Residence time distributions of different size particles in the spray zone of a Wurster fluid bed studied using DEM-CFD

Liang Li1, 2, Johan Remmelgas2, *, Berend G.M. van Wachem3, Christian von Corswant2, Mats Johansson2, Staffan Folestad2, Anders Rasmuson1

1Department of Chemical and Biological Engineering, Chalmers University of Technology, SE-412 96, Gothenburg, Sweden

2Pharmaceutical Development, AstraZeneca R&D, Mölndal, Sweden3Division of Thermofluids, Department of Mechanical Engineering, Imperial College London,

Exhibition Road, London SW7 2AZ, United Kingdom

*Correspondence should be addressed to Johan Remmelgas at

Tel +46-(0)-31-7065838 / Fax +46-(0)31-7763729

johan.remmelgas@astrazeneca.com.

Abstract

Particle cycle and residence time distributions in different regions, particularly in the

spray zone, play an important role in fluid bed coating. In this study, a DEM-CFD

(discrete element method, computational fluid dynamics) model is employed to

determine particle cycle and residence time distributions in a laboratory-scale Wurster

fluid bed coater. The calculations show good agreement with data obtained using the

positron emission particle tracking (PEPT) technique. The DEM-CFD simulations of

different size particles show that large particles spend a longer time in the spray zone

and in the Wurster tube than small particles. In addition, large particles are found on

average to move closer to the spray nozzle than small particles, which implies that the

large particles could shield small particles from the spray droplets. Both of these effects

suggest that large particles receive a greater amount of coating solution per unit area

per cycle than small particles. However, the simulations in combination with the PEPT

experiments show that this is partly compensated for by a longer cycle time for large

particles. Large particles thus receive more coating per unit area per pass through the

spray zone, but also travel through the spray zone less frequently than small particles.

Keywords: fluid bed, coating, spray zone, residence time distribution, discrete element

method

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1. Introduction

The Wurster process [1] has been widely used to coat particles in industry for a number

of different purposes [2]. In the pharmaceutical industry it is used to coat tablets or

pellets with drug substances or functional films that, e.g. control the release of the drug

substance [3-6]. The process typically takes place in a fluid bed, as illustrated in Figure

1, in which particles are kept near minimum fluidization by a fluidization air flow that is

supplied through a distributor plate at the bottom of the fluid bed. One or more two-

fluid nozzles located at the bottom of the bed supply an atomization air flow and a liquid

suspension in the form of droplets. The liquid droplets are deposited onto the particles

that pass through the spray zone. The particles are then dried by the air flow as they

move upwards and as they settle back towards the bottom of the fluid bed.

Figure 1 Schematic of the Wurster process and the different regions: 1) the spray zone, 2) the Wurster tube, 3) the fountain region, 4) the downbed region, and 5) the horizontal transport region.

The fluid bed can be divided into different regions as shown in Figure 1 [7-9]. The

particle coating cycle, i.e. the sequence of coating and subsequent drying, is also

illustrated in Figure 1. It is here defined as the trajectory in which the particle travels

through the spray zone, the Wurster tube, the fountain region and the downbed region

before it reappears in the spray zone to begin the next coating cycle. The total amount of

coating deposited onto a particle depends on the number of times the particle passes the

spray zone and on the amount of coating solution that the particle receives per pass [10-

13]. Thus it is clear that the cycle time distribution (CTD) and the residence time

distribution (RTD) in the spray zone of particles are important factors in determining

the quality of the product such as the film thickness and the film thickness variability.

Furthermore, the RTDs in different regions determine the drying rate of the particles in

different regions, which plays a key role in the film formation process.

There have been a number of experimental studies on CTDs and RTDs in previous work.

Mann and Crosby [14] and Shelukar et al. [12] measured the CTDs using radioactive or

magnetic particles in spouted beds and Wurster beds respectively, and San José et al.

[15] investigated the CTDs by monitoring colored particles in spouted bed dryer. While

the CTD certainly affects the amount of coating solution deposited onto the particles, the

RTD in the spray zone and the detailed motion of particles in the spray zone also play an

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important role. Moreover, it has been proposed that particles of one size receive a

smaller portion of the coating solution due to shielding by particles of a different size.

For example, Cheng and Turton [16] reported that the major cause of coating variation

can be attributed to particles receiving different amounts of coating when passing

through the spray zone. Recently, Li et al. [17] presented an experimental study of

particle cycle and residence time distributions in different regions using the positron

emission particle tracking (PEPT) technique. The results from the PEPT technique

confirmed clear differences in the RTD for different size particles, also for mixtures of

particles. Unfortunately, because of limitations with the PEPT technique the particle

motion in the spray zone could only partially be characterized. Additional studies were

therefore suggested by Li et al. [17] to provide further insight into the detailed particle

motion in the spray zone and its contribution to particle coating process.

