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Experimental validation of a 2-D population balance model for spray coating processes
Chemical Engineering Science 95 (2013) 360–365
Contents lists available at SciVerse ScienceDirect
Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Experimental validation of a 2-D population balance model for spray coating processes Jianfeng Li a, Ben J. Freireich b,d, Carl R. Wassgren b,c, James D. Litster a,c,n a
School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA c Department of Industrial Physical Pharmacy, Purdue University, West Lafayette, IN 47907, USA d The Dow Chemical Company, Midland, MI 48667, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 November 2011 Received in revised form 9 February 2012 Accepted 22 February 2012 Available online 1 March 2012
In this study, a series of spray coating experiments were carried out in a pilot scale Forberg-style paddle mixer to validate a previously published multi-dimensional population balance (PB) model (Li et al., 2011). Experiments were carried out using unimodal distributions of large (mean mass 0.45 g) and small (mean mass 0.27 g) particles, as well as bimodal distributions with a 1:1 mass ratio of the large and small particles. Experiments were performed at Froude numbers from 0.6 to 2 with the final coating mass to core particle mass ratio being 0.05. A fully two-dimensional distribution of the coated particles, with respect to solid core mass and coating mass, was obtained for each batch operation. For unimodal core particle distributions, the coating mass coefficient of variation was proportional to t 0.5 where t is the coating time, consistent with both the PB model and other published coating models. For the bimodal experimental series, the coating growth rate varied with particle mass m according to the relationship G ¼ mr where r ¼0.37. This value for the growth expression exponent r is smaller than that predicted for random coating (r ¼ 2/3) or observed experimentally in fluidized coating systems (r ¼1). This preferential spraying of small particles in the mechanical mixer indicates that the size dependence of coating mass growth rate is a strong function of the equipment geometry and particle flow field. When a growth exponent r¼ 0.37 was used, the coating distribution prediction from a discrete element method–population balance simulation compares well with the experimental results. Published by Elsevier Ltd.
Keywords: Population balance Paddle mixer Spray coating Multi-dimensional distribution Powder technology Granulation
1. Introduction Spray coating processes have widespread applications in the pharmaceutical, detergent, agrochemical, and food industries. A typical coating process consists of spraying an atomized coating solution onto the surface of dry, solid particles, and forming an ‘‘onion’’ structure of one or multiple layers surrounding the solid core (Saleh and Guigon, 2007). The key mechanism underlying the process is particle growth by layering, rather than other granulation phenomena such as agglomeration and attrition. Recently, researchers have been focused on the development of fundamental coating models to achieve better understanding of the important facets that affect the coating quality. A variety of modeling tools have been reported to predict the coating uniformity. The discrete element method (DEM) is a particle-level modeling tool that provides detailed dynamic
n Corresponding author at: School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA. E-mail address: [email protected] (J.D. Litster).
0009-2509/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.ces.2012.02.036
information as particles are mixed and sprayed (Kalbag and Wassgren, 2009). The Monte Carlo approach is another method for simulating the ‘‘random walk’’ of particles in the spray zone (Pandey et al., 2006). In the surface renewal model, the coating process is modeled as the sum of many short-time, spray zone visits. Based on that idea, Mann (1983) derived a relation to calculate the coating variability caused by the variation of the number of spray zone visits, and the variation of the coating amount an individual particle received during its single pass through the spray zone. Population balance (PB) modeling is yet another approach that can be used for modeling a coating process. A population balance is a process-level approach to simulating the temporal change of a particle number distribution over one or more dimensions, with incorporation of the rate phenomena contributing to layered growth (Wnukowski and Setterwall, 1989; Liu and Litster, 1993; Maronga and Wnukowski, 1997; Denis et al., 2003). Details of these modeling approaches have been summarized by Turton (2010). Excluding the work of Liu and Litster (1993), the abovementioned works refer only to monodisperse seed particle sizes. Liu and Litster derived a single-compartment PB that tracks the
J. Li et al. / Chemical Engineering Science 95 (2013) 360–365
distribution of coating mass on particles in a spouted bed. Because only a single compartment is used, the variability in coating mass must come from a size-dependent growth rate. The size dependence of the growth rate accounts for (i) the fact that particles in the spray receive different coating amounts depending on their size, and (ii) particles are presented to the spray more or less often depending on their size. Mathematically G¼
dm p ¼ J x2 ZðxÞaðxÞ dt 4
ð1Þ
where J is the total mass flux (mass flow per unit area), Z(x) is the average fraction of projected surface area particles of size x sprayed due to shielding by neighboring particles, and a(x) is the average fraction of time particles of size x spend in the spray. The dependence of the parameters Z and a on x, found empirically, results in Gpm. That is, particles gain coating mass at a rate proportional to their mass. Intuition suggests that particles gain mass in proportion to their surface area, Gpm2/3, so this result is surprising. Litster et al. (1993) showed that for a spouted bed, this stronger dependence on particle mass could be explained by the different trajectories that particles of different mass particles take within the spray zone. In general, we expect the size-dependent growth expression to depend strongly on the coater geometry and particle flow field. In this work, we experimentally examine the relative coating rates of binary seed particle sizes agitated in a Forberg-style mixer. The Forberg-style mixer is a commonly used, mechanically agitated mixer/coater in which particles are agitated by counter-rotating, twin-shaft paddles. Non-ideal particle flow is expected due to the complex mixer geometry. DEM simulations have been adopted to study the particle movements in this type of mixer (Hassanpour et al., 2011; Freireich et al., 2011). The models produce particle trajectories with a major vertical flow pattern (with the rotating paddle) and a minor horizontal flow pattern (along the shaft). This observation has been further verified using Positron Emission Particle Tracking (PEPT) to track an individual particle’s motion in the mixer (Hassanpour et al., 2011). Recently, Freireich et al. (2011) developed a compartmental approach for incorporating particle flow heterogeneity in the mixer, and further extended this approach to predict the coating distribution over polydisperse particles using the multi-scale, DEM–PB models (Li et al., 2011). In this approach, a compartment sub-model (CM) is generated based on the residence time distributions (RTD) data generated from DEM simulation, and a general 2-D PB model that accounts for particle growth and mixing mechanisms with the assumption of a power law growth rate expression. The study also shows the importance of a prerequisite understanding of the growth rate to an accurate model. Compared to other simpler models (e.g., Liu and Litster, 1993), the advantage of the Li et al. model lies in its integration with other particle-level modeling tools to account for particle flow heterogeneity and growth characteristics during the coating process. The multidimensional feature of the model presents a full 2-D distribution of particle mass and coating mass, and the compartmentalization of the mixer in the model captures the spray preference caused by both the effect of particle size and mixer geometry. The current work focuses on performing a series of coating experiments over polydisperse particles using the same Forberg-style mixer, and then generating a fully 2-D distribution with respect to particle coating mass and solid core mass. The objective is to validate the ability of the DEM–PB model to predict the coating variability observed experimentally.
