Chemical Engineering Science

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Local analysis of the tablet coating process: Impact of operation conditions

on ﬁlm quality

Daniele Suzzi

a

, Stefan Radl

a,b

, Johannes G. Khinast

a,b,n a

Research Center Pharmaceutical Engineering GmbH, Graz, Austria

b_{Institute for Process and Particle Engineering, Graz University of Technology, Inffeldgasse 21a, Graz, Austria}

a r t i c l e

i n f o

Article history: Received 3 August 2009 Received in revised form 15 July 2010

Accepted 16 July 2010 Available online 6 August 2010 Keywords: Multiphase ﬂow Simulation Mass transfer Pharmaceuticals Tablet coating Spray

a b s t r a c t

Spray coating is frequently used in the pharmaceutical industry to control the release of the active pharmaceutical ingredient of a tablet or to mask its taste. The uniformity of the coating is of significant importance, as the coating usually has critical functional properties. However, coating uniformity is difficult to predict without significant experimental work, and even advanced particle simulations need to be augmented by CFD models to fully describe the coating uniformity on a single tablet.

In this study we analyze the coating process by using detailed computational fluid dynamics (CFD) multiphase spray simulations. The impact and the deposition of droplets on tablets with different shape, as well as the production and evolution of the liquid film on the surface of the tablets are numerically modeled. Spray droplets are simulated with a Discrete Droplets Method (DDM) Euler– Lagrange approach. Models for multi-component evaporation and particle/wall interaction are taken into account. The wall film is treated with a two-dimensional model incorporating submodels for interfacial shear force, film evaporation and heat transfer between film, solid wall and gas phase. Our simulations show how different physical parameters of the coating spray affect the coating process on a single tablet. For example, we analyze for the first time the deposition behavior of the droplets on the tablet. The outcome of our work provides a deeper understanding of the local interaction between the spray and the tablet bed, allowing a step forward in the design, scale-up, optimization and operation of industrial coating devices. Furthermore, it may serve as a basis for the combination with state-of-the-art DEM pstate-of-the-article simulation tools.

1. Introduction

Coating is an important step in the production of many solid oral dosage forms, such as tablets and granules. The goal of film coating is the application of a thin polymer-based film on top of a tablet or a granule containing the active pharmaceutical ingredients (APIs). In the last years, more than half of all the pharmaceutical tablets were coated (IMS Midas Database, 2007). Functional coatings are usually adopted for taste masking or to alter the tablet’s dissolution behavior, for example by controlling the rate of dissolution via semi-permeable membranes or by making it resistant to gastric juice through enteric coatings. Furthermore, active ingredients may be incorporated in the film layer. Colored non-functional coatings are commonly used to improve visual attractiveness, handling and brand recognition. A well-known example is the ‘‘blue pill’’ VIAGRAs

by Pﬁzer Inc. Depending on the tablet’s dimension and coating functionality,

the ﬁlm thickness varies between 5 and 100

m

m. A detailed description of the coating process and the different coater devices is presented in the book ofCole et al. (1995).

Historically, this process was developed by the confectionery industry to sugar-coat different types of candies. The pharmaceutical industry implemented this technique using open bowl-shaped pan. Nowadays, sugar-coated tablets are rarely developed due to the intricacy of the process and the high degree of operator skill required. Instead, tablets are typically coated with a polymer ﬁlm of various compositions using modern equipment, such as drum and pan coaters.

The first commercially available pharmaceutical film-coated tablet was introduced to the market in 1954 by Abbott Laboratories. Tablets were produced in a fluidized bed coating column based on the Wurster principle (Wurster, 1953), which was further developed by Merck in their US and UK plants. This new technique could be realized due to the development of new coating materials based on cellulose derivatives, e.g., hydroxy-propyl methylcellulose. Nevertheless, in the following decades coating columns were substituted by side-vented pans and the use of aqueous film solutions, which reduce the use of organic solvents and the related costs of the recovery systems.

Contents lists available atScienceDirect

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Chemical Engineering Science

n

Corresponding author at: Research Center Pharmaceutical Engineering GmbH, Graz, Austria. Tel.: + 43 316 873 7978; fax: + 43 316 873 7963.

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Nowadays, tablet coating is typically carried out in pan coaters or ﬂuidized bed systems. Modern production-scale pan coaters have batch sizes ranging from 500 g to 2000 kg, have a fully perforated cylindrical drum and use two-material nozzles for an effective spray generation. Today’s ﬂuidized bed coaters allow continuous coating or have special internals to allow for coating processes involving coating solutions with high solid content (Porter, 2006). In this study we focus on pan coaters.

Although coating processes have been used for many decades, there are still serious challenges, as there is a lack of under-standing of how material and operating parameters impact product quality and cause problems, such as chipping (i.e., films become chipped due to attrition), blistering (i.e., local formation of blisters due to entrapment of gas), cratering (i.e., penetration of the coating solution into the bulk of the tablet causing crater-like structures), pitting (i.e., pits occur on the surface due to overheating of the tablet and partial melting), picking (i.e., parts of the film are removed due to sticking to other wet tablets), blushing (i.e., formation of spots due to phase-transitions of the polymer film), blooming (i.e., plasticizer concentrates at the surface, leading to a change of appearance), film cracking (i.e., cracking of the film upon cooling due to high stresses) and many others. Quite often, poor scale-up of the process and/or insuffi-cient process understanding is the cause of such production problems and batch failuresPandey et al. (2006a). Although the reasons for these manufacturing problems are more or less understood, it is still a challenge to predict the occurrence of such effects for new systems.

Therefore, in our work we focus on a basic understanding of the film formation process on single tablets, with the goal of being able to predict the impact of material and operation parameters on the film quality. The current study is a first step in this direction. We investigate the spray fluid dynamics and the film formation of a glycerin–water mixture on two different tablet shapes, i.e., a sphere and a biconvex tablet, held in one position. Our analysis is based on a rigorous computational model that uses well established physical submodels for momentum, heat and mass transfer. Thus, we are able to predict the transient development of the mean film thickness of a wetting coating solution on arbitrarily shaped surfaces. Our main objective is to provide, for the first time, a science-based and quantitative understanding of which physicochemical parameters influence the uniformity of the coating layer on a single tablet. This knowledge is the key for the design, optimization and the rational scale-up of such processes and can form the basis for further studies on rotating tablets or whole tablet beds.

2. Background

2.1. Spray system

A modern coating system is conceptually shown in Fig. 1, where the coating suspension is sprayed on top of a moving bed of the solid dosage form. The spray guns are usually mounted on an arm inside the pan and are directed towards the tablet bed. As the bed is moving, a tablet spends a fraction of a second in the spraying zone. The wet surface of the tablet needs to be dried to avoid sticking of the tablet to neighboring tablets, leading to manufacturing problems such as picking. However, too fast drying is counter-productive as well, as other problems may occur, such as the formation of a heterogeneous ﬁlm. The drying air is directed towards the surface of the tablet bed in order to achieve good heat and mass transfer (i.e., for immediate drying of the sprayed solution). The exhaust air can exit the pan through side opening, from inside the tablet bed (through an immersion

tube system) or through a perforated rotary pan. The latter design allows the drying air to flow through the tablet bed in co-flow with the injected spray, leading to a more efficient coating process. Several companies offer this type of equipment, such as Glatt, Bohle, Driam, Manesty or Nicomac, each system being significantly different to the other systems.

As shown inFig. 2, the coating process can be divided into three phases, i.e., spraying, wetting and drying. In an ideal process, each tablet or granule passes through the spray zone for a predefined number of times, where spray particles impact the surface and wet the tablet. The adhering film is dried before the next amount of solution is applied. This process continues until the particle is fully coated. The final film structure is typically non-homogeneous due to the presence of insoluble ingredients, such as pigments, and to the discontinuous and statistical nature of the coating process. A typical scanning electron microscope (SEM) image of a film-tablet coating illustrating the inhomogeneity of the coated layer is also shown inFig. 2.