In order to shed light on the detailed particle motion in the spray zone, DEM-CFD

(discrete element method, computational fluid dynamics) modeling may be employed.

In this modeling approach, every particle is modeled (as a discrete element) while the

gas phase is treated as a continuum. When the number of particles is large, as is typical

in particle coating processes, the computational time can become very long.  For many

particle coating systems used in the pharmaceutical industry, however, batch sizes of a

few hundred grams are often employed during development.  Depending on the particle

size, these systems thus contain between tens of thousands and a few million particles. 

Simulations involving tens of thousands of particles are fairly straightforward, while

simulations involving a few million particles are challenging but still feasible (see e.g.

[18]).  In the pharmaceutical industry, CFD-DEM modeling thus offers a unique

opportunity to study process systems that are commonly used for small-scale

production.

The discrete element method was proposed for granular assemblies by Cundall and

Strack [19] and was first introduced into research in fluid beds by Tsuji et al. [20]. The

DEM-CFD approach is increasingly applied in modeling of particle/powder processes

[21-29] and has become popular [30] because interparticle interactions are accounted

for in a straightforward manner. For example, Link et al. [22] assessed the capability of

DEM to reproduce several important flow regimes observed in a 3D spout-fluid bed and

van Buijtenen et al. [31, 32] investigated the effect of elevating the spout on the

dynamics of a (multiple) spout-fluidized bed. In the work by Fries et al. [26], an example

of the RTD in the spray zone of a Wurster coater was reported by means of DEM-CFD

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simulations. In addition, Yang et al. [29, 33, 34] presented the hydrodynamics in a 3D

spouted bed and found that the solid residence time is shortest in the spout region.

The aim of the present study is to establish and validate a DEM-CFD model for

simulations of particle motion in a Wurster fluid bed. This is performed as an important

step in developing a simulation tool for the entire particle coating process. By following

particle trajectories, the CTDs and RTDs in different regions of the Wurster fluid bed

process are determined and compared to data from recent PEPT experiments [17]. In

these recent experiments, it was pointed out that it is difficult to detect the tracer

particle in the spray region towards the bottom of the bed because the -rays tend to be

absorbed by the bulky metal parts in this region.  Since it was not possible to employ the

PEPT technique to measure the particle residence time in the spray zone, special

attention is in the present study paid to evaluate the predicted particle motion in the

spray zone.  The validated DEM-CFD model is thus employed to simulate particle motion

in the spray zone to gain an improved understanding of the coating process. These latter

simulations are used to predict the residence time in the spray zone and to examine

whether particles of one size may preferentially shield particles of a different size from

the spray droplets. Lastly, the results are discussed in the context of coating and the

effect on the overall coating process.

2. Mathematical model

2.1. Equations of particle motion

The motion of an individual particle is described using Newton’s second law

m p ,i

d v p ,i

dt=β

V p ,i

ε s( ug−v p , i)+m p ,i g−V p ,i∇P+F c ,i (1)

where m p ,i is the mass of the ith particle, vp ,i is the particle velocity, ug is the gas velocity,

g is the gravitational acceleration, V p , i is the particle volume, ∇P is the gas pressure

gradient, ε s is the particle volume fraction, F c, i is the contact force during particle-

particle and particle-wall collisions and β is the interphase momentum transfer

coefficient.

The particle volume fraction is calculated using

ε s=∑i=1

n V p ,i

V c (2)

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where V c is the volume of the computational cell. The coupling between the discrete

and continuous phase is handled based upon a multigrid technique [35], as described by

e.g. Bruchmüller et al. [36]. The particles are tracked on a so-called particle mesh, which

is a Cartesian mesh with the size larger than the particle. All the coupling terms,

including the volume fraction and the drag forces, are determined on the length-scale of

this particle mesh. In case the local fluid cell is smaller than a particle, the coupling

between that fluid cell and a particle occupying that fluid cell will be length-scale

weighted and thus remain physical. The procedure has been described and tested by

Mallouppas and van Wachem [37], and has been further worked out in the recent work

of Capecelatro and Desjardins [38].