361
chosen for model validation. In this application, the spray is applied for a short period of time: approximately one minute. The experiments were performed in a lab-scale, six liter, Forberg-style, dual axis, counter-rotating paddle mixer (Fig. 1; B-6XN Dynamic Air Corporation, St. Paul, MN, USA). At the beginning of the experiment, a batch of 3 kg spheroidal seed particles were poured and pre-mixed in the paddle mixer for 10 s at a constant mixing speed. Two kinds of seed particle populations were used in the experiments, namely, large and small particles. Both were composed of the same chemical composition and physical properties except the particle size (mass) (refer to Table 1 for details). Subsequently, a hot liquid solution was sprayed over the particle bed using an air atomizing spray nozzle. For each experiment, the spray pattern was re-calibrated to maintain a consistent, nearly circular spray patternation with a radius of 2.5 cm on the particle bed. The coating solution is quickly absorbed into the particle solid core once it is sprayed onto particle surface, so other mechanisms, such as liquid transfer and agglomeration, are negligible in this case. Particles were dried after each batch operation and approximately 100 sample particles were randomly collected with a riffle splitter. The mass of each particle was then measured. In addition, the corresponding coating mass content of each sample particle was measured using a desktop NMR tester calibrated to measure a specific component in the coating solution. Although the seed particles had not yet been coated, they contained a small fraction of coating material. The relationship between a particle’s total mass, mT, and the mass fraction of coating material it contains, p, is central to the current discussion. Therefore, in order to provide clarity, a 2-D distribution function n(mT, p) is defined such that n(mT, p)dmTdp gives the number fraction of particles with total mass between mT and mT þdmT whilst simultaneously having a coating material mass fraction between p and p þdp. This distribution can similarly be written in terms of the solid core mass m ¼(1–p)mT and the coating material mass mY ¼pmY using standard change of variable techniques. The initial (i.e., before any spray coating) distributions n(m, mY)
Fig. 1. Schematic of the experimental setup. Coater geometry is identical to that used in Freireich et al. (2011) and Li et al. (2011).
Table 1 Comparisons between the two kinds of seed particle properties. Parameters
Large particles Mean
Small particles
Std. dev. Mean Std. dev.
2. Materials and methods An industrial application consisting of spraying high value ingredients onto approximately 1 cm diameter particles was
Seed particle size (mm) 11.69 0.35 Seed particle mass, mT (g) 0.453 0.0375 Initial coating fraction, p0 (dimensionless) 0.131 0.0023
9.01 0.15 0.267 0.0207 0.125 0.0025
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J. Li et al. / Chemical Engineering Science 95 (2013) 360–365
are shown for the large and small particles in Figs. 2(a) and 3(a), respectively. The mean and standard deviation of total mass are computed using the normal definitions, i.e.,
mmT ¼
Z
p¼1 p¼0
Z
mT -1
mT nðmT ,pÞdmT dp mT ¼ 0
ð2Þ
and
smT
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Z p ¼ 1 Z mT -1 2 ¼ ðmT mmT Þ nðmT ,pÞdmT dp p¼0
ð3Þ
mT ¼ 0
and similarly for the fraction of coating material. Table 1 shows the results of these calculations. Note that the initial coating
Fig. 2. The evolution of 2-D number distribution for large particle series [Fr ¼1]. (a) t ¼0 (seed distribution), (b) t ¼10 s, (c) t ¼30 s and (d) t ¼60 s.
Fig. 3. The evolution of 2-D number distribution for small particle series [Fr ¼1]. (a) t ¼0 (seed distribution), (b) t ¼ 10 s, (c) t ¼30 s and (d) t ¼60 s.
J. Li et al. / Chemical Engineering Science 95 (2013) 360–365
Table 2 Operational parameters of the coating experiments.
Table 3 Compartmental model parameters.
Parameter
Value
Mass load, MT _Y Spray rate, M
3 kg 160 g/min
Mixing mass ratio (for bimodal series) Spray time, t Froude number, Fr
1:1 10–60 s 0.6–2
Parameter
material mass fraction, before any spray has been applied, is referred to as p0. Furthermore, the distributions of the large and small seed particles are sufficiently well separated to be distinguished from each other in a bimodal spray experiment. Lastly, the seed particles have a nearly uniform initial coating mass fraction, p0, independent of core mass. In this study, two types of experiments were designed. In the unimodal series, only one kind of particle was used for each batch while in the bimodal series, a mixed batch of the two kinds of particles was sprayed simultaneously. Spray time and paddle speed were studied at different levels; however, other operational parameters, such as the total mass load, spray rate, and mixing mass ratio (for bimodal series), were kept constant (Table 2). In Table 2, the Froude number is defined as Fr ¼
r o2 g
ð4Þ
where o is the paddle rotational speed, r is the paddle radius (for the B-6XN mixer, r ¼8 cm), and g is the acceleration due to gravity.