Depending on the desired functionality of the tablet film, different coating solutions are used in industrial practice. The injected spray commonly consists of a carrier solution or vehicle (e.g., water, alcohols, ketones, esters or chlorinated hydrocar-bons), polymers (e.g., cellulose ethers, acrylic polymers or copolymers), plasticizer (polyols as glycerol, organic esters or oils/glycerides) and insoluble solid components (e.g., talcum, pigments and opacifiers). The used vehicle has to be compatible with the chosen polymer, as this is essential for obtaining optimal film properties such as mechanical strength and adhesion. As pointed out byHogan (1982), the originally used organic vehicles have been steadily replaced by, mainly due to environmental and safety concerns. Several authors (e.g.,Bindschaedler et al., 1983)

Fig. 1.Schematic of a modern pan coater (side-vented) and domain for the spray analysis.

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analyzed the complex process of film formation from a water-polymer dispersion. Initially, the water-polymer is dispersed in the aqueous solution in the form of discrete particles. The dispersed particles have to come into contact, coalescence and finally form a continuous film.

An important factor in the film coating process is the quality of the spray, as the droplets interaction with the tablet surface strongly affects the drying behavior and the uniformity of the final polymer layer. Two types of spraying devices are commonly used in the film-coating technology: the hydraulic (airless) atomizer and the pneumatic (air-blast) atomizer. The first device requires high load pressures in order to produce adequate atomization of the viscous solutions. However, the absence of air to produce the spray reduces early droplet evaporation. In case of aqueous vehicles this can lead to product overwetting and to poor-quality coatings. For this reason pneumatic atomizers are mostly used for water-based coating solutions (Muller and Kleinebudde, 2006). The liquid jet instability and the atomization processes in these atomizers have been discussed by several researchers, e.g.,Varga and Lasheras (2003), as well as Mansour and Chigier (1995). A combined experimental and theoretical analysis of the atomiza-tion of highly viscous non-Newtonian liquids can be found in the work ofAliseda et al. (2008). In this study the breakup process is modeled through a two-stage instability mechanism, namely the primary Kelvin–Helmoltz instability followed by the secondary Rayleigh–Taylor instability. This study starts from the work of

Joseph et al. (2002), as well as ofYecko and Zaleski (2005). The main result ofAliseda et al. (2008)is a correlation between the Sauter mean diameter (SMD) of the disintegrating droplets and the atomizer geometry, as well as the ﬂuid-dynamical properties of the injected liquid (they used a solution of water and glycerol). In the absence of direct measurements of the real spray, e.g., through Laser Diffraction (LD) or Phase Doppler Anemometry (PDA) systems (Hirleman, 1996), these models may be helpful for the initialization of the ‘‘numerical spray’’. This approach is, for example, also adopted in our work, i.e., our simulations are based on a single mean diameter of the droplets that make up the spray. The liquids being atomized are often highly viscous and sometimes non-Newtonian ﬂuids, exhibiting complex physical mechanisms for primary and secondary breakup. In addition, droplet formation is also strongly affected by other physical properties of the coating solution, e.g., density and surface tension, as well as by the spray gun type. For example,Aulton et al. (1986)investigated the effects of different atomizers, such as Binks-Bullows, Walther Pilot, Schlick and Spraying Systems guns, showing strong effects of the atomizing air pressure on the resulting mean droplet diameter. Typical mass-averaged droplet sizes range between 20 and 100

m

m. The atomization properties, such as droplet size and velocity distribution, can be experimen-tally obtained via captive methods (these are methods in which droplets impinge on a ﬂat surface and the diameter of the droplets on the surface is measured using a microscope), photographic techniques or laser-light scattering methods (Lefebvre, 1989). Clearly, the characterization of the coating spray represents an important step in the design of a coating device, as it strongly affects the local behavior of the ﬁlm formation on the tablet surface.

The evaporation of individual species from the liquid phase making up the droplets has to be considered as well. It is clear that the composition of the droplets affects the mass transfer from the spray droplets and the tablet ﬁlm to the surrounding gas. For example,Chen and Thompson (1970) investigated the effect of sodium chloride on the vapor–liquid equilibrium of glycerol– water solutions.Gaube et al. (1993)studied aqueous solutions of PEG (often used in coating formulations) and dextran. A similar system was also studied byHammer et al. (1994), using sodium

sulfate instead of dextran.Eliassi et al. (1999)focused instead on the activity of water in aqueous PEG solutions with different molecular weights. Recent experimental work on PEG solutions has been extended byKazemi et al. (2007). The activity of water in aqueous sugar solutions has been analyzed in two studies ofPeres and Macedo (1996, 1997).

Finally, the interaction between droplets and surfaces represents a key issue in the description of coating processes. Experimental analyses and dimensional modeling of drop splash-ing processes can be found already at the beginnsplash-ing of the 20th century in the work ofWorthington (1908). The recent review of

Yarin (2006) comprehensively explains the processes leading to ﬁlm formation on thin liquid layers and dry surfaces, i.e., crown formation or splashing, drop spreading and deposition, receding (recoil), jetting, ﬁngering and rebound.

2.2. Tablet ﬂow in coaters

Experimental and numerical studies of the tablet ﬂow in pan coaters are gaining increasing interest in the scientiﬁc commu-nity.Sandadi et al. (2004)characterized the movement of tablets at the top of a granular bed in a rotating pan via a digital imaging system to measure the velocity distribution on the surface of the tumbling tablet bed.Tobiska and Kleinebudde (2001)investigated the mixing behavior in a new coater type (the Bohle BLC pan coater). They showed that the mixing behavior can be character-ized by a simple temperature measurement, i.e., the temperature difference between the spray and the drying zone. In another study the same authors characterized the coating uniformity in a Bohle lab-coater using standard procedures (mass variance, dissolution testing) (Tobiska and Kleinebudde, 2003).

Pandey et al. (2006b) tracked a single tracer tablet (white colored) in a bed of black tablets using a CCD camera. They recorded the centroid location, as well as the exposed area of the tracer tablet in the zone of interest, i.e., the spray zone. The camera was directly placed in the coater and oriented in the same direction as the spray. They analyzed the average surface velocity profile along the upper layer of the tablet bed. In addition,Pandey et al. (2006a)performed discrete element method (DEM) simula-tions confirming the shape of the velocity profiles along the top cascading layer of the tablet bed. The range of the velocities reported varied between 0.13 and 0.55 m/s.Pandey et al. (2006a)

proposed a characteristic velocityVfor the purpose of scaling the velocity proﬁle at the top of the granular bed:

V¼kRN2=3 g d

1=6 v1:8

ð1Þ

Herekis a constant,Ris the pan radius,Nis the pan rotation rate,gis the gravitational acceleration anddis the tablet size. The term

n

represents the fractional fill volume, defined as the ratio between the volume occupied by the bed and the total pan volume. The relation was verified using experimental data between

n

¼0.10 and 0.17 and rotational speeds between

o

¼6 and 12 rpm.Alexander et al. (2002)used a similar approach and scaled the maximum velocity at the top of the granular bed to obtain a dimensionless maximal velocityVS

max. For low rotational speeds (o30 rpm), they found that the value ofVS

max is between 2.5 and 3.8. All these scaling laws are useful for the estimation of the peak velocity in coaters and consequently for the time individual tablets stay in the spray zone.

Kalbag et al. (2008)used a single tracer sphere and a digital camera to measure the time that the marked tablet remains in the spray zone, also called spray residence time tR. They manually post-processed the videos (50 min runtime at 60 fps) to obtain consistent experimental results for the spray residence time. The authors deﬁned the dimensionless appearance frequency

a

i of

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tabletias the number of appearances of a tablet in the spray zone during one pan revolution. The dimensionless appearance frequency averaged over all tablets

a

can be expressed as

a

¼ 2

p

o

n

N ð2Þ

Here

D

tRis the average residence time per pass in the spray zone averaged over all tablets. The averaged dimensionless appearance frequencies were between

a

¼0:1 and

a

¼1:4. However, this value depends strongly on the coating fraction, i.e., the ratio of the average number of tablets exposed to the spray and the total number of tablets in the coater. Therefore, they proposed an average residence time of the tablets per pass, i.e.

