., on the sides of the tablets, and thus to a lower intra-tablet coating variability. These data can therefore help to identify the best location for the spray gun. The same analysis as the one described in the previous section was performed for translational and angular tablet velocities on a Eulerian grid of cells. Only the data of the upper cells in y-direction (thus on the bed surface) were collected along the bed location d. The reference system we used and an example of the raw data and the averaging line is presented in Fig. 16. The translational velocity distributions along the normalized tablet bed surface are presented in Fig. 17. As can be seen, an increase in the fill level leads to higher velocities on the tablet bed, as the tablets have higher potential energies. Apart from a small peak on top of the tablet bed mainly caused by bouncing tablets also observed in Fig. 7, the velocity distribution for the round shapes appears quite homogeneous along the tablet bed, as also reported by Pandey et al. (2006a) in the experimental and numerical analysis of a pan coater. However, the oval and biconvex shapes present a velocity peak around at 70% of the bed. The bi-convex tablets have a consistently higher velocity peak in comparison to the other two shapes. This behavior can be explained by the tendency of flat-shaped tablets to slide rather than rotate. It is clear that higher surface velocities should lead to lesser RTs under the spray zone. However, Figs. 11 and 12 clearly show that the bi-convex tablets result have the best overall behavior in terms of average fractional RT and its variance in the spray zone, i.e., the inter-tablet coating variability is minimized. Thus, a higher velocity under the spray does not directly imply that all tablets are

12 118 D. Suzzi et al. / Chemical Engineering Science 69 (2012) Fig. 15. Mean granular temperature S 2 fields for round, oval and bi-convex tablets at the different coater fill ratios (vertical cut in the middle of the bed). Fig. 16. Post-processing method of extracting tablet data on top of the tablet bed. equally transported to the surface of the bed. Based on the profiles in Fig. 15, we conclude that higher granular temperatures in the tablet bed interfere with the tablets recirculation pattern, and thus, lead to a poorer residence time distribution. Again, this can be explained by the tablets trajectories presented in Fig. 10. Fig. 18 shows the angular velocities on top of the tablet bed for all fill levels and tablet shapes. As expected, the bi-convex tablets have the lowest rotational velocities and the highest translational velocities on top of the tablet bed. This behavior can be explained by the shape of the particles, which inhibits the rotation around two main axes of the tablet, yet induced sliding. A conclusion we can reach from Fig. 18 is that if we focus on a standard spray gun position, e.g., at a normalized distance from the top of the tablet bed of 0.3, we obtain average rotational velocities of around 30 rad/s, 20 rad/s, and 15 rad/s for round, oval and bi-convex tablets, respectively. If we assume a RT of 0.1 s under the spray zone, for example, the various tablets will make average rotations of around 18.91, 12.61, and 9.41 during the time they collect coating material from the spray. This behavior can be directly correlated to the intra-tablet coating variability of the product, as a stronger rotation leads to a more homogeneous wetting of the tablet sides. As expected, the bi-convex tablets present the lowest average rotation under the spray gun, which correlates with the well-known problem of poor coating on the tablet band (Ho et al., 2007). At a normalized distance of 0.5 the rotation rate of all tablets is relatively similar and close to 20 rad/ s. The fill level seems to differently affect the rotational velocities for different tablets shapes. In fact, bi-convex and oval tablets present lower rotational velocities by increasing fill volume, while round shapes show an undefined trend. This could be connected