3. Model simulation In a PB model, the time evolution of the distribution function n of particles in the spray zone is computed by solving an equation of the form @n @ þ ðGnÞ ¼ ðinf lowÞðoutf lowÞ @t @mY
ð5Þ
where G is the mass-based particle growth rate due to the spray GðmY Þ ¼
dmY dt
363
ð6Þ
and the inflow and outflow terms are specific to the model formulation (see, for example, Freireich et al., 2011; Li et al., 2011). It is important to note the subtle difference between the usage of G in Eq. (5) as compared to the definition of G in Eq. (1). Eq. (1) defines G as the average rate of increase of particle coating mass regardless of position. Models such as the one presented in Eq. (1) (Liu and Litster, 1993) account for coating mass variability only through a particle size dependent growth rate. Eq. (5) gives G as the rate of increase of coating mass on particles currently in the spray zone, while the inflow and outflow terms account for an additional mechanism of non-uniformity due to size, which is the exchange of particles between sprayed and unsprayed zones. Details of the full compartmental PB model, and its link to the DEM model of particle flow in the mixer are given in Freireich et al. (2011) and Li et al. (2011). This DEM–PB modeling approach predicts the coating variability of polydisperse particles sprayed in a paddle mixer. This approach combines the DEM and PB models at a macroscopic flow scale to analyze the coating performance over long time periods, which depends more on particle flow characteristics rather than collision-scale dynamics. Due to the high computational cost of DEM simulations, monodisperse particles were used to generate the flow features. The corresponding CM parameters were obtained by curve fitting
Value
Spray shortcut fraction, lS (dimensionless) Spray characteristic time, TS (s) Bed shortcut fraction, lB (dimensionless) Bed characteristic time, TB (s) Bed recycling ratio, R (dimensionless) Number of bed compartments, B (dimensionless)
Fr ¼0.6
Fr¼ 1.0
Fr ¼2.0
0.309 0.128 0.237 1.112 1.838 67
0.380 0.114 0.222 0.839 3.283 62
0.374 0.118 0.218 0.632 6.511 46
the RTDs obtained from the DEM outputs (Table 3). Next, PB simulations were performed with the following conditions: 1. the experimentally measured initial seed distributions were assumed; 2. the PB model parameters were consistent with the CM parameters determined from the DEM simulations; and 3. a suitable growth rate exponent r was used (r ¼0.37 is adopted as discussed in Section 4.2).
4. Results and discussion 4.1. Unimodal experimental series The 2-D number distributions at different spray times, with respect to mY and m, are plotted in Figs. 2 and 3. Both seed particle distributions show a strong correlation between the coating mass and solid core mass, indicating a nearly uniform coating fraction before the spray is applied. The distribution spreads out quickly as the spray begins, especially for the large particles. Two assumptions are made in calculating the coated mass nmY on an individual particle. Firstly, the solid core mass does not change during the coating process; second, for each type of seed particle, the seed particles have a uniform coating mass percentage p0 which is independent of the core mass. This assumption is reasonable because the seed coating mass coefficient of variation is very small, 0.017 and 0.020 for the small and large seed particle populations, respectively (Table 1). The coated mass nmY at any time is then,
DmY ¼ mY mY 9t ¼ 0 ¼
pp0 mT 1p0
ð7Þ
The evolutions of the mean and coefficient of variance (CoV) of the coated mass nmY are calculated and presented in Fig. 4. Fig. 4(a) demonstrates that the mean of nmY increases linearly with spray time, with the model prediction as,
DmY ðtÞmodel ¼
_Y mT M t MT
ð8Þ
_ Y is the spray rate where MT is the total mass load per batch and M from Table 2. The measured and predicted coating rates are similar. The predicted rate for the small particles is within the experimental error. However, the model under-predicts the coating rate for the large particles. This mismatch may be due to the erosion of the cores in the experiments, which would result in a larger calculated coating mass according to Eq. (7). Fig. 4(b) shows the corresponding evolution of the CoV with 95% confidence intervals. The time points for the large particle series demonstrate the negative one-half power law dependence of CoV on spray time (Mann, 1983; Kalbag and Wassgren, 2009; Turton, 2010), while
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J. Li et al. / Chemical Engineering Science 95 (2013) 360–365
Fig. 5. Effect of Froude number on coating variability.
the spray zone. As a result, the overall coating distribution presents a larger variation at larger Fr. 4.2. Bimodal experimental series When the equipment is considered as a single well-mixed unit (e.g., Liu and Litster, 1993), G is the average growth rate over all time, and is assumed to be G ¼ kmr
Fig. 4. The evolution of coated mass distribution properties for unimodal coating experiments [Fr ¼ 1]. (a) Mean and (b) CoV.
for the small particle series the points are too scattered to draw a conclusion. Li et al.’s (2011) DEM–PB model predicted that the coating mass distribution should follow the negative one-half power law dependence for a small ratio of coating mass to particle mass, independent of the empirical growth law. The coating mass distribution will start to diverge from this law at larger coating mass ratios (mY/mp)40.05 where the coating growth rate is particle size dependent, and will exhibit noticeable differences when (mY/mp)40.1. In these experiments, the maximum coating to particle mass ratio is approximately 0.05. Within experimental error, the results are consistent with model predictions. The Froude number is one of the primary operational parameters that characterize mixing intensity in rotating devices. Fig. 5 shows the effect of the Froude number on the experimentally measured coating mass variance s2mY of the 2-D particle coating distributions for the unimodal series at time t ¼20 s. The increase in CoV with Fr is observed for both particle sizes studied. Furthermore, both particle sizes suggest a plateau in CoV for Fr41 starting at Fr ¼1. However, the difference in CoV for small and large Fr is more pronounced for the larger particles. This phenomenon can be explained by a flow regime change observed in the experiments. At Fr ¼0.6, the bed is in a nonfluidized state so that most particles visit the spray zone regularly as the paddle revolves. In a mechanically fluidized condition (large Fr), particle trajectories become more unpredictable, and there is a larger variation in the times between particle visits to
ð9Þ
where m is the particle mass, r is the growth rate exponent, and k is the constant coefficient that ensures a macroscopic mass balance of the spray. In the current study, since the DEM simulations use monodisperse seed particles, the CM describes the mean flow behavior of representative particle sizes instead of potential flow heterogeneity caused by particle size. Hence, the same form as Eq. (9) is adopted for the growth rate G, with the exponent r acting as a lumped parameter indicating the overall particle size effect from multiple factors on spray preference. These factors include the number of spray zone visits, the duration of each spray zone visit, and the average exposure area to the spray. The value of r equals 2/3 ideally when all these factors are size-independent, i.e., when particles receive coating mass proportionally to their surface area. The bimodal series experiments are designed to estimate an appropriate value of r for the specific mixer used in this study. While the two kinds of particles are sprayed simultaneously, their coating growth rates can shed light on the distribution of the spray materials over the two populations, i.e., the spray preference on particle size. The following equation, which is an extension of Eq. (9), can be used to estimate r: r ¼ lnðGlarge =Gsmall Þ=lnðmlarge =msmall Þ
ð10Þ
As mentioned previously, the coating mass growth in a spouted bed coater is found to be proportional to the raw seed mass, which indicates that the exponent r equals one (Liu and Litster, 1993). A similar phenomenon of spray preference for large particles is also found in fluidized bed coaters (Sudsakorn and Turton, 2000). In our study, an opposite trend has been observed. With the fitted growth rate G from Fig. 6 and the seed solid core mass m calculated from Table 2, the mass based growth rate r equals 0.37. This value suggests that smaller particles receive more coating than expected for polydisperse particles mixed in a Forberg-style paddle mixer. The previous studies were undertaken in fluidized systems where the concentration of particles in the spray zone is small and particles are moving in the same direction as the spray. In our
J. Li et al. / Chemical Engineering Science 95 (2013) 360–365
365
the model validation from these experiments is limited to only moderate coating mass to seed mass ratios of order 0.05.