D

tR¼L=V. HereLis the length of the spray zone andVis the

average velocity of tablets passing through the spray zone. The velocity at the top of the tablet bed is essential for the residence time in the spray zone, and hence, is expected to impact the ﬁlm quality on the tablet. The average residence time of the tablets per pass was found to be between 0.07 and 0.27 s, depending on the pan speed. The standard deviation of the average residence time per pass was in the order of 0.03–0.24 s and was strongly dependent on the chosen pan speed. These experimental results were reproduced by discrete element method (DEM) simulations. Clearly, the standard deviation is an important quality indicator for the coating uniformity as tablets with a short residence time in the spray region will have a thin or imperfect coating. Also, in their work Kalbag et al. introduced other metrics that characterize the mixing behavior in the bed, i.e., the circulation and the fractional residence times. The circulation timetC,iand the average circulation time per pass

D

tCcharacterize the total time the tablet spends away from the spray zone, and the average time interval between successive appearances of the tablet in the spray zone, respectively. Note that the sum of the tRandtCiis the total coating time. The fractional residence timefR is deﬁned as the ratio of time spent by a tablet in the spray zone to the total coating timet0. The average fractional residence time is

fR¼

tR

t0 ¼ n

N ð3Þ

wheretRis the average time the tablets spend in the spray zone,

nis the average number of tablets in the spray zone andNthe total amount of tablets inside the pan coater. The ration=Nis also referred to as the ‘‘coating fraction’’ and can be increased by increasing the size of the spray zone or by decreasing the number of tablets in the coater.

Theoretical models for predicting the surface renewal rates of the tablet bed in a rotary coating drum were reported byDenis et al. (2003). They found an excellent agreement between the prediction of their model and experimental results for spherical tablets and biﬂuid pneumatic nozzles.

Different groups are currently working on the numerical prediction of tablet flow in coaters (e.g., Dubey et al., 2008; Pandey et al., 2006a; Yamane et al. 1995). The coating event in the spray zone has up to now been described only with discrete element methods (DEM) and statistical deposition models for the tablets crossing the droplets region. One of the first attempts to couple a DEM solver with the computational fluid dynamics (CFD) gas flow in a rotating drum was proposed by Nakamura et al. (2006). However, they simply assumed that a tablet was coated if it was located within the spray region. This approach neglected resolving the droplets motion inside the drum and the local interaction of impacting drops on the tablet surface. Few additional studies have been reported on the CFD simulation of coating processes. The recently presented work ofMuliadi and Sojka (2009)analyzed the interaction between coating spray and air flow inside a pan coater. However, the authors did neither

consider the deposition of droplets on the tablets, nor the film formation processes. The recent paper byFreireich and Wassgren (2010) examined both analytically and computationally the influence of a tablet’s orientation on the coating uniformity, leading to a deeper understanding of the intra-tablet film variability.

3. Objectives

Currently, the optimization of industrial coaters is mostly done by means of experimental and empirical analysis. State-of-the-art computational approaches include the use of Discrete Elements Method (DEM) , which already represents a consolidated practice in particle technology. However, current studies lack a detailed description of the ﬁlm formation process on individual tablets or granules as only statistical tools for the ﬁlm deposition on the tablet surface are used. Such an approach cannot capture the local behavior of the complex particle–gas–liquid system. Clearly, the liquid deposition behavior is strongly affected by the interactions of the spray and the solid surface of the tablet to be coated. Hence, the presented work will focus on the understanding of the basic principles of the spraying and deposition processes on a single tablet or granule as shown schematically inFig. 2.

In summary, the major objectives of this work are

to model the spray, deposition on the tablet, the coating process, as well as the evaporation of the spray and the wall ﬁlm in order to estimate the effects of the drying gas ﬂow,

to numerically analyze the impact and deposition of droplets on particles with different shape,

to study the production and evolution of the liquid ﬁlm on the surface of the tablets and

to investigate how different process parameters affect the coating process on a single tablet.

For this purpose, a variation matrix was set up and the effect of each variation is analyzed in detail with respect to the ﬁlm quality. Also, the shape of the coated particle is varied, i.e., by considering a sphere and a standard tablet.

4. Model and numerical solution

In this section we present the 3D model used for the numerical analysis of the spray and the wall film. We adopted the 3D-CFD code AVL FIRE v2008 to simulate the dynamics of the coating spray and the film evolution on the tablet. We treat the coating process as a gas–liquid multiphase flow with deposition of a liquid film on the surface. For the description of the gas flow around the object to be coated we used the Reynolds averaged Navier–Stokes (RANS) equations including an appropriate turbu-lence model (k–

e

). As these models are well-known they are not described here. The main difﬁculty of our work is to accurately model the motion of individual droplets, i.e., the spray around the object, as well as the droplet deposition and the motion of the liquid already deposited on the tablet surface.

4.1. Spray simulation

In our work the simulation of sprays is performed via the Lagrangian DDM (Discrete Droplet Method) approach. This approach is also known as Lagrangian Monte Carlo method, which was ﬁrst proposed byDukowicz (1980). The basic concept is to track the paths of statistical parcels of real droplets in physical, velocity, radius and temperature space. Further

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submodels for drag, particle/wall interaction, evaporation, turbu-lent dispersion and breakup may be included in the simulation approach. In the DDM method each physical phenomenon occurring in a parcel, e.g., atomization or coalescence/collision, directly involves all the droplets making up the parcel. This allows a drastic reduction in the computational effort to simulate liquid sprays, which in reality consist of many millions of single drops. In our simulations, the effects of secondary atomization, collision and coalescence have been neglected. We are aware that close to the nozzle outlet this assumption is not valid due to the high droplet number density and velocity. For example

Edelbauer et al. (2006)and Suzzi et al. (2007)showed that the high liquid volume fraction close to the nozzle compromises the basic assumptions of the Lagrangian particle method. In this study we circumvent these difﬁculties by initializing the spray just outside the primary breakup region, a few centimeters down-stream the nozzle outlet. We then can neglect secondary breakup effects, as the Weber number of the droplets is, in our application, far away from critical values.

Mass, momentum and energy conservation equations are solved for each parceliof the spray. A parcel represents a certain number of individual droplets, depending on their radius and the spray rate. The continuity equation for each parcel can be written as

dmid

dt ¼ m_iE ð4Þ

where the term on the right hand side represents the mass source due to evaporation. In the Lagrangian DDM the momentum equation, i.e., Newton’s second law, is directly integrated over time for each spray parcel:

mid d u!id dt ¼F ! iDþF ! iGþF ! iPþF ! iEX ð5Þ

The terms on the right hand side of Eq. (6) represent the drag forceFiD, the gravity and buoyancy forceFiG, the pressure forceFiP, and the external forceFiEX. The drag force acting on the droplets is calculated as F ! iD¼ 1 2

r

gAdCD9!urel9!urel ð6Þ

where

r

g is the gas density, Ad the cross-sectional area of the droplet and!urelthe relative velocity between the gas phase and

the parcel. The termCdrepresents the drag coefﬁcient for a single sphere and is modeled in our work according to the formulation of

Schiller and Naumann (1993):

