LocalanalysisofthetabletcoatingprocessImpactofoperationconditionsonfilmquality.vv

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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, Austriab 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 2009Received in revised form

15 July 2010

Accepted 16 July 2010Available 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 significantimportance, 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 particle simulation tools.

& 2010 Elsevier Ltd. All rights reserved.

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 controllingthe 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 mm. A detaileddescription of the coating process and the different coater devices

is presented in the book of Cole 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 modernequipment, 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 at ScienceDirect

journal homepage: www.elsevier.com/locate/ces

Chemical Engineering Science

0009-2509/$- see front matter & 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2010.07.007

n Corresponding author at: Research Center Pharmaceutical Engineering GmbH,

Graz, Austria. Tel.: +43 316 873 7978; fax: +43 316 873 7963.

E-mail address: [email protected] (J.G. Khinast).

Chemical Engineering Science 65 (2010) 5699–5715

http://www.elsevier.com/locate/ceshttp://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.ces.2010.07.007mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.ces.2010.07.007http://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.ces.2010.07.007mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_1/dx.doi.org/10.1016/j.ces.2010.07.007http://www.elsevier.com/locate/ces


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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 failures Pandey 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 in Fig. 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 shownin Fig. 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 by Hogan (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.

Fig. 2. Conceptual scheme of the coating process.

D. Suzzi et al. / Chemical Engineering Science 65 (2010) 5699–57155700


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analyzed the complex process of film formation from a water-

polymer dispersion. Initially, the 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 usedin 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 of Aliseda 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 of Yecko and Zaleski (2005). The

main result of Aliseda 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 mm. 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), photographictechniques 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 by Hammer 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 by Kazemi et al. (2007). The activity of water in

aqueous sugar solutions has been analyzed in two studies of Peres

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 beginning of the 20th

century in the work of Worthington (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 thetumbling 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 velocityprofile 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 velocity V for the purpose of scaling the

velocity profile at the top of the granular bed:

V ¼ kRN 2=3 g

d

1=6v1:8 ð1Þ

Here k is a constant, R is the pan radius, N is the pan rotation

rate, g is the gravitational acceleration and d is the tablet size. The

term n represents the fractional fill volume, defined as the ratiobetween the volume occupied by the bed and the total pan

volume. The relation was verified using experimental databetween n¼0.10 and 0.17 and rotational speeds between o¼6and 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 velocity V S max

. For low rotational

speeds (o30 rpm), they found that the value of V S 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 t R. 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 ai of

D. Suzzi et al. / Chemical Engineering Science 65 (2010) 5699–5715 5701


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tablet i as 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 2p

o

n

N

ð2Þ

Here Dt R is the average residence time per pass in the spray

zone averaged over all tablets. The averaged dimensionless

appearance frequencies were between a ¼ 0:1 and a¼ 1:4.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. Dt R ¼ L=V . Here L is the length of the spray zone and V is 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

time t C ,i and the average circulation time per pass Dt C characterize

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

t R and t Ci is the total coating time. The fractional residence time f Ris defined as the ratio of time spent by a tablet in the spray zone to

the total coating time t 0. The average fractional residence time is

f R ¼ t Rt 0

¼ nN

ð3Þ

where t R is the average time the tablets spend in the spray zone,

n is the average number of tablets in the spray zone and N the

total amount of tablets inside the pan coater. The ratio n=N is 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 by Denis

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 of Muliadi 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 by Freireich 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 in Fig. 2.

In summary, the major objectives of this work are

to model the spray, deposition on the tablet, the coatingprocess, 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 dropletson particles with different shape,

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

to investigate how different process parameters affect thecoating 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 filmquality. 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 notdescribed 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 by Dukowicz (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 awarethat 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 parcel i of 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

dmiddt

¼ _miE 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:

midd u

!id

dt ¼ F

!iD þ F

!iG þ F

!iP þ F

!iEX ð5Þ

The terms on the right hand side of Eq. (6) represent the drag

force F iD, the gravity and buoyancy force F iG, the pressure force F iP ,

and the external force F iEX . The drag force acting on the droplets is

calculated as

F !

iD ¼1

2r g AdC D9 u

!rel9 u

!rel ð6Þ

where r g is the gas density, Ad the cross-sectional area of thedroplet and u

!rel the relative velocity between the gas phase and

the parcel. The term C d represents the drag coefficient for a single

sphere and is modeled in our work according to the formulation of

Schiller and Naumann (1993):