5. Conclusions
Fig. 6. Coating mass growth with time for the bimodal coating experiments.
In this study, lab scale spray coating experiments are performed in a Forberg-style mixer to validate a multi-scale DEM–PB model. Twodimensional particle distributions with respect to coating mass and solid core mass are generated for each batch. In the unimodal series experiments, the average coated mass increases linearly and the coated mass CoV decreases proportionally to the inverse of the square root of the spray time. Increasing Froude number results in a larger coating variability. The results of bimodal series experiments suggest a value of r¼0.37 for the growth rate constant used in the DEM–PB model. This spray characteristic is contrary to previous findings which showed preferential spray on large particles for spouted and fluidized bed coaters, indicating the size dependence of the growth rate is strongly influenced by equipment geometry or operation conditions. The study has also demonstrated that with flow-scale features characterized by the compartmental model and spray preference represented appropriately in the growth rate expression, the DEM– PB, multi-scale model is capable of predicting the full two-dimensional particle coating distribution. In the future, the DEM–PB model should be validated at coating mass to seed mass ratios above 0.1 to confirm its applicability to a wide range of coating conditions.
Acknowledgments
Fig. 7. Evolutions of coating mass for the bimodal series (dot points—experimental data; solid lines—model simulation).
mechanically agitated mixer, the particle concentration in the spray zone is large and particles are moving with random trajectories roughly perpendicular to the spray direction. We expect mechanisms for segregation of particles and the extent of shielding of larger particles in the spray zone to be different than those found in fluidized systems. Identifying the exact mechanism for bias towards coating smaller particles would require detailed particle tracer studies, e.g., using the PEPT technique, or analysis of DEM simulations for bimodal systems. However, it is clear that there is no universally ‘‘correct’’ value for r as it will be a strong function of the particle flow field and equipment geometry. 4.3. Comparisons between experimental and simulation results Fig. 7 shows the comparison of coating mass evolutions as a function of core mass for the bimodal series experiments. The mean coating mass for a specific solid core mass E(mY9m) is calculated as Z mY -1 EðmY 9mÞ ¼ mY nðm,mY ÞdmY ð11Þ mY ¼ 0
with the 95% confidence interval calculated using the Student-t distribution. Model simulation results (solid lines) show good agreement with experimental data at an earlier stage (t¼ 20 s), and a slight over-prediction on the coating growth rate at the endpoint (t ¼60 s). The discrepancy between the model and experimental data is possibly due to the loss of spray materials on the wall and paddles at long spray times. Some data points are presented with large error bars or with no error bars due to insufficient sample particles in those ranges. Note that, as discussed in Section 4.1,
This work was supported by the National Science Foundation (Grant number CBET-1034014) and the Procter and Gamble Company, Cincinnati, Ohio. The authors also appreciate the help from Vinit Murthy, Michelle Houston, and Ellery Johnson for facilitating the spray coating experiments. References Denis, C., Hemati, A., Chulia, D., Lanne, J.Y., Buisson, B., Daste, G., Elbaz, F., 2003. A model of surface renewal with application to the coating of pharmaceutical tablets in rotary drums. Powder Technol. 130, 174–180. Freireich, B., Li, J., Litster, J.D., Wassgren, C.R., 2011. Incorporating particle flow information from discrete element simulations in population balance models of mixer-coaters. Chem. Eng. Sci. 66, 3592–3604. Hassanpour, A., Tan, H.S., Bayly, A., Gopalkrishnan, P., Ng, B., Ghadiri, M., 2011. Analysis of particle motion in a paddle mixer using discrete element method (DEM). Powder Technol. 206, 189–194. Kalbag, A., Wassgren, C.R., 2009. Inter-tablet coating variability: tablet residence time variability. Chem. Eng. Sci. 64, 2705–2717. Li, J., Freireich, B.J., Wassgren, C.R., Litster, J.D, 2011. A general compartment-based population balance model for particle coating and layered granulation. AICHE J. doi:10.1002/aic.12678. /http://onlinelibrary.wiley.com/doi/10.1002/ aic.12678/abstractS. Litster, J.D., Hounslow, M.J., Liu, L.X., 1993. Bottom sprayed granulation and coating in a spouted bed. In: Proceedings of the Sixth International Symposium on Agglomeration (AGGLOS 93). Nagoya, pp. 123–128. Liu, L.X., Litster, J.D., 1993. Coating mass distribution from a spouted bed seed coater: experimental and modeling studies. Powder Technol. 74, 259–270. Mann, U., 1983. Analysis of spouted bed coating and granulation. 1. Batch operation. Ind. Eng. Chem. Process Des. Dev. 22, 288–292. Maronga, S.J., Wnukowski, P., 1997. Modelling of the three-domain fluidized-bed particulate coating process. Chem. Eng. Sci. 52, 2915–2925. Pandey, P., Katakdaunde, M., Turton, R., 2006. Modeling weight variability in a pan coating process using Monte Carlo simulations. AAPS Pharm. Sci. Tech. 7, 2–10. Saleh, K., Guigon, P., 2007. Coating and encapsulation processes in powder technology. In: Salman, A.D., Hounslow, M.J., Seville, J.P.K. (Eds.), Handbook of Powder Technology, Vol. 11: Granulation. Elsevier, NY, pp. 323–375. Sudsakorn, K., Turton, R., 2000. Nonuniformity of particle coating on a size distribution of particles in a fluidized bed coater. Powder Technol. 110, 37–43. Turton, R., 2010. The application of modeling techniques to film-coating processes. Drug Dev. Ind. Pharm. 36, 143–151. Wnukowski, P., Setterwall, F., 1989. The coating of particles in a fluidized-bed (residence time distribution in a system of two coupled perfect mixers). Chem. Eng. Sci. 44, 493–505.