The interphase momentum transfer coefficient is based on the Ergun equation [39] in

the dense regime and on the Wen and Yu drag correlation in the dilute regime [40],

β={(150ε s

2

ε g+1.75 ε s ℜp) μg

d p2 ε s>0.2

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ℜpC Dμg εs

d p2 εg

−2.65 εs ≤ 0.2(3)

where ε g=1−ε s is the gas volume fraction, μg is the dynamic viscosity of air, and d p is

the particle diameter. In equation (3), CD is the drag coefficient, which is written as

CD={24( 1+0.15 ℜp0.687

ℜp )ℜp<1000

0.44 ℜp≥ 1000(4)

where ℜp is the particle Reynolds number

ℜp=ε g ρg|ug−vp ,i|d p

μg (5)

In equation (5) ρg is the air density.

The angular momentum of the particle is calculated by

I p ,i

d ω p ,i

dt=∑T p ,i (6)

where I p ,i is the moment of inertia of the particle, ω p ,i is the rotational velocity and T p ,i

is the total torque acting on the particle.

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2.2. Soft sphere model

In general, particle-particle and particle-wall collisions can be modeled using the hard

sphere or soft sphere model. In the hard sphere model, the interaction forces are

assumed to be impulsive and all other forces are negligible during collisions [41]. In the

soft sphere model, the deformation of particles in contact is modeled by relating the

local linear deformation in the normal and tangential directions to a force in these

directions, using Hertz-Mindlin theory [42]. The hard sphere model is easier to use but

applicable only to binary collisions. The soft sphere model directly implements the

physics of collisions but is computationally costly. In this study, since there are dense

regions where many particles can be in contact for a long time, the soft sphere model is

used.

In the soft sphere model, deformation of particles is replaced with overlap of two

particles and the energy loss during collisions is taken into account through a spring-

dashpot system. This system is characterized using the spring stiffness, k , the damping

coefficient, η, and the friction coefficient, μ. The former two quantities are calculated

using Hertz contact theory [42, 43], as explained below.

The normal and tangential contact forces acting on the particle, F cn,ij and F ct , ij, are given

by

F cn,ij=−kn δn3 /2 nij−ηnj (v ij ∙n ij) nij (7)

F ct , ij={−k t δ t−ηtj vct if |Fct ,ij|≤ μ|F cn,ij|−μ|Fcn ,ij|tij if |Fct , ij|>μ|F cn, ij| (8)

where δ n and δ t are the normal and tangential displacements of the particle, nij and t ij

are unit vectors normal and tangential to the contact plane, respectively, vij is the

relative velocity between the ith and jth particles, and vct is the slip velocity of the contact

point.

The normal and tangential stiffnesses, k n and k t, are expressed by

k n=43 ( 1−σ i

2

Ei+

1−σ j2

E j)−1

( ri+r j

r ir j)−1/2

(9)

k t=8 (1−σ i2

H i+

1−σ j2

H j)−1

( r i+r j

ri r j )−1 /2

δ n1/2

(10)

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where E is the Young’s modulus of the particle, H is the shear modulus, σ is the

Poisson’s ratio and r is the radius. The suffixes n and t denote the components in the

normal and tangential directions, while the suffixes i and j denote the ith particle and the

jth particle respectively.

According to Tsuji et al. [20], the damping coefficients ηn and ηt represent the visco-

elastic dissipation of kinetic energy in the normal and tangential directions, respectively.

These are given as

ηn=2 α √mp¿ kn δn

1 /4

(11)

ηt=2α √mp¿k t (12)

where α denotes a constant related to the coefficient of restitution [44], and m p¿

represents the effective particle mass and is calculated by

m p¿=

m p ,i m p , j

m p , i+mp , j.

(13)

More detailed description of the model can be found in literature [19, 20, 30, 41].

2.3. Equations of gas flow

A characteristic time scale of the flow may be calculated based on the atomizer flow rate

and the nozzle diameter.  The Reynolds number thus calculated is approximately 104

and single-phase flow of air may therefore be expected to be turbulent. However, since

the Stokes number of the particles is quite large, turbulence is not expected to have a

direct influence on the particle trajectories.  In addition, for dense gas-solid flows, such

as the one in this study, the particle stress is expected to be much greater than the stress

due to turbulence [45].  A turbulence model is therefore not used in the DEM-CFD

model. The continuity and momentum equations for gas flow are then written as

follows

∂∂ t ( ε g ρg )+∇ ∙ ( εg ρg ug )=0

(14)

∂∂ t ( ε g ρgug )+∇ ∙ ( εg ρgug ug )=−ε g∇P−∇ ∙ (ε g τg )+εg ρg g−∑

i=1

n

β (ug−v p ,i ) (15)

where τ g is the viscous stress tensor for incompressible flow,

τ g=μg (∇ug+(∇ug )T ) (16)

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3. Experimental

3.1. The Wurster bed configuration

The model of the fluid bed used in this study is based on the geometry of the Strea-1

fluid bed. The fluid bed is 380 mm high, with top and bottom diameters of 250 mm and

114 mm respectively. Detailed dimensions are given in the experimental paper [17].

