7
Computational fl uid dynamics:
applications in
pharmaceutical technology
Ivana Masic, Jelena Parojcic, and Zorica Djuric,
Department of Pharmaceutical Technology and
Cosmetology, Faculty of Pharmacy, University of
Belgrade
Abstract: This chapter introduces the concept of computational
fl uid dynamics (CFD) and its applications in pharmaceutical
technology. Basic theoretical explanations on the mathematics of
fl uid fl ow and numerical grids are provided. CFD is a versatile tool
that is mainly used in complex dynamical process characterization.
Examples of CFD applications in development of inhalers, analysis
of dissolution apparatus hydrodynamics, and fl uidized bed process
simulations are presented.
Key words: Computational fl uid dynamics (CFD), numerical grids,
fl uid fl ow, inhalers, dissolution apparatus hydrodynamics, fl uid bed
processes.
7.1 Introduction
Fluid mechanics studies fl uid performance at rest and in motion. It can
be divided into: fl uid statics , the study of fl uids at rest; fl uid kinematics ,
the study of fl uid in motions; and fl uid dynamics , which deals with the
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effects of forces on fl uid motion. With the evolution in computer
technology, a branch of fl uid dynamics called computational fl uid
dynamics (CFD) has become a powerful and cost-e ffective tool for
simulating real fl uid fl ow.
The explanations for many natural phenomena, such as river fl ows,
ocean waves, wind currents, functioning of the human body (e.g.
cardiovascular and pulmonary system), lie in the fi eld of fl uid mechanics.
Fluid mechanics has, above all, a great importance in development and
performance optimization of complex engineering systems, such as
airplanes, ships, cars (Fay, 1994).
Recent results have announced the importance and possible applications
of fl uid mechanics in the fi eld of biomedicine. For example, some of the
procedures used in treatment of blood vessel obstruction (e.g. stenting,
balloon angioplasty, i n situ drug delivery for unclotting, bypass surgery,
etc.) have statistically signifi cant failure rates, which indicates a need for
a patient-s pecifi c approach and detailed study of fl uid dynamics before
and after intervention. The prediction and modeling of fl ows in vascular
and pulmonary systems on a patient-s pecifi c basis is still an obstacle, but
it is becoming more likely that CFD will fi nd its place in enhanced
diagnosis and planning of surgical procedures (Löhner et al., 2003). CFD
simulations may give valuable information regarding characteristics of
blood fl ow under complex fl ow conditions, as well as deformation
and fl ow of erythrocytes in microcirculation (Jafari et al., 2009). In
combination with medical imaging techniques, CFD might be a
powerful tool for patient- specifi c simulation of blood fl ow inside the
abdominal aorta bifurcation (Makris et al., 2011), or it might be used
to explain variable incidence of vascular dysfunction among
patients with surgically repaired coarctation of the aorta (Olivieri
et al., 2011). With future improvements in computing power, CFD is
expected to become a valuable tool in clinical practice, for diagnosis
and treatment of cerebral aneurysms (Wong and Poon, 2011a; Sforza
et al., 2012).
The knowledge and understanding of the movement of particles and
their deposition in the respiratory airways is important to ensure effective
treatment. CFD modeling may provide an insight into the mechanisms of
airfl ow and particle transport through the asymmetrically branched
airways structure (Calay et al., 2002). CFD has also been successfully
applied in the study of fl ow fi eld and micro- and nanoparticle deposition
in the human upper airway, from the nasal cavity to the end of the trachea
(Ghalati et al., 2012). Chronic obstructive pulmonary disease is
characterized by infl ammation that leads to narrowing and obstruction
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of the airways, which signifi cantly affects the airfl ow. CFD can serve as
an effective tool in clarifying the fl ow patterns in the airways of patients
suffering from this disease and may provide useful information regarding
treatment (Yang et al., 2006). Differences in the anatomy of the nasal
cavity may cause differences in the airfl ow, which may further affect the
amount of inhaled gases and particles. Also, certain types of nasal
morphology can result in increased fl ow to the olfactory region, and
potentially increased risk of transport to the brain via the olfactory nerve,
which indicates the need for more extensive tests to obtain more
information on the variability of air distribution. CFD seems to be a
useful tool in the study of inter- individual differences in nasal air
distribution, and therefore individual sensitivity to inhaled gases and
particles (Segal et al., 2008). The infl uence of post- surgical changes of
nasal anatomy on airfl ow characteristics was also investigated numerically
using CFD, which might be a relatively fast and effi cient approach in
surgical planning (Na et al., 2012).