Contents lists available at SciVerse ScienceDirect
Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Experimental validation of a 2-D population balance model for spray coating processes Jianfeng Li a, Ben J. Freireich b,d, Carl R. Wassgren b,c, James D. Litster a,c,n a
School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA c Department of Industrial Physical Pharmacy, Purdue University, West Lafayette, IN 47907, USA d The Dow Chemical Company, Midland, MI 48667, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 November 2011 Received in revised form 9 February 2012 Accepted 22 February 2012 Available online 1 March 2012
In this study, a series of spray coating experiments were carried out in a pilot scale Forberg-style paddle mixer to validate a previously published multi-dimensional population balance (PB) model (Li et al., 2011). Experiments were carried out using unimodal distributions of large (mean mass 0.45 g) and small (mean mass 0.27 g) particles, as well as bimodal distributions with a 1:1 mass ratio of the large and small particles. Experiments were performed at Froude numbers from 0.6 to 2 with the final coating mass to core particle mass ratio being 0.05. A fully two-dimensional distribution of the coated particles, with respect to solid core mass and coating mass, was obtained for each batch operation. For unimodal core particle distributions, the coating mass coefficient of variation was proportional to t 0.5 where t is the coating time, consistent with both the PB model and other published coating models. For the bimodal experimental series, the coating growth rate varied with particle mass m according to the relationship G ¼ mr where r ¼0.37. This value for the growth expression exponent r is smaller than that predicted for random coating (r ¼ 2/3) or observed experimentally in fluidized coating systems (r ¼1). This preferential spraying of small particles in the mechanical mixer indicates that the size dependence of coating mass growth rate is a strong function of the equipment geometry and particle flow field. When a growth exponent r¼ 0.37 was used, the coating distribution prediction from a discrete element method–population balance simulation compares well with the experimental results. Published by Elsevier Ltd.
Keywords: Population balance Paddle mixer Spray coating Multi-dimensional distribution Powder technology Granulation
1. Introduction Spray coating processes have widespread applications in the pharmaceutical, detergent, agrochemical, and food industries. A typical coating process consists of spraying an atomized coating solution onto the surface of dry, solid particles, and forming an ‘‘onion’’ structure of one or multiple layers surrounding the solid core (Saleh and Guigon, 2007). The key mechanism underlying the process is particle growth by layering, rather than other granulation phenomena such as agglomeration and attrition. Recently, researchers have been focused on the development of fundamental coating models to achieve better understanding of the important facets that affect the coating quality. A variety of modeling tools have been reported to predict the coating uniformity. The discrete element method (DEM) is a particle-level modeling tool that provides detailed dynamic
n Corresponding author at: School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA. E-mail address: [email protected] (J.D. Litster).
0009-2509/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.ces.2012.02.036
information as particles are mixed and sprayed (Kalbag and Wassgren, 2009). The Monte Carlo approach is another method for simulating the ‘‘random walk’’ of particles in the spray zone (Pandey et al., 2006). In the surface renewal model, the coating process is modeled as the sum of many short-time, spray zone visits. Based on that idea, Mann (1983) derived a relation to calculate the coating variability caused by the variation of the number of spray zone visits, and the variation of the coating amount an individual particle received during its single pass through the spray zone. Population balance (PB) modeling is yet another approach that can be used for modeling a coating process. A population balance is a process-level approach to simulating the temporal change of a particle number distribution over one or more dimensions, with incorporation of the rate phenomena contributing to layered growth (Wnukowski and Setterwall, 1989; Liu and Litster, 1993; Maronga and Wnukowski, 1997; Denis et al., 2003). Details of these modeling approaches have been summarized by Turton (2010). Excluding the work of Liu and Litster (1993), the abovementioned works refer only to monodisperse seed particle sizes. Liu and Litster derived a single-compartment PB that tracks the
J. Li et al. / Chemical Engineering Science 95 (2013) 360–365
distribution of coating mass on particles in a spouted bed. Because only a single compartment is used, the variability in coating mass must come from a size-dependent growth rate. The size dependence of the growth rate accounts for (i) the fact that particles in the spray receive different coating amounts depending on their size, and (ii) particles are presented to the spray more or less often depending on their size. Mathematically G¼
dm p ¼ J x2 ZðxÞaðxÞ dt 4
ð1Þ
where J is the total mass flux (mass flow per unit area), Z(x) is the average fraction of projected surface area particles of size x sprayed due to shielding by neighboring particles, and a(x) is the average fraction of time particles of size x spend in the spray. The dependence of the parameters Z and a on x, found empirically, results in Gpm. That is, particles gain coating mass at a rate proportional to their mass. Intuition suggests that particles gain mass in proportion to their surface area, Gpm2/3, so this result is surprising. Litster et al. (1993) showed that for a spouted bed, this stronger dependence on particle mass could be explained by the different trajectories that particles of different mass particles take within the spray zone. In general, we expect the size-dependent growth expression to depend strongly on the coater geometry and particle flow field. In this work, we experimentally examine the relative coating rates of binary seed particle sizes agitated in a Forberg-style mixer. The Forberg-style mixer is a commonly used, mechanically agitated mixer/coater in which particles are agitated by counter-rotating, twin-shaft paddles. Non-ideal particle flow is expected due to the complex mixer geometry. DEM simulations have been adopted to study the particle movements in this type of mixer (Hassanpour et al., 2011; Freireich et al., 2011). The models produce particle trajectories with a major vertical flow pattern (with the rotating paddle) and a minor horizontal flow pattern (along the shaft). This observation has been further verified using Positron Emission Particle Tracking (PEPT) to track an individual particle’s motion in the mixer (Hassanpour et al., 2011). Recently, Freireich et al. (2011) developed a compartmental approach for incorporating particle flow heterogeneity in the mixer, and further extended this approach to predict the coating distribution over polydisperse particles using the multi-scale, DEM–PB models (Li et al., 2011). In this approach, a compartment sub-model (CM) is generated based on the residence time distributions (RTD) data generated from DEM simulation, and a general 2-D PB model that accounts for particle growth and mixing mechanisms with the assumption of a power law growth rate expression. The study also shows the importance of a prerequisite understanding of the growth rate to an accurate model. Compared to other simpler models (e.g., Liu and Litster, 1993), the advantage of the Li et al. model lies in its integration with other particle-level modeling tools to account for particle flow heterogeneity and growth characteristics during the coating process. The multidimensional feature of the model presents a full 2-D distribution of particle mass and coating mass, and the compartmentalization of the mixer in the model captures the spray preference caused by both the effect of particle size and mixer geometry. The current work focuses on performing a series of coating experiments over polydisperse particles using the same Forberg-style mixer, and then generating a fully 2-D distribution with respect to particle coating mass and solid core mass. The objective is to validate the ability of the DEM–PB model to predict the coating variability observed experimentally.