The atomization air flow was supplied through a nozzle with a diameter of 5 mm located

3 mm above the bottom of the fluid bed. This nozzle was only a big circular inlet with

no opening for any liquid suspensions. Even in this case, the nozzle air velocity is high,

e.g. 50 m/s. This nozzle was used in the experiments in anticipation of future

computational work so as to avoid the numerical difficulties associated with simulating

sonic air flow while at the same time maintaining a high velocity jet.

The fluidization air flow passes through the bowl-shaped distributor, which consists of a

central base and an outer annular region. While the central base of the distributor is

fully open, the spray nozzle at the center implies that the region is also annular. The

outer annulus region of the distributor has a number of orifices with a diameter of 3

mm, as illustrated in Figure 2. A wire mesh screen was put over the distributor to

prevent particles from falling down below the distributor.

Figure 2 A sketch of the bowl-shaped distributor: 1) nozzle, 2) solid, 3) fully-opened central base, and 4) outer annulus

3.2. PEPT data

In this work, calculations using the DEM-CFD model are compared to recent PEPT

experimental data [17]; no additional experiments are performed. In the PEPT

measurement system, a radioisotope is incorporated into a tracer particle. As the tracer

particle moves around in the vessel the radioisotope decays in beta-decay and releases

back-to-back -rays. These γ γ-rays are detected via two large position sensitive

detectors. After a sufficient number of γ-rays are collected the location of the tracer

particle can be found through three dimensional triangulation. More details about the

technique and the algorithms used to determine the location have been reported by

Parker et al. [46-48].

3.3. Material

As a common material in the pharmaceutical industry, microcrystalline cellulose (MCC)

spheres were employed in the PEPT experiments, as well as a model particulate material 8

in the DEM-CFD simulations. The pellets that typically are used in practice have a

diameter that ranges from 200 µm to 1 mm. However, smaller or larger particles, such

as tablets, are also coated using the Wurster process. In order to limit the number of

particles, the particle size of 1749 and 2665 µm, which is still relevant and applicable to

product development, was selected. In the PEPT experiments, the particle size was

measured using a QICPIC Particle Size Analysis (Sympatec GmbH), and the sphericity

ranged from 0.85 to 0.95 (see [17] for a photograph of samples).

4. Numerical

4.1. Meshing

To solve the equations of particle motion and gas flow, a fully coupled multi-phase flow

solver, MultiFlow (www.multiflow.org) is employed. The model of the fluid bed is the

same as in the PEPT experiments. Figure 3 shows the global mesh and close-ups of the

surface mesh at the bowl-shaped distributor and nozzle. Approximately 65000

hexahedral cells are required based on a grid independence check via simulations of

single phase gas flow. The computational mesh near the distributor and inside the

Wurster tube is locally refined in order to properly capture the flow characteristics in

this region.

Figure 3 (a) The surface mesh of the fluid bed and (b) the close-up of the bowl-shaped distributor (from top view)

4.2. Boundary and initial conditions

In the recent PEPT experiments, the flow rates of the atomization and fluidization air

were measured separately using rotameters [17]. These measurements provide the

global flow rates, but they do not give any information about the flow distribution at the

distributor. In order to specify the flow distribution at the distributor, a single-phase

CFD model including the air supply chamber, the distributor, the wire mesh screen, and

the fluid bed was developed in Ansys Fluent. In this single-phase CFD model, the

distributor was modeled with all its orifices, but the wire mesh screen was included as a

region with a specified pressure loss (see e.g. [49]). The results obtained using this

single-phase CFD model (not shown) show that the air flow passing through the central

base of the distributor is in between 53% and 64% of the total fluidization air flow.

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In addition to this single phase CFD model, the particle velocity in the lower part of the

bed is also used as an indication of the flow distribution at the distributor. Since the

resolution of the PEPT measured particle trajectories towards the bottom of the bed is

low, it is necessary to employ measurements higher up. The resolution of the PEPT

measurements is estimated at several positions along the length of the Wurster tube and

a location at the middle of the Wurster tube, 90 mm above the bottom, is selected in

order to compare experimental data with calculated results.

The boundary condition employed in the DEM-CFD simulation reflects a flow

distribution where 55% of the fluidization flow enters normal to the boundary in the

central region and 45% enters normal to the boundary in the outer annulus region.