13 D. Suzzi et al. / Chemical Engineering Science 69 (2012) Fig. 17. Normalized tablets velocity on top of the tablet bed for round, oval and bi-convex tablets at the various coater fill ratios. Fig. 18. Tablets angular velocity on top of the tablet bed for round, oval and bi-convex tablets at the various coater fill ratios. to the higher rotational degree of freedom of spherical tablets, which can rotate around three main axes. An experimental assessment of these results is nevertheless needed to prove the simulation results. For example, a positron emission particle tracking (PEPT) technique (Seiler et al., 2008) would be most appropriate (although most expensive as well) to correctly validate the numerical results obtained in this work. 7. Conclusions and outlook In this study we numerically analyzed the tablet flow inside a continuous pharmaceutical coater using DEM simulations in order to gain better understanding of how a tablet s shape and fill height lead to inter-tablet coating variability. Beginning with an experimental characterization of tablet material properties,

14 120 D. Suzzi et al. / Chemical Engineering Science 69 (2012) three tablet shapes, namely bi-convex, oval and spherical, and three fill volumes were analyzed in detail. Based on the RSD of a binary mixture, the RT of the tablets in the spray zone, the mean velocities and the granular temperatures in the tablet bed, as well as on the average cascading translational and angular velocity on top of the tablet bed, we draw the following conclusions: The tablet shape plays a decisive role in the final quality of the coating process, at least in terms of inter-tablet coating variability. In general, bi-convex tablets showed a higher homogeneity, and thus, less standard deviation in terms of RT under a spray gun. Higher coater fill ratios generally decrease the quality of the coating process (slower mixing, lower fractional RT of the tablets in the spray zone, and higher RSD of inter-tablet coating). Nevertheless, for bi-convex tablets this trend is mitigated, meaning that higher fill ratios may be achieved without reduction of the final product quality and extending the process time. Higher rotational velocities on top of the tablet bed can be correlated to the intra-tablet coating variability of the final product. Here, round tablets show a better behavior under the spray gun. In addition, our study showed the following trends that have not been presented before: High granular temperatures inside the bed appeared to compromise the recirculation and renewal properties on the tablets under a spray gun. The round tablets had the highest granular temperatures and showed the poorest results in terms of inter-tablet coating variability. The patterns of the average velocities in a section of the tablet bed were very similar for all shapes and fill ratios. Nevertheless, the tablets flow patterns indicated a better behavior in terms of transport to the bed surface for bi-convex tablets. The presented results show how numerical simulations via DEM improve an understanding of the tablet mixing inside a real continuous coater, and thus, help to optimize a design space for the operation of this device. In conclusion, the expected behavior of the considered tablets can be summarized as follows: A generally poorer inter-tablet coating variability was detected for the round tablets. An increase in the fill ratio led to a significant decline in the expected coating variability between tablets. On the other hand, the higher rotation velocity on top of the tablet bed slightly affected by the fill ratio can be interpreted as a sign for better inter-coating variability of the final product. Oval tablets seem to generally follow the trends of the round tablets, but show a slightly better performance in terms of inter-tablet uniformity. Rotational velocities on top of the tablet bed for oval shapes were considerably lower than for the spherical ones. Bi-convex tablets delivered the best results in terms of the fractional RT in the spray zone and its standard deviation. The decline of these values with the increasing fill ratios was moderate, showing a lower sensitivity to a coater fill volume. The