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chosen for model validation. In this application, the spray is applied for a short period of time: approximately one minute. The experiments were performed in a lab-scale, six liter, Forberg-style, dual axis, counter-rotating paddle mixer (Fig. 1; B-6XN Dynamic Air Corporation, St. Paul, MN, USA). At the beginning of the experiment, a batch of 3 kg spheroidal seed particles were poured and pre-mixed in the paddle mixer for 10 s at a constant mixing speed. Two kinds of seed particle populations were used in the experiments, namely, large and small particles. Both were composed of the same chemical composition and physical properties except the particle size (mass) (refer to Table 1 for details). Subsequently, a hot liquid solution was sprayed over the particle bed using an air atomizing spray nozzle. For each experiment, the spray pattern was re-calibrated to maintain a consistent, nearly circular spray patternation with a radius of 2.5 cm on the particle bed. The coating solution is quickly absorbed into the particle solid core once it is sprayed onto particle surface, so other mechanisms, such as liquid transfer and agglomeration, are negligible in this case. Particles were dried after each batch operation and approximately 100 sample particles were randomly collected with a riffle splitter. The mass of each particle was then measured. In addition, the corresponding coating mass content of each sample particle was measured using a desktop NMR tester calibrated to measure a specific component in the coating solution. Although the seed particles had not yet been coated, they contained a small fraction of coating material. The relationship between a particle’s total mass, mT, and the mass fraction of coating material it contains, p, is central to the current discussion. Therefore, in order to provide clarity, a 2-D distribution function n(mT, p) is defined such that n(mT, p)dmTdp gives the number fraction of particles with total mass between mT and mT þdmT whilst simultaneously having a coating material mass fraction between p and p þdp. This distribution can similarly be written in terms of the solid core mass m ¼(1–p)mT and the coating material mass mY ¼pmY using standard change of variable techniques. The initial (i.e., before any spray coating) distributions n(m, mY)
Fig. 1. Schematic of the experimental setup. Coater geometry is identical to that used in Freireich et al. (2011) and Li et al. (2011).
Table 1 Comparisons between the two kinds of seed particle properties. Parameters
Large particles Mean
Small particles
Std. dev. Mean Std. dev.
2. Materials and methods An industrial application consisting of spraying high value ingredients onto approximately 1 cm diameter particles was
Seed particle size (mm) 11.69 0.35 Seed particle mass, mT (g) 0.453 0.0375 Initial coating fraction, p0 (dimensionless) 0.131 0.0023
9.01 0.15 0.267 0.0207 0.125 0.0025
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are shown for the large and small particles in Figs. 2(a) and 3(a), respectively. The mean and standard deviation of total mass are computed using the normal definitions, i.e.,
mmT ¼
Z
p¼1 p¼0
Z
mT -1
mT nðmT ,pÞdmT dp mT ¼ 0
ð2Þ
and
smT
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Z p ¼ 1 Z mT -1 2 ¼ ðmT mmT Þ nðmT ,pÞdmT dp p¼0
ð3Þ
mT ¼ 0
and similarly for the fraction of coating material. Table 1 shows the results of these calculations. Note that the initial coating
Fig. 2. The evolution of 2-D number distribution for large particle series [Fr ¼1]. (a) t ¼0 (seed distribution), (b) t ¼10 s, (c) t ¼30 s and (d) t ¼60 s.
Fig. 3. The evolution of 2-D number distribution for small particle series [Fr ¼1]. (a) t ¼0 (seed distribution), (b) t ¼ 10 s, (c) t ¼30 s and (d) t ¼60 s.
J. Li et al. / Chemical Engineering Science 95 (2013) 360–365
Table 2 Operational parameters of the coating experiments.
Table 3 Compartmental model parameters.
Parameter
Value
Mass load, MT _Y Spray rate, M
3 kg 160 g/min
Mixing mass ratio (for bimodal series) Spray time, t Froude number, Fr
1:1 10–60 s 0.6–2
Parameter
material mass fraction, before any spray has been applied, is referred to as p0. Furthermore, the distributions of the large and small seed particles are sufficiently well separated to be distinguished from each other in a bimodal spray experiment. Lastly, the seed particles have a nearly uniform initial coating mass fraction, p0, independent of core mass. In this study, two types of experiments were designed. In the unimodal series, only one kind of particle was used for each batch while in the bimodal series, a mixed batch of the two kinds of particles was sprayed simultaneously. Spray time and paddle speed were studied at different levels; however, other operational parameters, such as the total mass load, spray rate, and mixing mass ratio (for bimodal series), were kept constant (Table 2). In Table 2, the Froude number is defined as Fr ¼
r o2 g
ð4Þ
where o is the paddle rotational speed, r is the paddle radius (for the B-6XN mixer, r ¼8 cm), and g is the acceleration due to gravity.