Figure 4, which shows the average vertical particle velocity as a function of the radial

coordinate, illustrates that the particle velocity calculated in the DEM-CFD simulation

agrees with that measured in the PEPT experiment [17].

Figure 4 The average vertical particle velocity along the radial direction for case #1 (VMD 1749 µm, batch size 200 g, fluidization air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).

As already discussed, the atomizer flow is imposed as a velocity inlet normal to the

boundary at the nozzle. The walls of the fluid bed and the Wurster tube are set to be no-

slip for the gas flow. The outlet of the domain is considered to be pressure outlet. At the

start-up of the simulations, 200 g (between approximately 15000 and 270000 particles

depending on the particle size) particles are put into the vessel at a certain height above

the distributor and are allowed to settle down without any gas flow. After 2 s, when

particles are at rest near the bottom of the equipment, the gas flow is turned on.

4.3. Cycle and residence time distributions

For simplicity we define the start of a particle coating cycle when a particle enters into

the spray zone from the horizontal transport region or the lower region in the Wurster

tube. The particle coating cycle then ends when the particle reappears in the spray zone

after having subsequently traveled through the Wurster tube, the fountain, downbed,

and horizontal transport regions. When one particle coating cycle ends, the next one

begins. The particle coating cycle time is thus defined to be the time it takes for a

particle to complete one cycle.

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In the recent PEPT experiments [17], the bulk of the particulate material that was used

in each process experiment contained only one single tracer particle. This tracer particle

was then followed via PEPT monitoring for 1.5 hours and the cycle and residence time

distributions were calculated from different cycles for the same tracer particle. In the

present DEM-CFD simulations, on the other hand, the calculation of the cycle and

residence times is based on data from many particles within a short period of time. For

the pseudo-steady particle dynamics in this fluid bed, as long as one particle is followed

the information obtained (such as the particle velocity or the cycle time distribution) is

assumed to be representative of the motion of all particles in a short period.

This study does not include any liquid spray. However, it is nevertheless of interest to

understand the particle motion near the spray nozzle. A spray zone is therefore defined

as shown in Figure 5, which gives a schematic of the shape of the spray zone, i.e. a solid

cone. This model is mainly conceptual and similar to the one in the work by Fries et al.

[26]. The height of the spray zone, L, is assumed to be 45 mm, which corresponds to the

height where the cone approaches the tube wall. The spray half-angle, , is assumed toθ

be 30 degrees. In order to study the shielding effect of different size particles, an

entrance distance into the spray zone is defined as the distance between the spray

nozzle and the location where the particle enters the spray zone (see Figure 5).

Figure 5 A schematic of the spray zone

4.4. Simulation time

In order to estimate the required simulation time the cumulative cycle time

distributions are plotted for different simulation times, as shown in Figure 6. It can be

seen that the CTD is not sensitive to the simulation time provided that it is at least 25 s,

and this simulation time is therefore chosen for purposes of studying particle cycles and

the CTD. Similar plots were also made for the RTD in the spray zone and in the Wurster

tube (not shown). It was found that 10 s is sufficient in order to obtain a reasonable

compromise between the computational cost and the quality of the data in order to

calculate the RTD in the spray zone and in the Wurster tube.

Figure 6 The cumulative cycle time distributions for different simulation times (with the first 2 s discarded), for case #1 (VMD 1749 µm, batch size 200 g, fluidization air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).

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4.5. Simulation parameters

The parameters used in the simulations are presented in Table 1 and the operating

conditions for each case are summarized in Table 2. For Run #1 the same conditions as

the base case in the experimental study are used, and the results are used for evaluating

the DEM-CFD model in detail. Runs #2 and 3 with larger batch sizes of 400 g and 600 g

are used to further evaluate the model as well as to verify the interpretations made in

the experiments. The effect of particle size is studied in Runs #4 and 5 by increasing or

decreasing the particle size by approximately 0.8 mm. Lastly, the effect of mixtures with

different components is studied in Runs #6-8 by replacing 25%, 50% or 75% (by mass)

of 1749 µm particles with 2665 µm particles. A typical simulation is run in parallel using

32 CPUs and takes 12 hours per second.

Table 1 The numerical parameters used in the simulations [50-52].

Table 2 The operating conditions for each DEM-CFD simulation.

5. Results and discussion

In this study the performance of the DEM-CFD model is evaluated by comparing the

calculated results with the results from previous PEPT experiments for the base case

and for different batch sizes. In addition, simulations for different particle sizes and

mixtures of different particle sizes are performed with emphasis on evaluating the effect

on the RTDs in the spray zone and in the Wurster tube.