C D ¼

24

Redð1 þ0:15Red

0:687Þ, Redo103

0:44, RedZ103

8><>: ð7Þ

Here the particle Reynolds number Red is defined as

Red ¼ r g 9 u

!rel9Dd

m g ð8Þ

In order to calculate the temperature T id of 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):

midc p,ddT iddt

¼ LðT idÞ _miE þ _Q ð9Þ

Here, c p,d is the mean specific heat capacity of the droplets (i.e., an

average over all components in the droplet), L(T id) 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 the Abramzon

and Sirignano (1988) approach with the extension by Brenn 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 species j are calculated and summedup to yield the total mass loss due to evaporation:

_miE ¼X

j

_miE , j ð10Þ

In the multi-component evaporation model used in this work,

the mass transferred for each component j to the gas phase is

given by

_miE , j ¼pr g b gjDdSh

j lnð1 þBM , jÞ ð11Þ

The overbars in the gas density r g and the binary diffusioncoefficient b gj of species j in the gas phase indicate that these

values are evaluated at a reference temperature and composition

(for more details refer to AVL, 2008). Dd is the droplet diameter,

Sh j is the corrected Sherwood number of species j (defined below)

and BMj is the Spalding mass transfer number defined as

BM , j ¼w j,sw j,1

1w j,sð12Þ

Here, w j,s is the gas phase mass fraction of species j at the

surface of the drop (to be calculated from the vapor pressure of

species j at the droplet temperature) and w j,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

_miE ¼p k g c p,d

Dd Nu lnð1 þBT Þ ð13Þ

Here, k g 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):

Nu0 ¼ 2 þ 0:552Re1=2 Pr 1=3 ð14Þ

Sh0, j ¼ 2 þ0:552Re1=2 Sc j

1=3 ð15Þ

The corrected Nusselt and Sherwood numbers Nun and Sh j are

then calculated taking into account the deviation of the

streamlines due to the evaporating mass flow:

Nu ¼ 2 þðNu02Þ

F T , Sh j ¼ 2 þ

ðSh0, j2Þ

F M , jð16Þ

The temperature and mass correction functions F T and F M,j arecalculated as

F ðBÞ ¼ ð1 þBÞ0:7lnð1 þBÞ

B ð17Þ

using BT or BM,j for F T and F M,j, respectively. In the relation for the

temperature correction function F T , BT is the Spalding heat

transfer number defined as

BT ¼ ð1 þBM Þf1 ð18Þ

f¼c p,dc p, g

Sh

Nu1

Le ð19Þ

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

conditions and Le is the Lewis number. Finally, the heat transfer

rate _

Q between the droplet and the gas phase for the whole parcel



6/17

is defined as

_Q ¼ _miE c p,dðT 1T idÞ

BT LðT idÞ

ð20Þ

Mixture fractions and mixture properties for each component j

at the drop surface needed in Eq. (12) are calculated using the

activity coefficients g j:

x j,s ¼ x j,Lg j pv, j

p

ð21Þ

Here, x j,s and x j,L are the mole fraction of species j in the gas

and liquid phase, respectively. Note, that the mole fraction x j,s is

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

calculation for the mass transfer rate. pv,j is the vapor pressure of

pure species j and p is the total pressure. Instead of using Raoults’

law, i.e., assuming gi to be equal to 1, the activity coefficients usedin our work have been calculated using a group contribution

method (UNIFAC method, Peres and Macedo, 1997). This is in line

with the work of Attarakih 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 rate _miE , j for

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

calculate the mass fraction w j,s of each species j at the surfaceof the droplet (Eq. (21)),

calculate all physical properties at the reference conditions, calculate Nu0 and Sh0, calculate BM , j, F M , j, Sh j 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 number BT (Eq. (18)), thecorrected 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 number B

T until 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 of Mundo et al. (1995). Splashing or deposition occur

depending on the dimensionless droplet Reynolds and Ohnesorgenumbers, defined as

Re ¼ rLvd?Dd

mL, Oh ¼

mL ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirLsLDd

p ð22ÞThe (empirical) critical curve delimiting the splashing and

deposition regimes is shown in Fig. 3 and can be expressed as

Ohcrit ¼ 57:7Re1:25 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 spreading t s is of the order of (Rrim/Dd)10mLDd/sL (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 theorder of a few droplet diameters (see Fig. 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 theair 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. Somegeneral 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

Fig. 3. Droplets/wall deposition model: critical curve.