3. Model simulation In a PB model, the time evolution of the distribution function n of particles in the spray zone is computed by solving an equation of the form @n @ þ ðGnÞ ¼ ðinf lowÞðoutf lowÞ @t @mY
ð5Þ
where G is the mass-based particle growth rate due to the spray GðmY Þ ¼
dmY dt
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ð6Þ
and the inflow and outflow terms are specific to the model formulation (see, for example, Freireich et al., 2011; Li et al., 2011). It is important to note the subtle difference between the usage of G in Eq. (5) as compared to the definition of G in Eq. (1). Eq. (1) defines G as the average rate of increase of particle coating mass regardless of position. Models such as the one presented in Eq. (1) (Liu and Litster, 1993) account for coating mass variability only through a particle size dependent growth rate. Eq. (5) gives G as the rate of increase of coating mass on particles currently in the spray zone, while the inflow and outflow terms account for an additional mechanism of non-uniformity due to size, which is the exchange of particles between sprayed and unsprayed zones. Details of the full compartmental PB model, and its link to the DEM model of particle flow in the mixer are given in Freireich et al. (2011) and Li et al. (2011). This DEM–PB modeling approach predicts the coating variability of polydisperse particles sprayed in a paddle mixer. This approach combines the DEM and PB models at a macroscopic flow scale to analyze the coating performance over long time periods, which depends more on particle flow characteristics rather than collision-scale dynamics. Due to the high computational cost of DEM simulations, monodisperse particles were used to generate the flow features. The corresponding CM parameters were obtained by curve fitting
Value
Spray shortcut fraction, lS (dimensionless) Spray characteristic time, TS (s) Bed shortcut fraction, lB (dimensionless) Bed characteristic time, TB (s) Bed recycling ratio, R (dimensionless) Number of bed compartments, B (dimensionless)
Fr ¼0.6
Fr¼ 1.0
Fr ¼2.0
0.309 0.128 0.237 1.112 1.838 67
0.380 0.114 0.222 0.839 3.283 62
0.374 0.118 0.218 0.632 6.511 46
the RTDs obtained from the DEM outputs (Table 3). Next, PB simulations were performed with the following conditions: 1. the experimentally measured initial seed distributions were assumed; 2. the PB model parameters were consistent with the CM parameters determined from the DEM simulations; and 3. a suitable growth rate exponent r was used (r ¼0.37 is adopted as discussed in Section 4.2).
4. Results and discussion 4.1. Unimodal experimental series The 2-D number distributions at different spray times, with respect to mY and m, are plotted in Figs. 2 and 3. Both seed particle distributions show a strong correlation between the coating mass and solid core mass, indicating a nearly uniform coating fraction before the spray is applied. The distribution spreads out quickly as the spray begins, especially for the large particles. Two assumptions are made in calculating the coated mass nmY on an individual particle. Firstly, the solid core mass does not change during the coating process; second, for each type of seed particle, the seed particles have a uniform coating mass percentage p0 which is independent of the core mass. This assumption is reasonable because the seed coating mass coefficient of variation is very small, 0.017 and 0.020 for the small and large seed particle populations, respectively (Table 1). The coated mass nmY at any time is then,
DmY ¼ mY mY 9t ¼ 0 ¼
pp0 mT 1p0
ð7Þ
The evolutions of the mean and coefficient of variance (CoV) of the coated mass nmY are calculated and presented in Fig. 4. Fig. 4(a) demonstrates that the mean of nmY increases linearly with spray time, with the model prediction as,
DmY ðtÞmodel ¼
_Y mT M t MT
ð8Þ
_ Y is the spray rate where MT is the total mass load per batch and M from Table 2. The measured and predicted coating rates are similar. The predicted rate for the small particles is within the experimental error. However, the model under-predicts the coating rate for the large particles. This mismatch may be due to the erosion of the cores in the experiments, which would result in a larger calculated coating mass according to Eq. (7). Fig. 4(b) shows the corresponding evolution of the CoV with 95% confidence intervals. The time points for the large particle series demonstrate the negative one-half power law dependence of CoV on spray time (Mann, 1983; Kalbag and Wassgren, 2009; Turton, 2010), while
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Fig. 5. Effect of Froude number on coating variability.
the spray zone. As a result, the overall coating distribution presents a larger variation at larger Fr. 4.2. Bimodal experimental series When the equipment is considered as a single well-mixed unit (e.g., Liu and Litster, 1993), G is the average growth rate over all time, and is assumed to be G ¼ kmr
Fig. 4. The evolution of coated mass distribution properties for unimodal coating experiments [Fr ¼ 1]. (a) Mean and (b) CoV.
for the small particle series the points are too scattered to draw a conclusion. Li et al.’s (2011) DEM–PB model predicted that the coating mass distribution should follow the negative one-half power law dependence for a small ratio of coating mass to particle mass, independent of the empirical growth law. The coating mass distribution will start to diverge from this law at larger coating mass ratios (mY/mp)40.05 where the coating growth rate is particle size dependent, and will exhibit noticeable differences when (mY/mp)40.1. In these experiments, the maximum coating to particle mass ratio is approximately 0.05. Within experimental error, the results are consistent with model predictions. The Froude number is one of the primary operational parameters that characterize mixing intensity in rotating devices. Fig. 5 shows the effect of the Froude number on the experimentally measured coating mass variance s2mY of the 2-D particle coating distributions for the unimodal series at time t ¼20 s. The increase in CoV with Fr is observed for both particle sizes studied. Furthermore, both particle sizes suggest a plateau in CoV for Fr41 starting at Fr ¼1. However, the difference in CoV for small and large Fr is more pronounced for the larger particles. This phenomenon can be explained by a flow regime change observed in the experiments. At Fr ¼0.6, the bed is in a nonfluidized state so that most particles visit the spray zone regularly as the paddle revolves. In a mechanically fluidized condition (large Fr), particle trajectories become more unpredictable, and there is a larger variation in the times between particle visits to
ð9Þ
where m is the particle mass, r is the growth rate exponent, and k is the constant coefficient that ensures a macroscopic mass balance of the spray. In the current study, since the DEM simulations use monodisperse seed particles, the CM describes the mean flow behavior of representative particle sizes instead of potential flow heterogeneity caused by particle size. Hence, the same form as Eq. (9) is adopted for the growth rate G, with the exponent r acting as a lumped parameter indicating the overall particle size effect from multiple factors on spray preference. These factors include the number of spray zone visits, the duration of each spray zone visit, and the average exposure area to the spray. The value of r equals 2/3 ideally when all these factors are size-independent, i.e., when particles receive coating mass proportionally to their surface area. The bimodal series experiments are designed to estimate an appropriate value of r for the specific mixer used in this study. While the two kinds of particles are sprayed simultaneously, their coating growth rates can shed light on the distribution of the spray materials over the two populations, i.e., the spray preference on particle size. The following equation, which is an extension of Eq. (9), can be used to estimate r: r ¼ lnðGlarge =Gsmall Þ=lnðmlarge =msmall Þ
ð10Þ
As mentioned previously, the coating mass growth in a spouted bed coater is found to be proportional to the raw seed mass, which indicates that the exponent r equals one (Liu and Litster, 1993). A similar phenomenon of spray preference for large particles is also found in fluidized bed coaters (Sudsakorn and Turton, 2000). In our study, an opposite trend has been observed. With the fitted growth rate G from Fig. 6 and the seed solid core mass m calculated from Table 2, the mass based growth rate r equals 0.37. This value suggests that smaller particles receive more coating than expected for polydisperse particles mixed in a Forberg-style paddle mixer. The previous studies were undertaken in fluidized systems where the concentration of particles in the spray zone is small and particles are moving in the same direction as the spray. In our
J. Li et al. / Chemical Engineering Science 95 (2013) 360–365
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the model validation from these experiments is limited to only moderate coating mass to seed mass ratios of order 0.05.