5.1. Validation of the DEM-CFD model

5.1.1. The general particle movement for the base case

Figure 7 shows the particle velocity field determined in the DEM-CFD simulation and in

the PEPT experiment respectively. It is seen that the characteristic motion of the

particles in the Wurster fluid bed is predicted quite well using the DEM-CFD model. The

particles accelerate in the Wurster tube to reach a maximum velocity of approximately

3.0 m/s (this maximum value is difficult to observe in the figure due to an overlap of the

particle trajectories), and then fall down through the downbed region.

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Figure 7 The particle velocity field at a vertical cross-section through the center of the bed (a) simulated using DEM-CFD and (b) measured using PEPT (VMD 1749 µm, batch size 200 g, fluidization air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).

By following particle trajectories, the cycle time and the residence times in different

regions can be obtained. In Figure 8, the CTD of particles in the DEM-CFD simulation is

compared with the CTD determined in the PEPT experiment. Since the actual simulation

time is 25 s (with the first two seconds discarded), only particle cycles shorter than 25 s

are used for this comparison, both in the simulation and in the experiment. Since only

cycles that are shorter than 25 s are used for the comparison, the experimental values of

the cycle time and the RSD in the cycle time may be slightly different from those

presented in the previous experimental study [17] in which all cycles were included.

Figure 8 shows good agreement in terms of both the shape of the distribution and the

actual values. In the DEM-CFD simulation, the CTD has a larger percentage of short cycle

times compared to the CTD in the PEPT experiments. This difference may be attributed

to a greater weight factor of short cycles in the DEM-CFD simulation since the DEM-CFD

model follows many particles for a short time whereas the PEPT experiment follows a

single tracer particle for a long time.

Figure 9 shows the mean residence times of particles in different regions and the mean

fractions of the cycle time spent in different regions. The DEM-CFD simulation predicts

that particles spend the longest time in the horizontal transport region, and that the

residence time is considerably shorter in the Wurster tube and in the fountain and

downbed regions. This result corresponds closely to the corresponding values measured

in the PEPT experiment, especially in terms of the mean fractions of the cycle time spent

in different regions. That is, particles spend 19% of cycle time in the Wurster tube, 5%,

4% and 73% of cycle time in the fountain, downbed and horizontal transport regions in

both the DEM-CFD simulation and in the PEPT experiment.

Figure 8 The cycle time distribution (for cycles shorter than 25 s) calculated in the DEM-CFD simulation and measured in the PEPT experiment (VMD 1749 µm, batch size 200 g, fluidization air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).

Figure 9 (a) The mean residence times in different regions and (b) the mean fractions of the cycle time spent in different regions for case #1 (VMD 1749 µm, batch size 200 g, fluidization air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).

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5.1.2. Effect of batch size

In addition to the general particle movement for a batch size of 200 g, simulations of

different batch sizes of 400 g and 600 g are also performed. It is clearly shown in Figure

10, which shows the time-averaged solids fraction at a vertical cross-section through the

center of the bed for different batch sizes, that a higher fountain is obtained with an

increase in the batch size. As reported earlier [17], this increase in the fountain height is

due to a higher gas flow rate and, hence, a faster acceleration of particles in the Wurster

tube. In the PEPT experiments, this effect was attributed to an increased resistance in

the downbed region, which increased the air flow rate through the Wurster tube. Here it

is possible to verify this interpretation by noting that the dense region in the downbed

region increases when the batch size increases. As a result, the air flow rate passing

through the Wurster tube increases from 34.9 m3/h to 40.1 m3/h, and to 51.7 m3/h

when the batch size increases from 200 g to 400 g, and to 600 g respectively.

It is also of interest to examine the effect of the batch size on the cycle time. In addition,

the relative standard deviation (RSD) in the cycle time is calculated, since a variability in

the cycle time can affect the quality of the product. Figure 11 shows the effect of batch

size on the cycle time as well as on the RSD in the cycle time. There is good agreement

between the measured and calculated mean cycle time. The measured and calculated

values of the RSD do not agree so well, which could be due to the fact that spherical

particles are assumed and the VMD of particles is employed in the simulations rather

than the actual particle size distribution. But there is good agreement in the trend of a

decreased RSD when increasing the batch size, except for the very slight increase in the

RSD determined experimentally (from 63 to 66%) when the batch size increases from

200 to 400 g. This slight increase in the experimental RSD is different from the values of

the RSD calculated based on all cycles, i.e. 77 and 76% for 200 and 400 g respectively

[17]. Since only particle cycles shorter than 25 s are used for the comparison in Figure

11, the RSD in the cycle time is smaller than the RSD presented in the earlier study.