CD¼ 24 Red ð1þ0:15Red0:687Þ, Redo103 0:44, RedZ103 8 > < > : ð7Þ

Here the particle Reynolds numberRedis deﬁned as

Red¼

r

g9u ! rel9Dd

m

g ð8Þ

In order to calculate the temperatureTidof the droplets, it is necessary to calculate the heat and mass transfer rate to account for both the convective and latent heat loss of the droplets. The energy conservation equation for each parcel of droplets under the assumption of a uniform droplet temperature is (AVL, 2008): midcp,d

dTid

dt ¼ LðTidÞm_iEþQ_ ð9Þ

Here,cp,dis the mean speciﬁc heat capacity of the droplets (i.e., an

average over all components in the droplet),L(Tid) is the latent heat of evaporation (assumed to be a function of the droplet temperature) and Q_ is the heat transfer rate between the surrounding gas and the droplets. As the spray consists of a

mixture of components, i.e., glycerol and water, the calculation of the mass transfer rate (i.e., the evaporation process) represents a key challenge in the simulation model. The multi-component evaporation model used in this work is based on theAbramzon and Sirignano (1988)approach with the extension byBrenn et al. (2003). The main difference to the single-component case is that mass transfer of every component is taken into account separately, while heat transfer is still globally described. Hence, the evaporation rates of each speciesjare calculated and summed up to yield the total mass loss due to evaporation:

_ miE¼ X j _ miE,j ð10Þ

In the multi-component evaporation model used in this work, the mass transferred for each component jto the gas phase is given by

_

miE,j¼

pr

g

b

gjDdShjlnð1þBM,jÞ ð11Þ

The overbars in the gas density

r

g and the binary diffusion

coefﬁcient

b

gj of species jin the gas phase indicate that these

values are evaluated at a reference temperature and composition (for more details refer toAVL, 2008).Ddis the droplet diameter, Sh

j is the corrected Sherwood number of speciesj(deﬁned below)

andBMjis the Spalding mass transfer number deﬁned as BM,j¼

wj,swj,1 1wj,s

ð12Þ

Here, wj,s is the gas phase mass fraction of species jat the surface of the drop (to be calculated from the vapor pressure of species j at the droplet temperature) and wj,N is the bulk gas phase mass fraction. The total mass transfer rate can be also derived from the energy balance (Eq. (9)) at the surface of the drop, as _ miE¼

p

kg cp,d DdNulnð1þBTÞ ð13Þ

Here,kg is the heat conductivity at a reference temperature and

composition, and Nun

is the corrected Nusselt number deﬁned below. In order to account for the relative motion between spray particles and gas phase, a Nusselt and Sherwood number is ﬁrst computed according to the empirical relations of Ranz and Marshall (1952):

Nu0¼2þ0:552Re1=2_Pr1=3

ð14Þ

Sh0,j¼2þ0:552Re1=2Scj1=3 ð15Þ

The corrected Nusselt and Sherwood numbersNun andSh

j are

then calculated taking into account the deviation of the streamlines due to the evaporating mass ﬂow:

Nu ¼2þðNu02Þ FT , Sh j¼2þ ðSh0,j2Þ FM,j ð16Þ

The temperature and mass correction functionsFTandFM,jare calculated as

FðBÞ ¼ ð1þBÞ0:7lnð1þBÞ

B ð17Þ

usingBTorBM,jforFTandFM,j, respectively. In the relation for the temperature correction function FT, BT is the Spalding heat transfer number deﬁned as

BT¼ ð1þBMÞf1 ð18Þ

f

¼cp,d cp,g Sh Nu 1 Le ð19Þ

Here,cp,g is the gas phase speciﬁc heat capacity at reference

conditions andLeis the Lewis number. Finally, the heat transfer rateQ_ between the droplet and the gas phase for the whole parcel

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is deﬁned as _ Q¼m_iE cp,dðT1TidÞ BT LðTidÞ ð20Þ

Mixture fractions and mixture properties for each componentj at the drop surface needed in Eq. (12) are calculated using the activity coefﬁcients

g

j:

xj,s¼xj,L

g

j

pv,j

p ð21Þ

Here,xj,sandxj,L are the mole fraction of speciesjin the gas

and liquid phase, respectively. Note, that the mole fractionxj,sis

directly related to the mass fraction wj,s that is used in the

calculation for the mass transfer rate.pv,jis the vapor pressure of pure speciesjandpis the total pressure. Instead of using Raoults’ law, i.e., assuming

g

ito be equal to 1, the activity coefﬁcients used in our work have been calculated using a group contribution method (UNIFAC method,Peres and Macedo, 1997). This is in line with the work ofAttarakih et al. (2001), which described water– glycerol mixtures using the UNIFAC method and used the Antoine equation to describe the temperature-dependency of the vapor pressure.

In summary, the calculation of the mass transfer ratem_iE,jfor

each species and the heat transfer rate is performed using the following procedure:

calculate the mass fractionwj,sof each speciesjat the surface

of the droplet (Eq. (21)),

calculate all physical properties at the reference conditions,

calculateNu0andSh0,

calculateBM,j, FM,j,Shj and the mass rate of change for each

species from Eqs. (12), (16) and (17), as well as the total mass transfer rate from Eq. (10),

evaluate the Spalding heat transfer numberBT(Eq. (18)), the corrected Nusselt number Nun

(Eq. (16)) as well as the total mass transfer rate from the energy balance (Eq. (13)),

compare the total mass transfer rates from Eqs. (9) and (13) and correct the heat transfer numberBTuntil both total mass transfer rates are equal,

evaluate the heat transfer rate from Eq. (20).

The presented simulations are performed with a two-way coupling between the continuous and the discrete phases, i.e., all source terms for mass, momentum and energy can be also found in the transport equations for the gas phase.

4.2. Droplet impact

The numerical model describing the interaction between impacting droplets and the wall (i.e., the tablet surface) is based on the work ofMundo et al. (1995). Splashing or deposition occur depending on the dimensionless droplet Reynolds and Ohnesorge numbers, deﬁned as Re¼

r

Lvd?Dd

m

L , Oh¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

m

L

r

L

s

LDd p ð22Þ

The (empirical) critical curve delimiting the splashing and deposition regimes is shown inFig. 3and can be expressed as

Ohcrit¼57:7Re1:25 ð23Þ

The ratios of the incoming and outgoing tangential and the normal velocities are also included in the spray-wall interaction model, leading to empirically determined ratios of 1.068 and 0.208 for smooth walls, respectively. This critical curve is valid for the impact of single droplets, i.e., we neglect droplet–droplet interactions during the impact. Since the mass loading of droplets is relatively low, this assumption is expected to be valid.

Furthermore, we do not take into account the exact shape of the liquid ﬁlm and assume a planar ﬁlm surface on the tablet. This assumption is supported by the fact that (i) the characteristic time of drop spreadingts is of the order of (Rrim/Dd)10

_m

_LDd/

_s

L (Rrim) being the characteristic rim radius, Yarin, 2006), and hence, is very small for the small droplets considered in our work and (ii) the tablet will be quickly covered by a ﬁlm with a thickness in the order of a few droplet diameters (seeFig. 10).

According to the local properties of the impacting droplets either the liquid mass is transferred to the wall ﬁlm (deposition) or new particles are generated (splashing regime), which rebound away from the tablet surface. Speciﬁcally, the secondary droplets could then

evaporate and not deposit (i.e., spray drying effect),

deposit on the coater wall,

exit the coater with the exhaust air, or

deposit on another tablet.

In our study we neglect the last option. The ﬂow path of these droplets can only be analyzed using a detailed simulation of the air ﬂow inside a coater. This will be part of a future study.

As we have a binary mixture of glycerol and water, the physical properties of the droplets (i.e., density, surface tension and viscosity) are a function of the local composition and temperature. In our work we have taken this information from tabulated values from a manufacturer’s speciﬁcation (The Dow Chemical Company, 2009) using linear interpolation.