7/17

behavior, we make the assumption of a relatively thin film, i.e.,

the film thickness is much smaller (o500 mm) than thecharacteristic 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 100mm. It can beexpected 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 beparallel 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 liquidfilm, i.e., the interfacial shear stress, as well as the pressuregradient 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 thecoating 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 sandgrain 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 per Table 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 filmcurvature 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 liquidphase on the tablet and is presented here for a Cartesian

coordinate system:

@d

@t þ

@du1@ x1

þ@du2@ x2

¼ 1

rsm ð24Þ

The terms d and r represent the thickness and the density of thewall film, sm is 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

term sm (due to deposition of droplets on the tablet and evaporation

from the film) and the mean velocity components u1 and u2 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 and u2 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 theviscous and turbulent dissipation within the film (see Fig. 4)

t!ð yÞr

¼ ðnþemÞ@ u

!

@ y ð25Þ

Table 1

Basis set (B) of the simulation parameters.

Parameter Symbol Value

Droplet diameter Dd 20 mmDroplets injection velocity vd 15 m/s

Gas temperature T g 298.15 K

Droplets temperature T d 298.15 K

Tablet temperature T TAB 298.15 K

Total injected mass M inj 0.1 g

Injection time t inj 0.1 s

Mass fraction of glycerol in water w 20 wt%

x

y

wallfilm’s

surface

wall(tablet)

Fig. 4. Stress and velocity distribution in the wall film.



8/17

Here, P

m denotes the turbulent eddy viscosity within the frame-

work of Boussinesq’ hypothesis for the description of turbulent

dissipation. t!ð yÞ and 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!ð yÞ uniquely defines the shape of the velocity profile in the film once the turbulent eddy viscosity

Pm

is known.

The interfacial shear stress t!

I induced by the gas flow, thecomponent of the gravitational force g

!99 parallel to the wall, as

well as the longitudinal pressure gradient @ p=@ x determine the

distribution of shear stress across the film, given by

t!ð yÞ ¼ r g !

99@ p

@ x

ðd yÞ þ t!I ð26Þ

The calculation of the interfacial shear stress t!I is 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!I using anapproximation 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 roughness ks as a function of wall shear stress and film

thickness. ks is 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!

and y in Eq. (25) into dimensionless coordinates by introducing

the friction velocity ut ¼ ffiffiffiffiffiffiffiffiffiffiffiffitW =r

p (see, for example, Holman,

1989). Here, tW is the wall shear stress, i.e., the stress at y ¼0.Thus, we define the dimensionless wall film velocity u

!þ¼ u

!=ut

and the dimensionless wall distance y þ ¼ yut=n.

Hence, we obtain

@ u!þ

@ y þ ¼

t!ð y þ Þ=tW 1 þem=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 em is equal to zero, the integration of Eq. (27) leads to ananalytical solution for the dimensionless velocity profile (see, for

example Prandtl 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 enginesapplications (AVL, 2008). By integrating over the film thickness,

we obtain the mean film velocity u for laminar flow:

u!

¼ d

6m 2d 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., ema0)requires the definition of the eddy viscosity em as a function of thedimensionless 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, andthus, 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 (mLV /sL) (for mL¼102 Pa s, sL¼7 10

2 N/m,

V ¼30 m/s) yields a quantity b1, indicating small surface tension

effects. However, in regions where the characteristic film velocity

V is 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

rd @h

@t þr Uðh u

!Þ

¼ ð _hS , fw

_hS , fg _mE hE þ_hS ,imp þ

_hS ,ent Þ 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 thewall, 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 ( _mE is 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 _mE 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 , j ¼ r g b g , j1wI , j

@w j

@ y

I

ð30Þ

Here, r g is the density of the gas phase, D j,2 is the moleculardiffusion coefficient of the evaporating species j in the gas, wI,j is

the mass fraction of each evaporating species j at the interface and

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

fraction at the interface. r g , D j,2 and wI,j can be calculated from theideal 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

in AVL (2008).



9/17

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 (forthe technique refer to Hirleman (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 lineperpendicular 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 mm, as well as an initial velocity of 15 m/s was selected as abase 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 in Table 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 m 0.18 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

Fig. 7. Simulation domain and section of the 3D-hybrid computational mesh.