Apart from the simulated RSD values, good agreement between the DEM-CFD

simulations and the PEPT experiments is obtained for the cycle times, residence times

and the trend of RSD. In the next sections it is therefore of interest to focus on the

simulation results for different particle sizes and mixtures of different particle sizes.

Figure 10 The solids fraction at a vertical cross-section through the center of the bed for different batch sizes: a) 200 g, b) 400 g and c) 600 g (VMD 1749 µm, fluidization air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).

14

Figure 11 The mean cycle time and RSD for different batch sizes (VMD 1749 µm, fluidization air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).

5.2. Simulating with the DEM-CFD model

5.2.1. Effect of particle size

Figure 12 shows that there is a significant effect of the particle size on the residence

times in the spray zone and in the Wurster tube. When the particle size increases from

1000 µm to 2665 µm, there is an almost seven-fold increase in the residence times in the

spray zone, from 0.032 s to 0.214 s. For the same increase in the particle size, the

increase in the residence time in the Wurster tube increases by a factor of almost 4, from

0.36 s to 1.38 s. These results indicate that large particles reside longer in the spray zone

than small particles. If all particles of the same size in the spray zone receive the same

amount of coating per unit time, large particles will then obviously receive more coating

per unit area per pass than small particles. Fortunately, as large particles stay longer in

the Wurster tube, they will also have a greater chance of drying as they move upwards

through the Wurster tube.

Figure 13 shows the RTDs in the spray zone for different size particles. Figure 13 shows

that small particles have a narrow RTD in the spray zone while the RTD becomes much

wider for large particles. This difference can be attributed to different terminal

velocities for different size particles. For the same fluidization air flow rate, large

particles are more likely to recirculate in the Wurster tube [17] and return to the spray

zone than small particles. This effect can result in a wider distribution in the coating

thickness.

Figure 12 The simulated residence times in the spray zone and in the Wurster tube for different size particles.

Figure 13 The simulated residence time distributions in the spray zone for different size particles.

5.2.2. Effect of mixtures of different size particles

Figure 14 shows the mean residence times in the spray zone and in the Wurster tube for

small and large particles in mixtures with different fractions of small and large particles.

15

These 200 g mixtures of 1749 µm and 2665 µm particles contain 25%, 50% and 75%

2665 µm particles. It is seen that large particles stay longer both in the spray zone and in

the Wurster tube. A longer residence in the spray zone can lead to more coating being

deposited on the particle surface.

Moreover, as shown in Figure 15, the large particles enter the spray zone closer to the

spray nozzle than the small particles. This latter effect occurs because a greater gas

velocity is required to accelerate the large particles. The large particles therefore have to

move closer to the nozzle, where the gas velocity is higher, to be able to move upwards

through the Wurster tube. The smaller entrance distance into the spray zone for the

large particles can result in the large particles shielding the small particles from the

spray droplets. This effect [53], in addition to the effect of a longer residence time in the

spray zone, suggests that the large particles receive more coating solution per cycle than

the small particles. This was experimentally observed by Wesdyk et al. [54] for beads

with a size distribution in the no. 14-20 mesh range.

5.2.3. Effect on coating thickness

Based upon the simulation results above, the effect of the residence time in the spray

zone, the entrance distance into the spray zone, the cycle time and the particle diameter

on the coating thickness may be explored in terms of a simple model. In order to develop

such a model, it is noted that the total amount of coating per unit time deposited on the

surface of a particle, mfilm, can be expected to be proportional to the spray rate, m, the

time spent in the spray zone, t spray, and the number of coating cycles, N cycle. In addition,

the probability that a spray droplet is deposited onto a particle can be expected to be

proportional to the cross-sectional area of the particle and to the droplet flux, which

decreases quadratically with the distance from the spray nozzle for a solid-cone spray

zone. This simple model may thus be written

dmfilm

dt =K (rentrance ) m( t spray

t cycle )( π d p2/4

rentrance2 ) (17)

where t cycle 1/ N cycle is the cycle time, which is available in Li et al. [17], and K

represents other factors that may affect the amount of coating solution that the particle

receives such as the shielding effect. Since the shielding effect is predominantly entrance

distance dependent, K should be a function of the entrance distance, i.e. K 1/rentrance.

The rate of increase in the coating thickness can then be written

16

dlfilm

dt= 1

ρfilm π dp2

dmfilm

dt (18)

where ρ film is the density of the coating film.