4.3. Wall ﬁlm model

The deposition, flow and drying of the coating solution on a tablet is critical for the quality of the tablet coating. In order to predict the distribution of the coating solution on the tablet, it is necessary to model the flow of the deposited fluid film. Some general theoretical models to describe film formation and its flow on objects are available in literature (e.g.,Yih, 1986; Baumann and Thiele, 1990). However, they are still not used in the pharmaceu-tical coating technology. In our work, we tried to adopt some of these models for the prediction of film formation on tablets using the modeling assumptions described in the next chapter. 4.3.1. Model assumptions

Due to the high viscosity of the coating solution compared to the surrounding air, the fluid film is only slowly flowing over the tablet. In addition, evaporation of volatiles from the film, as well as heat transfer from and to the surrounding gas are major factors impacting that distribution of the film. In order to obtain a detailed but computationally still tractable prediction of the film

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behavior, we make the assumption of a relatively thin ﬁlm, i.e., the ﬁlm thickness is much smaller (o500

m

m) than the characteristic dimensions of the simulated domain. For ﬁlm coating processes this assumption is valid, as the ﬁnal coating layer thickness is typically in the range of 100

m

m. It can be expected that the film thickness will be of the same order of magnitude. Following this assumption, the volume of the film can be neglected and no adaptation of the computational grid is necessary. Furthermore, the film surface can be assumed to be parallel to the solid wall. Thus, the wall film is modeled as a two-dimensional layer with a spatially distributed thickness

d

. Due to the small dimensions and the small velocity of the film, interfacial shear stresses and wall friction influence the film much more than inertial forces and lateral shear (see Cebeci and Bradshaw, 1977). For this reason, we have neglected these effects in the momentum conservation equation of the wall film, significantly reducing computational costs. When neglecting inertial forces we assume that the film is at a steady state. Thus, the velocity profile of the film is instantaneously determined by the forces acting on the wall film. In this work, the following effects have been taken into account:

the stress induced by the surrounding gas ﬂow on the liquid ﬁlm, i.e., the interfacial shear stress, as well as the pressure gradient induced by the surrounding gas;

body forces, i.e., gravitational acceleration;

multi-component evaporation from the ﬁlm, taking into account individual diffusion coefﬁcients of each component in the gas phase;

interaction with impinging droplets, i.e., deposition of the coating solution on the film, as well as the change of droplet size due to splashing on the droplet (Mundo et al., 1995). This effect has already been detailed in Section 4.1 of this paper. The impact of film deformation on the interaction between the gas phase and the film (momentum, heat and mass transfer) is taken into account via empirical models for the ‘‘equivalent sand grain roughness’’ of the film. In addition, we solve the enthalpy equation of the wall film in order to predict its temperature, i.e., we take into account conductive and convective heat transfer, as well as latent heat effects due to evaporation. In our model we assume laminar flow behavior. This hypothesis is acceptable as turbulence occurs only at large Reynolds numbers not obtained in the film. Film entrainment, i.e., the re-dispersion of the wall film into the gas flow via detachment of droplets from the film, does not play a significant role in our application and is therefore excluded. The droplet spreading after the impact at the tablet surface is accounted for in the statistics of the Lagrangian DDM method. The hypothesis of parcels containing a certain number of real droplets leads to the assumption that the droplets impacting on a tablet mesh face homogeneously distribute on it. The average number of real droplets in such a parcel is in the order of a few thousand (for the parameters as perTable 1). Thus, we assume

that the film created by these droplets is uniform and is well described with a mean film thickness. This allows us also to use a two-dimensional flow model for the film spreading (see the next section). Furthermore, we have assumed the tablet to be non-porous, i.e., the coating suspension cannot penetrate into the tablet. Also, we take into account the change of the liquid-phase density and viscosity due to temperature or composition change. The spreading of the wall film around the edges of the tablet land is highly important for the coating quality. Anyhow, the high film curvature and the deriving surface tension effects would only locally affect the transport equation for the wall film in a tiny fraction of the total surface area. Thus, we neglect the effects in this area.

4.3.2. Governing equations

In this section, the governing equations that are used to model the above effects are described. Other aspects, e.g., such as the numerical discretization or alternatives to the models used in our work, can be found in the user guide of the software used (AVL, 2008).

Here we introduce the film thickness equation, which represents the basic governing law for the wall film flow. It is a modified formulation of the continuity equation for the liquid phase on the tablet and is presented here for a Cartesian coordinate system: @

d

@tþ @

d

u1 @x1 þ @

d

u2 @x2 ¼ 1

r

sm ð24Þ

The terms

d

and

r

represent the thickness and the density of the wall film,smis the area-specific mass source term for the liquid in the wall film. Since in our case the wall (i.e., the tablet surface) is a closed surface, no boundary conditions (BCs) but only initial conditions (ICs) are needed, i.e., zero film thickness at time zero. Eq. (24) can be solved in a straightforward manner once the source termsm(due to deposition of droplets on the tablet and evaporation from the film) and the mean velocity componentsu1 andu2 are known. The source term sm is known from the spray solution as described in Section 4.1 of this paper. The mean velocity components u1 andu2 are calculated from a momentum balance of the liquid film. In our work we use an analytical solution for the wall film’s momentum equation, which is motivated by the assumptions made above. Thus, the momentum equation reduces to a balance of the shear stress imposed on the film !

t

I and the

viscous and turbulent dissipation within the ﬁlm (seeFig. 4)

t

! ðyÞ

r

¼ ð

n

þ

e

mÞ @!u @y ð25Þ Table 1

Basis set (B) of the simulation parameters.

Parameter Symbol Value

Droplet diameter Dd 20mm

Droplets injection velocity vd 15 m/s

Gas temperature Tg 298.15 K

Droplets temperature Td 298.15 K

Tablet temperature TTAB 298.15 K

Total injected mass Minj 0.1 g

Injection time tinj 0.1 s

Mass fraction of glycerol in water w 20 wt%

x

y

wall

film’s

surface

wall

(tablet)

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Here,Pmdenotes the turbulent eddy viscosity within the frame-work of Boussinesq’ hypothesis for the description of turbulent dissipation.!

t

ðyÞand!u represent two-dimensional vectors in the plane of the wall for the shear stress and the velocity, respectively. Both depend on the wall-normal coordinate y. Clearly, the local distribution of the shear stress!

t

ðyÞuniquely defines the shape of the velocity profile in the film once the turbulent eddy viscosityPm is known.

The interfacial shear stress !

t

I induced by the gas ﬂow, the

component of the gravitational force!g99parallel to the wall, as well as the longitudinal pressure gradient @p=@x determine the distribution of shear stress across the ﬁlm, given by

t

! ðyÞ ¼

r

!g99@p @x ð

d

yÞ þ!

t

I ð26Þ

The calculation of the interfacial shear stress!

t

Iis non-trivial,

as the interfacial stress itself influences the flow of the gas over the film due to the deformation of the phase boundary. In our work, this effect is taken into account by calculating!

t

Iusing an

approximation of the velocity profile in the gas phase, i.e., the so-called wall functions, with coefficients that depend on the wall shear stress and on the film thickness. In essence, we model the deformation of the film surface by a correlation for the equivalent sand grain roughnessksas a function of wall shear stress and film thickness.ksis then used to calculate a characteristic Reynolds number, and finally we can correlate this Reynolds number with the coefficients in the wall function. Due to this complex interaction between film flow and interfacial shear stress, it is necessary to iteratively solve for the mean film velocity, as detailed below. Details of this calculation can be found in AVL (2008).

To obtain the velocity profile in the film, we first transform!u andy in Eq. (25) into dimensionless coordinates by introducing the friction velocity ut¼

ffiffiffiffiffiffiffiffiffiffiffiffi

t

W=

r

p

(see, for example, Holman, 1989). Here,

t

Wis the wall shear stress, i.e., the stress at y¼0. Thus, we deﬁne the dimensionless wall ﬁlm velocity!uþ¼!u=ut and the dimensionless wall distanceyþ_¼_yu

t=

n

. Hence, we obtain @!uþ @yþ ¼

t

! ðyþ_Þ₌

_t

W 1þ

e

m=

n

ð27Þ

This equation represents a general formulation of the film flow, both for turbulent and laminar films, with or without gravity, interfacial shear or pressure gradients. In case of laminar flow, where

e

mis equal to zero, the integration of Eq. (27) leads to an analytical solution for the dimensionless velocity profile (see, for examplePrandtl et al., 1990). In our case, we assume a laminar flow of the wall film. This assumption is justified by the fact that in our simulations the wall shear stress and the film thickness are significantly below 1.2 Pa and 0.2 mm, respectively, values for which a transition from laminar to turbulent flow has been observed in the literature for internal combustion engines applications (AVL, 2008). By integrating over the film thickness, we obtain the mean film velocityufor laminar flow:

u ! ¼

d

6

m

2

d

r

g ! 99 dp dx þ3!

t

I ð28Þ

Eq. (28) is used in the film thickness equation (Eq. (24)) to solve for the time evolution of the film thickness. We stress once more, that due to the assumption of negligible inertial forces the mean film velocity adapts instantaneously to the stresses acting on it. The film velocity is, however, transient due to the inherently instationary flow of the surrounding gas flow resulting in an instationary interfacial stress. Also, the mass, and consequently the thickness of the wall film, change with time due to droplet deposition and evaporation of the coating solution.