5. Conclusions
Fig. 6. Coating mass growth with time for the bimodal coating experiments.
In this study, lab scale spray coating experiments are performed in a Forberg-style mixer to validate a multi-scale DEM–PB model. Twodimensional particle distributions with respect to coating mass and solid core mass are generated for each batch. In the unimodal series experiments, the average coated mass increases linearly and the coated mass CoV decreases proportionally to the inverse of the square root of the spray time. Increasing Froude number results in a larger coating variability. The results of bimodal series experiments suggest a value of r¼0.37 for the growth rate constant used in the DEM–PB model. This spray characteristic is contrary to previous findings which showed preferential spray on large particles for spouted and fluidized bed coaters, indicating the size dependence of the growth rate is strongly influenced by equipment geometry or operation conditions. The study has also demonstrated that with flow-scale features characterized by the compartmental model and spray preference represented appropriately in the growth rate expression, the DEM– PB, multi-scale model is capable of predicting the full two-dimensional particle coating distribution. In the future, the DEM–PB model should be validated at coating mass to seed mass ratios above 0.1 to confirm its applicability to a wide range of coating conditions.
Acknowledgments
Fig. 7. Evolutions of coating mass for the bimodal series (dot points—experimental data; solid lines—model simulation).
mechanically agitated mixer, the particle concentration in the spray zone is large and particles are moving with random trajectories roughly perpendicular to the spray direction. We expect mechanisms for segregation of particles and the extent of shielding of larger particles in the spray zone to be different than those found in fluidized systems. Identifying the exact mechanism for bias towards coating smaller particles would require detailed particle tracer studies, e.g., using the PEPT technique, or analysis of DEM simulations for bimodal systems. However, it is clear that there is no universally ‘‘correct’’ value for r as it will be a strong function of the particle flow field and equipment geometry. 4.3. Comparisons between experimental and simulation results Fig. 7 shows the comparison of coating mass evolutions as a function of core mass for the bimodal series experiments. The mean coating mass for a specific solid core mass E(mY9m) is calculated as Z mY -1 EðmY 9mÞ ¼ mY nðm,mY ÞdmY ð11Þ mY ¼ 0
with the 95% confidence interval calculated using the Student-t distribution. Model simulation results (solid lines) show good agreement with experimental data at an earlier stage (t¼ 20 s), and a slight over-prediction on the coating growth rate at the endpoint (t ¼60 s). The discrepancy between the model and experimental data is possibly due to the loss of spray materials on the wall and paddles at long spray times. Some data points are presented with large error bars or with no error bars due to insufficient sample particles in those ranges. Note that, as discussed in Section 4.1,
This work was supported by the National Science Foundation (Grant number CBET-1034014) and the Procter and Gamble Company, Cincinnati, Ohio. The authors also appreciate the help from Vinit Murthy, Michelle Houston, and Ellery Johnson for facilitating the spray coating experiments. References Denis, C., Hemati, A., Chulia, D., Lanne, J.Y., Buisson, B., Daste, G., Elbaz, F., 2003. A model of surface renewal with application to the coating of pharmaceutical tablets in rotary drums. Powder Technol. 130, 174–180. Freireich, B., Li, J., Litster, J.D., Wassgren, C.R., 2011. Incorporating particle flow information from discrete element simulations in population balance models of mixer-coaters. Chem. Eng. Sci. 66, 3592–3604. Hassanpour, A., Tan, H.S., Bayly, A., Gopalkrishnan, P., Ng, B., Ghadiri, M., 2011. Analysis of particle motion in a paddle mixer using discrete element method (DEM). Powder Technol. 206, 189–194. Kalbag, A., Wassgren, C.R., 2009. Inter-tablet coating variability: tablet residence time variability. Chem. Eng. Sci. 64, 2705–2717. Li, J., Freireich, B.J., Wassgren, C.R., Litster, J.D, 2011. A general compartment-based population balance model for particle coating and layered granulation. AICHE J. doi:10.1002/aic.12678. /http://onlinelibrary.wiley.com/doi/10.1002/ aic.12678/abstractS. Litster, J.D., Hounslow, M.J., Liu, L.X., 1993. Bottom sprayed granulation and coating in a spouted bed. In: Proceedings of the Sixth International Symposium on Agglomeration (AGGLOS 93). Nagoya, pp. 123–128. Liu, L.X., Litster, J.D., 1993. Coating mass distribution from a spouted bed seed coater: experimental and modeling studies. Powder Technol. 74, 259–270. Mann, U., 1983. Analysis of spouted bed coating and granulation. 1. Batch operation. Ind. Eng. Chem. Process Des. Dev. 22, 288–292. Maronga, S.J., Wnukowski, P., 1997. Modelling of the three-domain fluidized-bed particulate coating process. Chem. Eng. Sci. 52, 2915–2925. Pandey, P., Katakdaunde, M., Turton, R., 2006. Modeling weight variability in a pan coating process using Monte Carlo simulations. AAPS Pharm. Sci. Tech. 7, 2–10. Saleh, K., Guigon, P., 2007. Coating and encapsulation processes in powder technology. In: Salman, A.D., Hounslow, M.J., Seville, J.P.K. (Eds.), Handbook of Powder Technology, Vol. 11: Granulation. Elsevier, NY, pp. 323–375. Sudsakorn, K., Turton, R., 2000. Nonuniformity of particle coating on a size distribution of particles in a fluidized bed coater. Powder Technol. 110, 37–43. Turton, R., 2010. The application of modeling techniques to film-coating processes. Drug Dev. Ind. Pharm. 36, 143–151. Wnukowski, P., Setterwall, F., 1989. The coating of particles in a fluidized-bed (residence time distribution in a system of two coupled perfect mixers). Chem. Eng. Sci. 44, 493–505.