Considering the growing research interest in pharmaceutical
applications of CFD, the aim of this chapter is to provide an overview
of recent scientifi c results and to give an insight into the possibilities
for application in this fi eld. This chapter aims to provide the reader with
a brief theoretical background and basic terminology related to CFD
methods, without going into details of mathematics and numerical
algorithms. Being primarily intended for researchers working in the
fi eld of pharmaceutical technology, we will focus on possible applications
of this technique in testing and optimization of manufacturing
processes, device/equipment performance, effectiveness of drug delivery
systems, etc.
7.2 Theoretical background
CFD is an area of fl uid dynamics that deals with fi nding numerical
solutions to equations describing the fl uid fl ow to obtain a numerical
description of the entire fl ow fi eld. CFD offers signifi cant time and
cost savings, as well as comprehensive information about fl uid fl ow
in the investigated system, whereas experimental methods are limited
to measurements at certain locations in the system. Moreover,
numerical simulations allow testing of the system under conditions
in which it is not possible or is diffi cult to perform experimental tests.
In accordance with the applicability and advantages offered by
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this method, a number of commercial CFD software packages are now
available.
CFD is based on the analysis of fl uid fl ow in a large number of points
(elements/volumes) in the system, which are further connected in a
numerical grid/mesh. The system of differential equations describing the
fl uid fl ow is converted, using appropriate methods, to a system of
algebraic equations at discrete points. The obtained system of algebraic
equations, which can be linear or nonlinear, is large and requires the use
of computers to be solved. With the increase in speed and available
computer memory, more complex problems can be solved relatively
quickly using the CFD method. Finally, the solution presents fl ow
quantities at the grid points (Sayma, 2009).
CFD software packages are based on highly complex nonlinear
mathematical expressions derived from fundamental equations of fl uid
fl ow, heat, and mass transfer, and can be solved by complex algorithms
built into the program. Fluid fl ow in a given system can be simulated for
defi ned inlet and outlet conditions (also called boundary conditions).
Modeling outputs are usually presented numerically or graphically.
7.2.1 Mathematical description of the fl uid fl ow
The kind of equations describing fl uid fl ow are differential equations,
which represent the relationship between fl ow variables and their
evolution in time and space. Basic equations of fl uid fl ow include Euler’s
equations for inviscid fl ow and Navier–Stokes equations for laminar fl ow
of viscous fl uid. With appropriate modifi cations, the Navier–Stokes
equations can also be used for turbulent fl ow. Namely, the variation in
time for turbulent fl ow is random, and detailed information on its
variation is of little relevance. The average quantity is more useful for
practical application. The mean value of fl ow quantity is determined in a
time interval that is suffi ciently large to neglect small variations, but
suffi ciently small to take into account large, signifi cant variations. The
Reynolds- averaged Navier–Stokes equations are based on this principle,
and represent the primary means for describing turbulent fl ows. Different
approaches are further applied to obtain a closed system of equations,
that is, to obtain an appropriate number of equations for a given number
of variables, which is called turbulence modeling (Blazek, 2005; Sayma,
2009). More detailed information on fl ow governing equations and
turbulent modeling methods can be found in numerous fl uid mechanics
textbooks.
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7.2.2 Discretization of the fl ow
governing equations
In order to solve the system of differential equations representing the fl ow,
the fi rst step is to defi ne discrete points in space, called grid points or grid
nodes. These points are connected to form a numerical grid. Numerical
methods further convert the system of continuous differential equations
into a system of algebraic equations that represent the fl ow at the grid
points and interdependency of fl ow at those points and their neighboring
points. The values of the fl ow variables at the grid points are the unknowns
in a system of algebraic equations that have to be solved. The most
commonly used discretization methods are the fi nite difference method,
the fi nite element method, and the fi nite volume method. In unsteady fl ow,
when the solution at a discrete point varies with time, discretization of
time dimensions may also be needed (Blazek, 2005; Sayma, 2009).
The fi nite difference method is the simplest and among the fi rst methods
used to discretize the differential equations, and was introduced by Euler
in 1768. This method is applicable only in the case of a uniform,
structured grid, that is, numerical mesh having a high degree of regularity.
This method is based on the application of Taylor series expansions for
discretization of derivatives of the fl ow variables in differential equations.
If we assume that the dependent variable is a function of space coordinate
x, spatial discretization will be performed by dividing the spatial domain
into equal space intervals of Δ x ( Figure 7.1 ). The value of the dependent
Figure 7.1 Illustration of fi nite difference grid
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variable at a given point can be expressed as a function of the value at a
neighboring point and its change due to the shift of Δ x (Blazek, 2005;
Sayma, 2009).