mixing speed was slightly lower for higher fill ratios, but this metric does not seem to affect the inter-tablet coating variability directly. The rotational behavior in the spray zone, and thus, the intra-coating variability was unfavorable in this case, as bi-convex shape appears to be rotating two to three times less fat than the spherical one. The next steps will include the analysis of various coater rotational speeds and the development of a spraying/coating model directly in the DEM solver. Furthermore, variable friction coefficients and tablets cohesion as a function of the amount of coating material on the tablet surface are currently under investigation. The analysis of the numerical impact due to the amount of glued spheres in a tablet would also be an important enhancement to this work, as well as an experimental validation of the presented computational results. In order to obtain a better understanding of the local coating process, the results of the DEM simulations will be coupled with detailed Computational Fluid Dynamics computations of film formation on a single sphere via an already-published method (Suzzi et al., 2010). Finally, these results will be presented in terms of an in-silico design space based on the Quality by Design principles (Muzzio et al., 2008), described, for example, in several ICH guidelines, including ICH Q8 (R2), ICH Q9, and ICH Q10. Acknowledgments We thank Bernd Grabherr, Thomas Fränkel and Carsten Wieland of DRIAM Anlagebau GmbH for supporting this work and for supplying the CAD surfaces of the coater chamber and the test tablets. We acknowledge DEM Solutions Ltd. and Christoph Herrmann for the support with the computational code EDEM. References Adam, S., Suzzi, D., Radeke, C., Khinast, J.G., An integrated Quality by Design (QbD) approach towards design space definition of a blending unit operation by Discrete Element Method (DEM) simulation. Eur. J. Pharm. Sci. 42, Alexander, A., Shinbrot, T., Muzzio, F.J., Scaling surface velocities in rotating cylinders as a function of vessel radius, rotation rate, and particle size. Powder Technol. 126, Brone, D., Muzzio, F.J., Enhanced mixing in double-cone blenders. Powder Technol. 110, Cunningham, C., Hansell, J., Nuneviller 3rd, F., Rajabi-Siahboomi, A.R., Evaluation of recent advances in continuous film coating processes. Drug Dev. Ind. Pharm. 36 (2), Chang, R.K., Leonzio, M., The effect of run-time on the inter-unit uniformity of aqueous film coating applied to glass-beads in a Hi-Coater. Drug Dev. Ind. Pharm. 21 (16), Denis, C., Hemati, A., Chulia, D., Lanne, J.Y., Buisson, B., Daste, G., Elbaz, F., A model of surface renewal with application to the coating of pharmaceutical tablets in rotary drums. Powder Technol. 130, Di Renzo, A., Di Maio, F.P., Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chem. Eng. Sci. 59 (3), Dubey, A., Portillo, P.M., Muzzio, F.J., Study of tablet coating thickness uniformity using LIBS, DEM and compartment modeling. In: 2008 AIChE Annual Meeting, Philadelphia, US. Dziugys, A., Peters, B.,, A new approach to detect the contact of twodimensional elliptical particles. Int. J. Numer. Anal. Methods Geomech 25 (15), FDA, Guidance for Industry: PAT A Framework for Innovative Pharmaceutical Development, Manufacturing, and Quality Assurance. Pharmaceutical CGMPs. Freireich, B., Wassgren, C., Intra-particle coating variability: analysis and Monte-Carlo simulations. Chem. Eng. Sci. 65, Goldhirsch, I., Introduction to granular temperature. Powder Technol. 182, Ho, L., Müller, R., Römer, M., Gordon, K.C., Heinämäki, J., Kleinebudde, P., Pepper, M., Rades, T., Shen, Y.C., Strachan, C.J., Taday, P.F., Zeitler, J.A., Analysis of sustained-release tablet film coats using terahertz pulse damaging. J. Controlled Release 119, Hogue, C., Shape representation and contact detection for discrete element simulations of arbitrary geometries. Eng. Computation 15, 374. Kalbag, A., Wassgren, C., Penumetcha, S.S., Perez-Ramos, J.D., Inter-tablet coating variability: residence times in a horizontal pan coater. Chem. Eng. Sci. 63, Kodam, M., Bharadwaj, R., Curtis, J., Hancock, B., Wassgren, C., Force model considerations for glued-sphere discrete element method simulations. Chem. Eng. Sci. 64 (15), Kruggel-Emden, H., Rickelt, S., Wirtz, S., Scherer, V., A study on the validity of the multi-sphere Discrete Element Method. Powder Technol. 188 (2), Lacey, P.M.C., Developments in the theory of particle mixing. J. Appl. Chem. 4,