The integration of Eq. (27) for turbulent ﬂows (i.e.,

e

ma0) requires the deﬁnition of the eddy viscosity

e

mas a function of the dimensionless wall distance y+. However, since the ﬁlm ﬂow remains laminar in our work, this is not discussed here.

In the momentum equation (see Eq. (25)) for the film flow, surface tension effects near the front of the film have been neglected, since these effects (i) will be limited to the front of the film, as the curvature of the film is significant only in this region, (ii) we assume that the coating solution wets the surface, and thus, spreading is governed by viscous flow as the curvature at the edge of the film is small. Furthermore, a rough estimate of the capillary number (

m

LV/

s

L) (for

m

L¼102Pa s,

s

L¼7102N/m, V¼30 m/s) yields a quantityb1, indicating small surface tension effects. However, in regions where the characteristic film velocity Vis low, the capillary number is small and surface tension may influence film spreading. In order to take into account surface tension and contact angle effects, a detailed resolution of the front of the film is necessary. This will be considered in further studies.

Next, we describe the enthalpy equation for the wall film to obtain the film temperature distribution on the tablet. The simplest approach would be to assume that the film has the same temperature as the tablet. This is only valid, if the film is very thin and heat transfer between tablet and film is very fast. In our work, we assume that the gas phase, the wall film and the wall (i.e., the tablet) have different temperatures. Assuming a homogeneous film temperature over the film thickness, the enthalpy equation for the film can be written as

r

d

@h @tþrUðh u ! Þ ¼ ðh_S,fwh_S,fgm_EhEþh_S,impþh_S,entÞ ð29Þ

The first two terms on the right hand side of Eq. (29) represent the heat fluxes in W/m2_{between film and wall, and between film}

and the gas phase, respectively. In our work, these terms are modeled using appropriate correlations for the Nusselt number, i.e., predictions for the heat transfer coefﬁcient based on experimental data have been used. Also, the temperature of the wall, i.e., the tablet, has been assumed to be uniform. The third, fourth and ﬁfth term on the right hand side of Eq. (29) denote the enthalpy change due to evaporation (m_Eis the evaporation mass

ﬂux in kg/(m2_{s)), the area-speciﬁc enthalpy transfer from spray}

droplet via impingement and the area-speciﬁc enthalpy loss from droplet entrainment, respectively.

Similar to the ﬁlm thickness equation, the enthalpy equation is solved by using the result of the simpliﬁed momentum equation for!u, i.e., Eq. (28).

Finally, the total evaporation mass ﬂux m_E from the ﬁlm

has to be modeled. The evaporation process can be described by Stefan’s law of unidirectional diffusion, which is used in our work, i.e., _ mE,j¼

r

g

b

g,j 1wI,j _@w j @y I ð30Þ

Here,

r

gis the density of the gas phase,Dj,2is the molecular

diffusion coefﬁcient of the evaporating speciesjin the gas,wI,jis the mass fraction of each evaporating speciesjat the interface and

ð@wj=@yÞI is the gradient in wall-normal direction of the mass

fraction at the interface.

r

g,Dj,2andwI,jcan be calculated from the

ideal gas law, empirical correlations and the saturation pressure, respectively. However, the gradient of the mass fraction at the interface depends on the local flow conditions and is therefore not known. In our work we use the analogy to the turbulent velocity profile to approximate this gradient, taking into account the rough surface of the wall film. Details of this model can be found inAVL (2008).

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5. Results

5.1. Base case deﬁnition

As mentioned above, our goal was to investigate the influence of different operating parameters on the film formation on coated tablets. In order to define a realistic base set of parameters for our simulations, experimental investigations of a spray gun via Phase Doppler Anemometry (PDA) technique have been performed (for the technique refer toHirleman (1996), the measurements have been performed by us at Duesen-Schlick GmbH, Germany).

This experimental method is capable of simultaneously measur-ing diameter, velocity and mass flux of the injected spray droplets. The chosen nozzle was a Schlick 930Form 7-1 S35 ABC, typically used for pharmaceutical coating processes. Atomizing air (AA) and pattern air (PA) were both set equal to 1.2 bar, leading to an injected mass flow of approximately 60 g/min. The distribution of droplet diameter and velocity at a distance of 200 mm from the nozzle tip are shown in Figs. 5 and 6, respectively. These average values were obtained by scanning the spray along a line perpendicular to the spray axis. As well known in the literature, real sprays have a range of drop sizes and velocities, which will greatly influence their trajectories, their interaction and influence on the turbulent gas flow, evaporation time, likelihood of bouncing, and degree of coverage on the tablet’s surface. In order to understand in detail the behavior of different droplet sizes and velocities, we considered variations of mono-disperse droplet population in order to quantify the singular effects of diameter and velocity variations. Mono-dispersed droplets size of 20

m

m, as well as an initial velocity of 15 m/s was selected as a base case, which is a good compromise between the volume- and number averaged data in Figs. 4 and 5. The temperature in the computational domain was initially set to room conditions (i.e., 298.15 K). The base set of parameters is defined inTable 1. As already discussed in Section 4.1, these values are the initial conditions of a few centimeters downstream the nozzle outlet where secondary atomization, collision and coalescence become insignificant. Standard values for the physical properties of the air and water have been used. The physical properties (viscosity, density) of the glycerol–water mixture have been taken from the manufacturer’s specifications (The Dow Chemical Company, 2009).

A hybrid three-dimensional computational grid has been generated with a structured wall layer around the tablet (see

Fig. 7). This structured wall layer is three cells in depth in order to sufﬁciently resolve the wall-near region. The computational grid consisted of a rectangular box with a cross section of 0.18 m0.18 m and a length of 0.25 m. The spray nozzle was located at the upper part and in the center of the box. The distance between spray nozzle and the object (granule, tablet) to be coated has been set to 15 cm, which is a realistic value in industrial practice. Typically, round convex tablets were used in our work. The tablet’s main diameter was chosen to be 10 mm, and the

Fig. 5.Phase Doppler Anemometry (PDA) measurements of droplets size distribution (average values 200 mm from the nozzle tip).

Fig. 6.Phase Doppler Anemometry (PDA) measurements of droplets velocity distribution (average values 200 mm from the nozzle tip).

150 mm

Tablet

Spray nozzle

Droplets

g

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height-to-diameter ratio was set to 0.67:1. The band thickness and the cap radius of curvature were equal to 3 and 7.6 mm, respectively. The box was modeled to be open on top and bottom, in order to allow for a gas ﬂow induced by the injected liquid spray. In our work we oriented the top surface of the tablet perpendicular to gravity and to the incoming droplets. The effects of different tablet orientations with respect to the spray, as well as the impact of different tablet bed angles (and thus gravity) will be part of future work.