The fi nite element method , as a method for solving partial differential
equations, was developed between 1940 and 1960, and its application
was later extended to fl uid fl ow problems. Unlike the fi nite difference
method, the fi nite element method can be applied in problems with
complex geometry and unstructured grids of various shapes. The distinct
difference between these methods is that the fi nite difference method
requires only the values of the variables at grid nodes, without information
about behavior between the nodes, while the fi nite element method takes
into account variations within each element. The fi nite element method
involves discretization of computational domain and discretization of
differential equations. Discretization of the spatial domain considers its
subdivision into non-o verlapping elements of various shapes. In two-
dimensional problems, triangular or rectangular elements are commonly
used, while the most common element types for three-d imensional
problems are the tetrahedral, hexahedral, and prismatic elements
( Figure 7.2) . Each element is formed by connecting a number of nodes/
Figure 7.2 Example of: (a) triangular; (b) tetrahedral; and
(c) prismatic element
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points into an element, and the number of nodes depends on the type of
element. The number of nodes in each element depends not only on the
number of angles in the element, but also on the type of element
interpolation function. After grid formation, the next step is to choose
interpolation functions that describe the variation of the fi eld variables
over the element. These functions are usually polynomial, because they
can be easily integrated or differentiated. The element equations can be
assembled into a system of equations, with the solution being the
unknown variables at grid points. The most commonly used method for
discretization of differential equations is Galerkin’s method of weighted
residuals (Sayma, 2009).
The fi nite volume method was developed in the 1970s. This method of
discretization uses the integral forms of the Navier–Stokes and Euler’s
equations. The solution domain is divided into control volumes, and the
integral forms of the equations are applied for each volume separately.
The center of control volume, in which fl ow variables are sought, can be
placed in the center of the grid cell when the control volume corresponds
to grid cell, or control volume can be centered on the grid node
( Figure 7.3 ). The values of variables at control volume boundaries are
determined by interpolation from the values at the centers. The main
advantage of this method is fl exibility. It can be applied both in the case
of structured and unstructured networks, making it suitable for fl ow
analysis in cases of complex geometry (Blazek, 2005; Sayma, 2009).
Figure 7.3 Illustration of: (a) cell- centered; and (b) node- centered
control volume
7.2.3 Numerical grids
Grid generation involves division of physical space into a large number
of geometrical elements, such as grid cells, that are formed by connecting
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Figure 7.4 Illustration of: (a) structured; and (b) unstructured grid
grid points with straight lines. There are two basic types of numerical
grids that differ in the way the grid points are connected: structured and
unstructured. A structured grid is characterized by regularity in the
connection, which means that every grid point is surrounded by the same
number of neighboring points. This is not the case with unstructured
grids, where every point is surrounded by a different number of neighbors
( Figure 7.4 ). A grid can also have both structured and unstructured parts,
as in the case of viscous fl ows, where a boundary layer can be structured
and the rest of the domain unstructured. The numerical algorithm should
be developed to suit the type of grid used. In most cases, numerical
algorithms written to use the structured grids cannot be used on
unstructured grids, while those written to use unstructured grids can be
applied on structured grids (Blazek, 2005; Sayma, 2009).
7.3 Application of CFD in
pharmaceutical technology
CFD has been recognized as a promising tool for the analysis and
optimization of various pharmaceutical unit operations, process
equipment, drug delivery devices, quality control equipment, etc.
Application of CFD methods in pharmaceutical product and process
development may lead to better process understanding, reduced number
of experiments, and reduced cost and time savings (Pordal et al., 2002;
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Karanjkar, 2003; Kukura et al., 2003). Some interesting examples of
CFD applications in pharmaceutical technology will be presented in the
following sections.
7.3.1 Inhaler development
Inhalers have been used for a long time for drug delivery to the lower
respiratory tract, in order to achieve local or systemic effects. Pressurized
metered-d ose inhalers (MDIs) have been extensively used in the treatment
of respiratory diseases, such as asthma, cystic fi brosis, emphysema, etc.