Using equations (17) and (18), the relative rate of increase of the coating thickness

between the large and small particles for different mixtures can be explored in a post-

processing step, as illustrated in Figure 16. Figure 16 shows that the large particles only

have a slightly larger increase in the coating thickness than the small particles when the

fraction of large particles in the mixture is 25%. In this mixture the mean cycle times for

the small particles and the large particles are 4.95 s and 7.94 s respectively [17], which

indicates that the small particles pass through the spray zone 1.64 times more

frequently than the large particles. On the other hand, the large particles stay 1.48 times

longer in the spray zone and move 1.06 times closer to the spray nozzle than the small

particles. As a result, the increase in the residence time in the spray zone of the large

particles is almost compensated for by the decrease in the number of passes through the

spray zone. The end result in this particular case is that the large particles grow only

slightly faster than the small particles. As the fraction of large particles in the mixtures

increases from 25%, however, the difference in the cycle time between small and large

particles decreases while the difference in the residence time in the spray zone

increases. For these latter mixtures, the large particles therefore have a greater rate of

increase in the coating thickness than the small particles.

Figure 14 The simulated residence times of small and large particles in (a) the spray zone and in (b) the Wurster tube for different mixtures of small and large particles.

Figure 15 The simulated entrance distance into the spray zone of small and large particles for different mixtures of small and large particles.

Figure 16 The simulated relative rate of increase of the coating thickness between the large and small particles for different mixtures of small and large particles.

6. Conclusions

In this study, coupled DEM-CFD simulations have been performed to study particle

motion in a Wurster fluid bed. The particle trajectories were used to identify particle

cycles and to determine the CTDs and RTDs of particles in different regions.

17

The DEM-CFD model was validated by comparing the particle velocity field as well as

cycle and residence time distributions with results from recent PEPT experiments. The

general characteristic particle motion was successfully captured and the residence times

of particles in different regions were found to correspond closely to the experimental

results. A shorter cycle time with a larger batch size was also predicted by the DEM-CFD

simulations, in agreement with the PEPT monitored experiments.

The effect of particle size and mixtures of different size particles were studied in the

DEM-CFD simulations. The results show that large particles spend a longer time in both

the spray zone and the Wurster tube, suggesting that large particles get greater amount

of coating solution per cycle compared to small particles. This difference is however,

partly compensated for by the fact that large particles pass through the spray zone less

frequently than small particles due to their longer cycle times.

The DEM-CFD simulations also show that the large particles on average enter the spray

zone closer to the spray nozzle than the small particles. This indicates that the large

particles can shield the small particles from the spray droplets, and that the large

particles therefore receive a greater amount of coating solution per pass than what

would be anticipated based on their larger size, and the longer time spent in the spray

zone.

A simple conceptual model was developed to predict the effect of the residence time in

the spray zone, the cycle time, and the entrance distance on the relative rate of increase

of the film thickness between large and small particles. This model showed that as the

fraction of the large particles in the mixture increases, they have a greater rate of

increase in the coating thickness than the small particles. Due to its simplicity, however,

this model should be further developed in the future.

Acknowledgements

This work is undertaken within the EU seventh framework program, the PowTech Marie

Curie Initial Training Network (Project no. EU FP7-PEOPLE-2010-ITN-264722). The

experiments were financially supported by AstraZeneca R&D.

18

Dr. Andy Ingram at University of Birmingham is gratefully acknowledged for the

cooperation in the experimental work. The authors would also thank the high

performance computing (HPC) team at AstraZeneca R&D for their support throughout

the simulations.

Notation

CD drag coefficient

d p particle diameter, m

E Young’s modulus, Pa

F c contact force, N

g gravity vector, m/s2

H shear modulus, Pa

m p mass of the particle, kg

n normal unit vector

t tangential unit vector

I p moment of inertia, kg∙m2

P pressure, N/m2

ℜp particle Reynolds number

t time, s

u velocity vector of gas phase, m/s

vp velocity vector of the particle, m/s

V p volume of the particle, m3

ω p rotational velocity of the particle, rad/s

19

Greek symbols

ε g gas volume fraction

ε s particle volume fraction

β interphase momentum transfer coefficient, kg/(m3∙s)

μg dynamic viscosity, Pa∙s

μ friction coefficient of particles

ρ density, kg/m3

η damping coefficient

σ Poisson ratio

τ viscous stress tensor, N/m2

Subscripts

g the gas phase

p the particle

i , j the ith or jth particle

n the normal direction

t the tangential direction

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