In order to test the mesh quality and the convergence of the numerical simulation, preliminary test runs have been performed for pure water droplets and continuous spray injection. Based on these results a computational time step of 1104

s was shown to be adequate in order to describe all the important scales of the process. The convergence criteria for the residuals have been chosen as 1104

for momentum, turbulence and species conservation equation, and 1106_{for the energy conservation}

equation. A grid dependency study has also been performed to assess the quality of the computational mesh. For this purpose we used the well-accepted Grid Convergence Index (GCI) from

Roache et al. (1986). Three meshes made of 15,527, 3884 and 1205 face cells on the biconvex tablet surface, respectively, called mesh 1, mesh 2 and mesh 3, were used. The average ﬁlm thickness

f

after 0.25 s has been chosen as the key variable for the GCI study. The face cells numbersN, the grid reﬁnement factors

r21 and r32, the values of the key variables

f

, the approximate

relative error ea21_{, the extrapolated relative error} _eext21_{, the}

extrapolated solution

f

ext21 and the fine-grid convergence index GCIfine21 _{are shown in}_{Table 2}_{. According to these results, the film}

thickness appears nearly equal for the ﬁnest and the middle mesh, leading to a deviation of only 0.020%. Thus, mesh 2 was used for further simulations. Note that theGCImethod accounts only for discretization errors and not for modeling errors.

A typical example of our results is presented inFig. 8. The initial choice of pure water leads to increased wall film evaporation compared to realistic cases. The evaporation process mainly takes place in the upstream part of the tablet, indicated by the low film thickness and the significant accumulation of water vapor near the upper edge of the tablet. Clearly, evaporation as well as the flow of the film induced by the interfacial shear stress seems to surpass the accumulation of water by droplet deposition in this region of the tablet. Furthermore, it can be seen fromFig. 8that the evaporated water is transported along the cylindrical part of the tablet into the wake region of the flow. Accumulation of water vapor is highest near the cylindrical part of the tablet, whereas water vapor accumulation in the wake region is less pronounced. In both regions, i.e., in the wake and the cylindrical part, the high vapor concentration leads to a decreased evaporation rate, resulting in locally higher film thicknesses. It should be noted that in a ‘‘real’’ tablet bed a single tablet is not suspended in space and the wake would be significantly different (or even not present). Hence, the results for the rear part of the tablet may change significantly. Nevertheless, the goal of our study was to compare the effects of different process parameters on the film formation process. Thus, the major aim was to analyze the droplets collision and the film spreading on the surface of the singular tablet. A more detailed reproduction of the tablet bed environment was included in further analysis.

Furthermore, our analysis describes only one pass of a tablet through the spray zone at a deﬁned angle with respect to the spray. In a real system, tablets will enter the spray zone multiple times at different angles, thus resulting in a statistical distribution of the coating layer. Nevertheless, the presented analysis is important as it details under which conditions a uniform layer can be achieved and how the operating conditions impact the coating process.

Table 2

GCI calculation of discretization error.

Parameter Symbol Value

Face cells number N1;N2;N3 15,527; 3884; 1205

Grid refinement factor (mesh 2 to 1) r21 2.0 Grid refinement factor (mesh 3 to 2) r32 1.8 Average film thickness (mesh 1) f1 1.606e4 m Average film thickness (mesh 2) f2 1.596e4 m Average film thickness (mesh 3) f3 1.370e4 m

Extrapolated solution _f21

ext 1.60626e4 m

Approximate relative error e21

a 0.62%

Extrapolated relative error e21

ext 0.016%

Fine grid convergence index _GCI21

fine 0.020%

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5.2. Variations

In a second step, the main parameters of the base set have been modiﬁed and a glycerol–water mixture has been used in order to mimic a realistic coating process. Two different tablet shapes have been considered, i.e., a sphere and a convex tablet with the main diameter equal to 10 mm. Furthermore, following parameters has been varied:

droplets diameterDd,

environmental gas temperatureTg,

droplets injection velocityvg,

glycerol mass fraction in the coating solutionw.

In order to reduce the amount of simulations, only one variable has been varied at once, resulting in the variation stars shown in

Fig. 9. Simulations have been performed for a total time span of 0.5 s, whereas the injection of droplets stopped after 0.1 s. This choice was motivated by typical tablets velocities and residence times in the spray zone of industrial coaters, as described by

Kalbag et al. (2008)and also discussed in Section 2.2 of this paper.

5.3. Analysis of the results

Fig. 10 shows the transient behavior of the ﬁlm formation process for both the sphere, as well as the tablet. Clearly, during the injection of droplets for 0.1 s they primarily deposit at the front of the surface to be coated. However, after the injection has stopped (t¼0.1 s), the ﬁlm is more or less uniformly distributed

over the sphere and the tablet. Thus, the transport of the liquid phase on a tablet to be coated is substantial, and it is important to model this part of the process. In our simulations the spreading of the ﬁlm is mainly inﬂuenced by the stress from the gas phase, the momentum introduced by the impacting droplets and by gravity to a smaller extent. The eventual tumbling of the tablet is not taken into account in the current work.

The results in Figs. 8 and 10 show that the ﬁlm thickness reaches 70 and 100

m

m already after a single ‘‘pass’’ in the spray. However, as discussed in the introduction, typical ﬁlm thick-nesses after an entire coating operation are less than 100

m

m. The explanation is that the typical film thickness refers to a solid film, whereas in our simulations the film thickness in a single ‘‘pass’’ refers to a liquid film with suspended polymers. Thus, the drying process is not completed and the film mainly consists of the liquid components.

According to the results inFig. 10, the spreading of the film seems to be completed after approx. 0.4 s for the base conditions in our study. As can be seen, even the shape of the coated object strongly influences the film thickness distribution as well as the total mass deposited. For example, in case of the tablet, a significant higher amount of droplets deposit on the surface leading to a substantially higher film thickness. Also, the location of the maximum film thickness after 0.5 s is different for the sphere (hmax at a polar angle of approx. 1201) and the tablet (hmaxat the backside of the tablet).

In the following section, results for different cases are presented at a spray time of 0.5 s. The curves shown in Figs. 11 and 12 represent the cumulative frequency distributions of the local ﬁlm thickness for all the cases in both variation stars.

Fig. 9.Variation star for sphere (left) and tablet (right). The base case conditions (B) are speciﬁed inTable 1.

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These plots have been derived from the simulation results by defining classes for the film thickness and allocating the fraction of the surface that fits into these classes. Thus, the cumulative frequency distribution represents the fraction of surface area that is covered with a film with a thickness lower or equal than a certain value. A wide distribution of the film thickness on the surface, i.e., poor coating uniformity, is indicated by a small slope of the curve. On the contrary, a narrow distribution, i.e., a good coating uniformity, is indicated by a steep increase of the curve. Concentrating on the case for a sphere (Fig. 11), we see that the base case, as well as the cases 2–5, behave similarly and do not show significantly different mean wall film thicknesses. In contrast, case 1 (droplet size increase from 20 to 50

m

m) shows a significantly lower mean wall film thickness. A significant fraction of the surface does not seem to be covered by liquid at all. This is indicated by the fact that the first class of the cumulative frequency distribution has a value of approx. 0.37, i.e., 37% of the surface have a lower film thickness than the first class that has been analyzed. Looking at the shape of the distribution, it can be seen that for the base case, as well as for the cases 3–5, the distribution is bimodal, i.e., the distribution shows two regions with a local maximum in the slope. Such a bimodal distribution indicates that there exist zones with substantial different film thicknesses. In summary, only the increase in droplet size (case 1) results in a significant decrease in spray deposition, consequently leading to uncoated spots on the surface. The best conditions with respect to surface coverage by the film are realized in case 2,

because the cumulative frequency distribution has the smallest initial slope.