However, MDIs have certain disadvantages, such as the need for
coordination of MDI actuation and patient inhalation, high oropharyngeal
drug deposition, the absence of a dose counter, etc. These disadvantages,
together with environmental concerns regarding the use of
chlorofl uorocarbon (CFC) as propellants, have led to increased research
efforts directed towards development of alternative devices, such as dry
powder inhalers (DPIs). These inhalers release a metered quantity of
powder in the airfl ow, which is drawn through the device by the patient’s
inspiration. Besides the optimization of formulation and selection of an
appropriate metering system design, an important factor that determines
the performance and effi ciency of DPIs is fl ow path design. Namely, the
main limitation being attributed to these inhalers is pronounced
dependence of the dose being delivered on the inspiratory fl ow rate
(Prime et al., 1997).
CFD has been used to study the performance of MDIs and nebulizers
of various designs. However, DPI performance seems to be most
dependent on the airfl ow through the device, such as on the patient’s
inspiration, in order to achieve suffi cient turbulence to fl uidize the powder
bed. Therefore, DPIs represent interesting candidates for application of
CFD in the development process (Wong et al., 2012).
Coates et al. have extensively investigated the infl uence of various
design features on DPI performance by using CFD (Coates et al., 2004,
2005, 2006, 2007). An interesting study conducted by this research
group is related to the infl uence of grid structure and mouthpiece length
on device performance (Coates et al., 2004). A fl ow rate of 60 L/min,
which is the fl ow rate that can be easily achieved by the patient, was
applied in this study, and laser Doppler velocimetry techniques were used
for validation of computational results. Changes were made in the
structure of the complete grid, and two additional modifi ed grids were
obtained (F igure 7.5) . It was shown that grid structure signifi cantly
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Figure 7.5 Schematic representation of different grid structures:
(a) full grid case; (b) grid case 1; and (c) grid case 2
(reprinted from Coates et al., 2004; with permission
from John Wiley & Sons)
infl uenced the fl ow fi eld in the mouthpiece. With the increase of grid
voidage, the straightening effect of the grid on airfl ow decreased
( Figure 7.6) , leading to an increased amount of powder retained within
the device. The mouthpiece length was found to have less signifi cant
infl uence on inhaler performance, with slightly reduced device retention
in a shorter mouthpiece.
In one of the studies that followed, Coates et al. (2007) investigated the
infl uence of mouthpiece geometry on the extent of throat deposition and
on the amount of drug retained in the inhaler. CFD analysis was performed
Figure 7.6 CFD simulated particle tracks of dispersed powder:
(a) full grid case; (b) grid case 1; and
(c) grid case 2 (reprinted from Coates et al., 2004;
with permission from John Wiley & Son)
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at fl ow rates of 60 and 100 L/min, and models obtained were validated
using laser Doppler velocimetry techniques. Different mouthpiece
designs, cylindrical, conical, and oval, were analyzed. The authors found
pronounced infl uence of mouthpiece geometry on fl ow fi eld in the
mouthpiece, which affected the velocity of the exiting airfl ow. It was
shown that the axial component of the velocity vector, not the radial
component, controls the amount of throat deposition. It was demonstrated
that by minor changes in mouthpiece geometry, the amount of throat
deposition may be reduced.
Aerosolization in DPIs is based on the energy provided by the patient’s
inspiration, and in order to achieve drug delivery to the respiratory tract,
particles need to have an aerodynamic diameter of approximately 1 to
5 µ m. Particles within this size range have a high surface area, which
leads to high cohesive and adhesive forces, resulting in a poor
aerosolization effi ciency. Two common formulation approaches utilized
to overcome this problem are the carrier- based system and the
agglomeration- based system (Young et al., 2007). In the carrier- based
system, the micronized drug adheres to the larger carrier particle and
during inhalation separates from the carrier, after which it is inhaled into
the lungs, while the carrier particles are retained in the oropharynx. In
the agglomeration- based system, the micronized drug is agglomerated
with the micronized excipient, and during the patient’s inhalation,
turbulence and collisions between agglomerates and the inhaler walls
break the agglomerates, and both drug and the excipient are inhaled into
the lungs.