10/17

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 1 104 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 1 104 for momentum, turbulence and species

conservation equation, and 1 106 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 numbers N , the grid refinement factors

r 21 and r 32, the values of the key variables f, the approximate

relative error ea21, the extrapolated relative error eext

21 , the

extrapolated solution fext 21 and the fine-grid convergence index

GCI fine21 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 the GCI method accounts only for

discretization errors and not for modeling errors.

A typical example of our results is presented in Fig. 8. The initialchoice 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 from Fig. 8 that 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 N 1; N 2; N 3 15,527; 3884; 1205

Grid refinement factor (mesh 2 to 1) r 21 2.0

Grid refinement factor (mesh 3 to 2) r 32 1.8

Average film thickness (mesh 1) f1 1.606e4 m

Average film thickness (mesh 2) f2 1.596e 4 m

Average film thickness (mesh 3) f3 1.370e4 m

Extrapolated solution f21ext 1.60626e 4 m

Approximate relative error e21a 0.62%

Extrapolated relative error e21ext 0.016%

Fine grid convergence index GCI21fine 0.020%

Fig. 8. Simulation with water droplets. Color code in the gas phase denotes water vapor mass fraction. Color code on the tablet denotes film thickness.



11/17

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 diameter Dd, environmental gas temperature T g , droplets injection velocity v g , glycerol mass fraction in the coating solution w.

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 (t ¼0.1 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 mm 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 mm. Theexplanation 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 in Fig. 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

(hmax at 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 in Table 1.

Fig. 10. Time evolution of the film at different time steps for a sphere (top) and the tablet (bottom) for the base conditions ( Table 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 mm) showsa 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 in Fig. 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

in Fig. 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 at t ¼0.5 s (for the base case B defined in Table 1 and the variations in

Fig. 9).

Fig. 12. Cumulative frequency distribution of the local film thickness of the coated

tablet at t ¼0.5 s (for the base case B defined in Table 1 and the variations in Fig. 9).

Fig. 13. Time evolution of the film mass on the surface of the coated tablet (for the

base case B defined in Table 1 and the variations in Fig. 9).



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time profile of evaporation for case 1 is significantly different

from that of the base case. As can be seen from Fig. 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 adecrease 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 hmaxhmean

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. In Fig. 13 we 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

(see Fig. 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 theincreased 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 filmthickness 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.

In Fig. 15 we 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

t ¼0.5 s (for the base case B defined in Table 1 and the variations in Fig. 9).



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cases (i.e., 1 and 4), the sphere shows a slightly higher variance

compared the tablet. This indicates that the change to a splashing

regime reduces the importance of the flow of the liquid on the

object to be coated. In contrast to the mean film thickness where

there was almost no effect of the gas temperature, this parameter

seems to have a pronounced effect on the film thickness variance

(see cases 2 and 3, note that the y-axis has a logarithmic scale and

that case 3 has an almost 18-fold higher s2 value than the basecase!). This strong sensitivity with respect to the temperature can

be explained by the significant change of the film’s viscosity,

which strongly decreases with temperature. Consequently, the

film can flow more easily over the tablet and can accumulate at

the rear part of the tablet’s surface, resulting in an uneven

distribution of the coating solution. However, the glycerol

content, i.e., the change of the viscosity with glycerol content at

the temperature of the base case, shows only a negligible effect. Inthe cases where splashing occurs (cases 1 and 4), the variance

drops below the value for the base case. The relative variance, i.e.,

s2=h2mean (data not shown), however, is still higher as in the basecase. This is especially true for the case of a larger droplet size,

where we observe an almost 9-fold increase of the relative

variance compared to the base case. Thus, the occurrence of

splashing seems to decrease the quality of the coating

significantly.

Similar trends are observed in Fig. 16, in which we focus on the

d value, i.e., on the ratio of maximum to mean film thickness. For

the tablet, the gas temperature has again a strong effect on the

coating quality and the influence of the glycerol content is small.

This can be interpreted by the fact that there will be an

accumulation of coating solution at the rear part of the tablet,

resulting in a spot with an extremely high film thickness. Also, the

droplet size seriously influences the coating quality of the tablet,

whereas droplet velocity does not significantly alter the d value.

This is also true for the sphere.

Finally, we present Fig. 17 which shows the fraction of the

surface to be coated that has received no coating. Clearly, in those

cases where splashing occurs (cases 1 and 4) Z is between 27% and

67%, whereas for all other situations Z is below 12%. Thus,

splashing results in a significant reductio

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