For the tablet (results shown in Fig. 12), the situation is different and cases 1, 4 as well as 5 indicate significant effects on the film thickness distribution. Same as for the sphere, the larger droplet diameter (case 1) results in a much lower deposition of droplets on the surface. This is caused by splashing and rebound of the droplets from the tablet’s surface. In addition, a significant part of the tablet’s surface is not covered, indicated by a value of approx. 0.26 for the first class of the cumulative frequency distribution. Case 4 (i.e., a droplet velocity of 30 m/s compared to 15 m/s of the base case) shows mainly two effects on the film thickness distribution: (i) the film thickness after 0.5 s is only a fraction of that obtained in the base case as indicated by the shift to the left of the distribution. This is due to splashing of droplets on the tablet; (ii) the coating quality decreases as there exist regions that are completely free of liquid. This is again indicated by a high value for the first class in the cumulative frequency distribution for case 4 inFig. 12. Finally, case 5 (higher glycerol content of the liquid phase) shows similar trends, i.e., a slightly reduced film thickness, as well as decreasing coating uniformity. The decreased film thickness for the higher glycerol content can be attributed to a change in physical properties of the droplets (density, viscosity and surface tension) resulting in a reduced deposition on the tablet. The decreasing coating quality is due to the higher viscosity of the coating film, resulting in lower mean film velocities on the film. Consequently, the film cannot spread as quickly as in the case of lower glycerol concentration. The optimal conditions with respect to the coverage of the surface with the film seem to be case 3, as here the initial slope is smallest. However, also the base case, as well as case 2, indicate acceptable coverage of the surface with the coating solution.

The time evolution of the total film mass on the tablet is shown inFig. 13. A total of 100 mg has been injected, of which only a fraction impacts on the tablet’s surface. 80 mg of the total mass are water and 20 mg are glycerol, the latter having a very low vapor pressure, leading to a significantly lower evaporation rate compared to water. In the base case approximately 9.4 mg of the coating liquid are deposited after 0.15 s. In the following, the film mass starts to decrease, due to the fact that the injection of droplets is stopped and evaporation of the film starts. After 0.5 s the film mass has nearly linearly decreased to 8.4 mg (10%), indicating an almost constant mean evaporation rate. Compared to the base case, the bigger droplets (case 1) appear to deposit consistently less than the smaller ones, resulting in a peak value of only 0.85 mg for the total film mass after 0.12 s. This can be explained by the significantly higher Reynolds number of the impacting droplets (case 1 leads to a 2.5-fold increase in the Reynolds number, but only to a 37% decrease in the Ohnesorge number), which leads to the occurrence of splashing. Also, the

Fig. 11. Cumulative frequency distribution of the local ﬁlm thickness of the coated sphere att¼0.5 s (for the base case B deﬁned inTable 1and the variations in Fig. 9).

Fig. 12. Cumulative frequency distribution of the local ﬁlm thickness of the coated tablet att¼0.5 s (for the base case B deﬁned inTable 1and the variations inFig. 9).

Fig. 13.Time evolution of the ﬁlm mass on the surface of the coated tablet (for the base case B deﬁned inTable 1and the variations inFig. 9).

(13)

time profile of evaporation for case 1 is significantly different from that of the base case. As can be seen fromFig. 13, after the peak value of the film mass has been reached in case 1, evaporation takes place at a relatively high rate, until the film mass has been reduced to 0.39 mg, i.e., half of the peak value, after approx. 0.2 s. At this point the evaporation rate reduces significantly due to the fact that glycerol mass fraction increased (water is evaporating first due to the higher vapor pressure from the glycerol–water mixture). This results in a decrease of the vapor pressure of the film liquid, causing a pronounced decrease in the evaporation rate. The final film mass is 0.32 mg, i.e., the total loss of film mass in the second phase of the evaporation of the film is marginal. Comparing the base case with case 4, i.e., a higher droplet velocity, we observe a similar shape of the time profile for the total film mass as in case 1: In case 4 the peak value of the film mass is significantly less (4.4 mg after 0.14 s) compared to the base case. This is again due to splashing, as the Reynolds number of the droplets is again higher than in the base case. Also the evaporation rate of the film on the tablet is significantly higher due to the higher gas velocity induced by the higher droplet velocity. This leads to a nonlinear time profile of the film mass caused by the accumulation of glycerol in the film, because a significant fraction of the water has already evaporated. In summary, the total loss of film mass after 0.5 s for case 4 is 2.3 mg or 52% due to evaporation, which is significantly more than in the base case. Thus, the tablets are already relatively dry after 0.5 s.

The presence of more glycerol in the coating solution (case 5) leads to (i) a lower level of film mass on the surface, as well as to (ii) a significantly lower mean evaporation rate from the film. The initially deposited droplet mass is 7.3 mg after 0.15 s, whereas the final film mass after 0.5 s is 7.1 mg (2.7%). The first effect, i.e., the lower level of film mass, can be explained by the change of the physical properties (i.e., density, surface tension and viscosity) of the spray droplets, such that the deposition rate is decreased. The second effect, i.e., the reduced evaporation, is again due to the lower vapor pressure in case of a higher glycerol mass fraction in the film liquid.

Case 2 (higher temperature) does not show a strong effect on the total film mass time profile. Obviously, the coating process is not very sensitive with respect to small changes in the gas temperature, i.e., the evaporation rate seems unaffected. Also, for case 3 (significantly higher gas temperature) the evaporation rate is only slightly increased (evaporation loss of 1.3 mg compared to 1.0 mg in the base case after 0.5 s). Thus, even the wide range of gas temperatures does not significantly alter the time evolution of the total film mass present on the tablet.

5.4. Assessment of the coating quality

In order to analyze the coating quality, i.e., the homogeneity and the uniformity of the obtained ﬁlm, the following quality indicators have been analyzed:

mean ﬁlm thickness (hmean),

variance of the ﬁlm thickness on the surface (

s

2_),

delta (

d

), deﬁned as the quotient of the maximum (hmax) and the mean (hmean) ﬁlm thickness value:

d

¼ hmax

hmean

ð31Þ

According to this deﬁnition a perfectly homogeneous ﬁlm would have a

d

value equal to 1:

zero-thickness surface fraction (Z).

This factor is the fraction of tablet surface that are not covered by the coating ﬁlm.

Based on these indicators, other parameters may be derived to assess the coating quality. For example, the relative standard deviation of the coating thickness can be easily obtained by dividing the mean value by its variance. InFig. 13we have already discussed the rate of change of the total film mass for a tablet, a quantity which is directly proportional to the mean film thickness introduced in this section. Here we focus once more on the comparison of the mean film thicknesses obtained for different cases. However, we also include the results for the coated sphere (seeFig. 14). As can be seen, in the base case, as well as in cases 2, 3 and 5, the mean film thickness is significantly lower for the sphere compared to the tablet. This indicates that under the droplet deposition parameters defined in the base case (which essentially do not change in the cases 2, 3 and 5), the sphere receives consistently a lower amount of coating liquid, i.e., sphere and tablet behave similar and are nearly unaffected by temperature and viscosity of the coating solution. This indicates, as already mentioned in the discussion of Fig. 13, that the increased evaporation rate due to a higher temperature does not play a significant role under the conditions used in this work. However, when changing droplet size (case 1) or droplet velocity (case 4), the sphere receives more coating solution compared to the tablet. This change is thought to stem from a regime change from droplet deposition to splashing. Obviously, in the case of spheres the deposition is significantly less reduced in the splashing regime compared to tablets. We believe that this behavior is due to the differences in the separation behavior of the gas flow. The gas flow is aligned longer with the sphere’s surface, and droplets generated by splashing have a second chance to deposit. For the tablet, the flow separates early, i.e., at the beginning of the cylindrical region, and droplets are less prone to impact a second time. Hence, we conclude that the mean film thickness deposited on a given surface depends mainly on its shape (e.g., we observe an almost 50% decrease in the case of a sphere compared to the tablet for case 3) as well as the impact parameters (Re,Oh) of the droplets. The solution’s viscosity, as well as the air temperature, show only minimal effects on the mean film thickness.

InFig. 15we analyzed the film thickness variance on coated sphere and tablet. We observe that we have a similar situation as for the mean film thickness. Thus, the variance is lower for the sphere compared to the tablet for cases B, 2, 3 and 5, i.e., in the case where almost no splashing occurs. This clearly indicates that the coating solution can flow more easily over the regularly shaped sphere. In contrast, the edges on the tablet make it more difficult to obtain an even distribution of the film. In the other

Fig. 14.Mean ﬁlm thickness on coated sphere (left bars) and tablet (right bars) at t¼0.5 s (for the base case B deﬁned inTable 1and the variations inFig. 9).