Wong et al. (2011b) investigated the infl uence of the grid structure on
mechanisms of break-u p and aerosolization in agglomeration-b ased DPI
systems. The authors designed various grids that differ in wire diameter
and aperture sizes, and applied CFD analysis to evaluate the infl uence of
impaction against a grid structure at different fl ow rates (60, 100, or
140 L/min) on agglomerate break-u p and aerosolization effi ciency. It was
found that impaction against the grid structure is the prevalent break-u p
mechanism when compared with turbulence generated by the grid. It was
shown that if the agglomerate passes through the center of the large grid
aperture without impacting upon the grid structure, it will encounter
minimal forces acting to break it up, because the turbulence kinetic
energy in the center of the grid aperture is small (F igure 7.7) . If the
agglomerate impacts upon the grid, it will break into fragments that will
be re- entrained in close proximity to the edges, that is, into regions of
high integral shear and turbulence kinetic energy, which act to further
break up these fragments. It was also found that at higher fl ow rates,
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Figure 7.7 Turbulence kinetic energy across the center plane of a
grid aperture at 140 L/min: (a) 1999 μ m; and
(b) 532 μ m grid aperture size (reprinted from Wong
et al., 2011b; with permission from John Wiley & Sons)
agglomerates impact upon the grid structure with greater force, and are
re-e ntrained into higher velocity fl ow fi elds, thus encountering stronger
turbulent shear fl ow. The authors emphasized the importance of the
optimal balance between aperture size, wire diameter, and grid void
percentage, in order to achieve effi cient break- up and aerosolization.
Donovan et al. (2012) investigated the infl uence of device design, size,
and morphology of carrier particles on performance of the carrier-b ased
DPI system. Carrier particle trajectories were modeled with CFD and the
results were compared with those obtained by in vitro drug deposition
studies. Two commercial DPIs with different geometries were used in the
study: the Aerolizer® (Plastiape S.p.A., Italy) and the Handihaler®
(Boehringer Ingelheim Inc., USA). Distinct differences in velocity profi les
and particle trajectories (F igure 7.8 ) within the two inhalers were
observed. It was found that fl uid fl ow within the Aerolizer® promotes
particle collisions with the inhaler wall and swirling particle motion inside
the mouthpiece. However, collisions are less frequent in the Handihaler,
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Figure 7.8 Carrier particle trajectory inside the inhaler at 60 L/min
(from left, d particle = 32, 108, and 275 μ m): (a) Aerolizer®,
(b) Handihaler® (reprinted from Donovan et al., 2012;
with permission from John Wiley & Sons)
and particles are accelerated and directed towards the inhaler wall and
then towards the inhaler exit, without any swirling motion. It was
observed that the number of particle-i nhaler collisions is more dependent
on carrier particle size in the case of the Aerolizer®, than in case of the
Handihaler®, with a greater number of collisions when larger carrier
particles were used. This was attributed to the presence of the swirling
motion and longer residence time inside the mouthpiece of the Aerolizer®.
Furthermore, the performance of the Aerolizer® was infl uenced by carrier
particle morphology, while performance of the Handihaler® was relatively
independent of surface roughness. Coupling the CFD simulations with i n
vitro results, the authors concluded that impaction- based forces are not
the dominant mechanism in drug detachment from carrier particles in the
Handihaler®, in contrast to the Aerolizer®, and therefore both physical
properties of the carrier and the predominant detachment mechanism
have to be taken into account when analyzing DPI performance.
7.3.2 Dissolution apparatus hydrodynamics
Since the 1960s and 1970s, when the importance of dissolution tests in
drug quality control assessment was recognized and extensive work was
done on development and standardization of dissolution apparatus, until
nowadays dissolution testing has become an indispensable tool for
quality control of various dosage forms, and the fi eld of its possible
applications has been considerably expanded (Dressman and Krämer,
2005). Dissolution testing is widely used in the pharmaceutical industry
for optimization of formulation, testing of batch- to-batch reproducibility,
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stability testing, obtaining marketing approval for new and generic drugs,
testing how the post-a pproval changes made to formulation or
manufacturing procedure affect drug product performance, development
of an in vitro- in vivo correlation, etc.
The choice of an appropriate dissolution apparatus and experimental
conditions is of great importance, as it can considerably affect the results.
Knowledge of the hydrodynamic conditions specifi c to the selected
dissolution apparatus is important, since small differences in
hydrodynamic conditions can result in misleading conclusions. However,
comprehensive knowledge of hydrodynamics, both i n vitro and in vivo ,
is still lacking (Dressman and Krämer, 2005). The results of the studies,
which will be presented in the following text, indicate that CFD can be
successfully applied for simulation, analysis, and gaining insight into the
hydrodynamic conditions present in different dissolution apparatuses.
The USP paddle apparatus is the most widely used dissolution
apparatus with a relatively simple design, but there are still problems
related to the reproducibility of the results and development of an in
vitro- in vivo correlation. This can be partly attributed to the complex
hydrodynamics, which are not well understood and seem to be variable
at different locations within the vessel. It was shown that small differences
in tablet position within the vessel can affect the hydrodynamics, leading
to pronounced differences in dissolution rates (Healy et al., 2002).