15 D. Suzzi et al. / Chemical Engineering Science 69 (2012) Leuenberger, H., New trends in the production of pharmaceutical granules: batch versus continuous processing. Eur. J. Pharm. Biopharm. 52 (3), Mellmann, J., The transverse motion of solids in rotating cylinders forms of motion and transition behavior. Powder Technol. 118 (3), Muzzio, F.J., Ierapetritou, M., Portillo, P., Llusa, M., Levin, M., Morris, K.M., Soh, J.L.P., McCann, R.J., Alexander, A., A forward-looking approach to process scale-up for solid dose manufacturing. In: Augsburger, L.L., Hoag, S.W. (Eds.), Pharmaceutical Dosage Forms: Tablets Volume 3: Manufacture and Process Control, Informa Health Care, USA, pp Pandey, P., Turton, R., Joshi, N., Hammerman, E., Ergun, J., 2006b. Scale-up of a pancoating process. AAPS PharmSciTech. 7, E1 E8. Pandey, P., Song, Y.X., Kayihan, F., Turton, R., 2006a. Simulation of particle movement in a pan coating device using discrete element modeling and its comparison with video-imaging experiments. Powder Technol. 161, Porter, S.C., Scale-up of film coating. In: Levin, M. (Ed.), Pharmaceutical Process Scale-Up, Taylor & Francis, New York, pp Portillo, P.M., Vanarase, A.U., Ingram, A., Seville, J.K., Ierapetritou, M.G., Muzzio, F.J., Investigation of the effect of impeller rotation rate, powder flow rate, and cohesion on powder flow behavior in a continuous blender using PEPT. Chem. Eng. Sci. 65 (21), Radl, S., Modeling of Multiphase Systems in Pharmaceutical Applications. Ph.D. Thesis, TU Graz. Radl, S., Kalvoda, E., Glasser, B.J., Khinast, J.G., Mixing characteristics of wet granular matter in a bladed mixer. Powder Technol. 200, Reklaitis, G.V., Khinast, J.G., Muzzio, F.J., Pharmaceutical engineering science new approaches to pharmaceutical development and manufacturing. Chem. Eng. Sci. 65 (21), iv vii. Rosato, A.D., Lan, Y.D., Richman, M.W., On the calculation of self-diffusion invertically agitated granular beds. Powder Technol. 182, Sandadi, S., Pandey, P., Turton, R., In situ, near real-time acquisition of particle motion in rotating pan coating equipment using imaging techniques. Chem. Eng. Sci. 59, Sarkar, Avik, Wassgren, Carl, Continuous blending of cohesive granular material. Chem. Eng. Sci. 65 (21), Seiler, C., Fryer, P.J., Seville, J.P.K., Statistical modelling of the spouted bed coating process using positron emission particle tracking (PEPT) data. Can. J. Chem. Eng. 86 (3), Suzzi, D., Radl, S., Khinast, J.G., Local analysis of the tablet coating process: impact of operation conditions on film quality. Chem. Eng. Sci. 65 (21), Teunou, E., Poncelet, D., Batch and continuous fluid bed coating review and state of the art. J. Food Eng. 53, Thakral, N.K., Thakral, S., Continuous tablet coaters: developments, advantages and limitations. Innovations Pharm. Technol. March 2009, Tobiska, S., Kleinebudde, P., A simple method for evaluating the mixing efficiency of a new type of pan coater. Int. J. Pharm. 224, Tobiska, S., Kleinebudde, P., Coating uniformity and coating efficiency in a Bohle Lab-Coater using oval tablets. Eur. J. Pharm. Biopharm. 56, 3 9. Vanarase, A.U., Alcala, M., Jerez Rozo, J.I., Muzzio, F.J., Romañach, R.J., Realtime monitoring of drug concentration in a continuous powder mixing process using NIR spectroscopy. Chem. Eng. Sci. 65 (21), Wilson, K.E., Crossman, E., The influence of tablet shape and pan speed on intra-tablet film coating uniformity. Drug Dev. Ind. Pharm. 23 (12), Yamane, K., Sato, T., Tanaka, T., Tsuji, Y., Computer-simulation of tablet motion in coating drum. Pharm. Res. 12, Zhu, H., Zhou, Z., Yang, R., Yu, A., Discrete particle simulation of particulate systems: A review of major applications and findings. Chem. Eng. Sci. 63,

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