Extensive work has been carried out by a research group at the School of
Pharmacy, Trinity College, Dublin, to elucidate hydrodynamics in paddle
dissolution apparatus by using CFD simulations (McCarthy et al., 2003,
2004; D’Arcy et al., 2005). McCarthy et al. (2003) revealed the presence
of a low-v elocity domain directly below the center of the rotating paddle.
Interestingly, they found that this domain is surrounded by a high velocity
region, with 3- to 4-fold difference in fl uid velocity within a distance of
approximately 8 to 10 mm. The authors postulated that these pronounced
differences in fl uid velocities within a small area, where the dosage form
is located during the test, might be a reason for variable results. Indeed,
when a cylindrical tablet was placed at the bottom of the vessel, fl uid
fl ow was even more complicated (F igure 7.9) . The results of this study
indicate that CFD simulations can provide thorough information on
hydrodynamics throughout the dissolution vessel, in contrast to laser
Doppler measurements, which can provide limited information about
fl uid velocity values at certain positions in the vessel.
In the study that followed, McCarthy et al. (2004) applied CFD to
simulate the infl uence of paddle rotational speed on hydrodynamics in a
dissolution vessel. It was found that the magnitude of both axial and
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Figure 7.9 CFD simulations of fl uid fl ow: (a) below the paddle in
the USP dissolution apparatus at 50 rpm; and (b) in the
USP dissolution apparatus with a compact of 8.5 mm
height situated at the base of the vessel (reprinted from
McCarthy et al., 2003; with permission from Springer)
tangential components of velocity increased linearly with increase in
paddle rotational speed from 25 to 150 rpm. Application of CFD provided
an insight into the three-d imensional mixing route throughout the paddle
apparatus, which has not been possible to achieve with velocimetry
measurements. Path-l ines of fl uid mixing from a plane 0.5 mm above the
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base of the vessel revealed that there is no dead zone of mixing between
the regions above and below the paddle (at the level of the paddle), as
previously assumed. The authors also observed that the time needed for
complete mixing may largely differ, depending on the paddle rotational
speed applied (F igure 7.10) . They also simulated the fl uid fl ow around a
cylindrical compact positioned at the base of the vessel. It was found that
fl uid fl ow above the planar surface of a compact undergoes solid body
rotation. Fluid fl ow next to the curved surface was more complex, with
high shear rates for a region within approximately 3 mm from the base of
the compact, associated with a higher dissolution rate in this region.
D’Arcy et al. (2005) investigated the infl uence of different locations of
the cylindrical compacts of benzoic acid within the vessel on dissolution
rate and variability in dissolution results. CFD was used to examine the
relationship between variability in dissolution rate and variation in local
hydrodynamics. Cylindrical compacts (diameter 13 mm) were fi xed to one
of three positions: central (in the centre of the vessel base); position 1 (next
to the central position); and position 2 (next to the position 1). Dissolution
was investigated from top planar surface, from curved side surface, and
Figure 7.10 Path- lines of fl uid fl ow tracked with time for 5 seconds
from an initial plane 0.5 mm above the base of the
USP paddle dissolution vessel at 25, 50, 100, and
150 rpm (reprinted from McCarthy et al., 2004; with
permission from Springer)
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from compact with all surfaces exposed. A signifi cantly lower dissolution
rate from the central position compared to the dissolution rates from
positions 1 and 2 was observed, regardless of the compact surface exposed.
There was greater variability in dissolution results in case of control
compacts that were not fi xed during testing than in compacts that were
fi xed to one of three positions. It was concluded that small changes in case
of position within the area, where a dosage form is usually located during
testing, can result in noticeable differences in dissolution rate. It was also
found that CFD can be successfully applied to the interpretation of the
results. Namely, higher velocities were observed around the compacts in
off- center positions than in a central position. Furthermore, CFD
simulations of the compacts in positions 1 and 2 showed variations in
velocity gradients in the vicinity of the compact surface that infl uenced the
shape of the compact during dissolution. It was suggested that this could
be important in cases of coated or layered dosage forms, because all
surfaces would not be exposed to equal hydrodynamic conditions and
therefore would not dissolve at equal rates ( Figure 7.11 ).
Figure 7.11 Photograph of compact after undergoing dissolution
for 1 h in: (a) position 1 and (c) position 2. Velocity
vectors surrounding the compact in: (b) position 1 and
(d) position 2. Left side of the compact in (a) and (b) is
facing the center of the base of the vessel; the front of
the compact in (c) and (d) is facing the center of the
base of the vessel (reprinted from D’Arcy et al., 2005;
with permission from John Wiley & Sons)
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The basket dissolution apparatus (Apparatus 1) was the fi rst offi cial
dissolution apparatus, introduced into the USP in 1970. Despite its long
and wide application in dissolution testing, the hydrodynamics present in
this apparatus have not yet been fully clarifi ed. D’Arcy et al. (2006) used
CFD to simulate fl uid fl ow within the basket dissolution apparatus at
different stirring speeds. Results obtained by CFD simulations were
compared with results from fl ow visualization techniques and with
published ultrasound-p ulse-echo velocity data. It was shown that CFD
can give good predictions of fl uid fl ow within basket apparatus. Regions
of high velocity radiating from the side of the basket, and the area of low
velocity in the upper portion of the basket, were observed (F igure 7.12 ).
It was found that at the same rotational speed, the velocities present
inside the basket are of a similar (slightly lower) magnitude than those at
the base of the vessel of the paddle apparatus.
D’Arcy et al. also successfully applied CFD simulations for the analysis
of the hydrodynamics in fl ow- through apparatus (USP apparatus 4),
effects of hydrodynamics on mass transfer in a low velocity pulsing fl ow,
and the effects of the dissolved compounds on local hydrodynamics in
fl ow- through apparatus (D’Arcy et al., 2010, 2011).
Figure 7.12 Contours of velocity magnitude around the basket at
50 rpm (reprinted from D’Arcy et al., 2006; with
permission from Elsevier)
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7.3.3 Fluidized bed process simulation
Fluid bed processors are used in the pharmaceutical industry for various
unit operations, such as mixing, drying, granulation, and coating. Solid
particles in fl uid bed processors are fl uidized, that is, suspended in air that
moves upwards through the processing chamber and counteracts the
gravitational forces acting on the particle bed. Agglomeration/coating is
achieved by spraying the binder/coating liquid on fl uidized particles. There
are different types of fl uid bed processors and, depending on nozzle
position spraying can be performed from the top, from the bottom, or into
the bed in a tangential direction (Fukumori and Ichikawa, 2006; Dixit and
Puthli, 2009). Drying can be achieved by introducing hot air into the
fl uidized bed. The main advantage of the fl uid bed processor is the ability
to perform different unit operations within the same piece of equipment,
reducing the costs, processing time, and mass losses, which would be due
to the transfer from one piece of equipment to another. However, there are
numerous parameters that can affect the product quality, including
apparatus design (direction of fl uid fl ow, distributor plate design, processing
chamber geometry, type and position of nozzle, etc.), process (fl uidizing air
fl ow rate, fl uidizing air temperature and humidity, atomizing air pressure,
liquid fl ow rate, etc.), and formulation of related parameters (binder/
coating material type and quantity, binder/coating solvent type, powder
particle density, size distribution, shape, surface roughness, etc.) (Summers
and Aulton, 2007; Dixit and Puthli, 2009). Therefore, process optimization
usually requires laborious and extensive experimental work and thorough
process understanding, which is the main obstacle for the wider use of fl uid
bed processors in the pharmaceutical industry. Application of numerical
modeling techniques, such as CFD, might improve process understanding
and reduce the experimental work.
One of the most important factors affecting the effi ciency of the fl uid
bed process is the air fl ow and its distribution within the processing
chamber. An air distributor plate controls the movement and distribution
of the air entering the chamber, and thus the movement of particles.
Therefore, the air distributor plate design is one of the most critical
equipment related parameters, and different types of air distributor plates
have been designed (Dixit and Puthli, 2009). Depypere et al. (2004) used
CFD to investigate the effects of the air distributor design and the
upstream air supply system on the airfl ow in a top- spray fl uid bed
processor. CFD simulations were verifi ed by experimental methods,
using air mass fl ow rate, pressure drop, and inner wall temperature
recordings. CFD modeling revealed that the lateral air inlet results in a
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Computer-aided applications in pharmaceutical technology
Figure 7.13 CFD simulations of the airfl ow in cases of different
equipment designs: (a) pre- distributor; (b) ceramic ball
packing; and (c) bottom plenum air inlet (reprinted
from Depypere et al., 2004; with permission from
Elsevier)
non- homogeneous airfl ow towards the distributor, and possible
confi guration changes that might improve airfl ow conditions were
investigated. It was found that inclusion of a pre- distributor or ceramic
ball packing layer, or the relocation of the air inlet from the side to the
bottom of the chamber, could be potential solutions for achieving
homogeneous airfl ow conditions ( Figure 7.13 ).
The Wurster processor is a type of bottom-s pray fl uid bed processor
with characteristic design, making it suitable for tablet and pellet coating,
or it can be used for production of fi ne agglomerates (F igure 7.14) . It is a
kind of spouted bed system with a characteristic draft tube in a lower
central part of the processing chamber. An air distributor plate has a
larger area of the openings in the central region, below the draft tube,
leading to characteristic movement of particles within the chamber. The
particles fl uidized in the annular part, between the draft tube and the
chamber, are conveyed pneumatically in a vertical direction. The particles
are sprayed within the draft tube, and then particle velocity is reduced in
the upper expansion chamber, leading to the return of particles towards
the annular part, that is, towards the bottom of the fl uidizing chamber
(Fukumori and Ichikawa, 2006; Dixit and Puthli, 2009).
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Computational fl uid dynamics: applications in pharmaceutical technology
Figure 7.14 Schematic representation of a Wurster processor
Karlsson et al. (2009) used multiphase CFD to simulate particle and
gas motion, with detailed information about temperature and moisture
content. The simulation showed characteristic circulation of particles in
the processing chamber, which is in agreement with experimental
observations. It was found that the moisture content in the particle phase
decreases when the particles pass through the draft tube, showing that
most of the drying takes place in the Wurster tube ( Figure 7.15 ). Mass
transfer was also found to decrease with increase in height in the Wurster
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Computer-aided applications in pharmaceutical technology
Figure 7.15 Moisture content after 50 s simulation in: (a) particle
phase; and (b) gas phase (reprinted from Karlsson
et al., 2009; with permission from John Wiley & Sons)
tube, due to the increasing amount of moisture in the gas phase and the
decreasing relative velocity between the phases. Moisture evaporation
was followed by a temperature decrease in both the particle and gas
phases. The simulated moisture content and temperature of the air were
in good agreement with experimental measurements. The infl uence of
spray rate, inlet air temperature, and moisture content on drying was
investigated. It was found that higher air temperature gave rise to faster
drying, with no regions with saturated air, while higher spray rate and
higher moisture content in the inlet air resulted in larger regions of the air
saturated with water. Rajniak et al. (2009) used CFD coupled with a
population balance model to analyze gas–solid fl ow and granule growth
within a Wurster fl uid bed processor. The authors concluded that further
work is required for development of more effective algorithms for
solution of the CFD-PB models. They found that simulations with the
CFD-PB model are computationally demanding and still not practical for
fi tting to experiments, but can provide useful information that can be
used for development of simplifi ed models.
Fries et al. (2011) coupled the Discrete-Element-Method and CFD
simulations to develop a model combining gas and particle dynamics
with a simple model of particle wetting. The infl uence of the apparatus
geometry (Wurster vs. top- spray fl uid bed granulator) and process/
equipment related parameters was also analyzed. Simulation results
revealed considerable differences in particle motion and air velocity
inside the investigated granulators (F igure 7.16) . In the Wurster processor,
directed high velocity motion of the particles within the draft tube was
observed, while particle motion within the top-s pray granulator was
random. The average air velocity was lower in the top- spray granulator
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Computational fl uid dynamics: applications in pharmaceutical technology
Figure 7.16 Particle positions and velocity distributions inside:
(a) Wurster- coater: and (b) top- spray granulator, at the
simulation time t = 1.4 s (reprinted from Fries et al.,
2011; with permission from Elsevier)
then in the Wurster granulator. In order to investigate the effects of
particle and fl uid dynamics on particle wetting, the residence time of the
particles inside the spray zone was monitored. The Wurster granulator
was characterized by a narrow residence time distribution, resulting in
homogeneous particle wetting, while the top- spray granulator was
characterized by wide residence time distribution, due to the irregular
particle motion. It was shown that the velocity of the air injected via the
nozzle and position of the draft tube in the Wurster granulator can affect
fl uid and particle dynamics.
Chua et al. (2011) used theoretical analysis coupled with CFD
simulations to predict granule–granule and droplet–granule collision
rates of fl uidized bed melt granulation in a top-s pray granulator. CFD
simulations provided interesting information about hydrodynamics in
the region around the spray nozzle. Higher granular temperature was
observed around the spray nozzle, indicating higher collision rates in this
region ( Figure 7.17 ). Due to the atomizing air fl ow effects, granules
within the spray zone are rapidly pushed towards the bottom, resulting
in solids concentrated at the walls. The range of granule–granule and
droplet–granule collision rates was determined, and droplet–granule
collision was found to be much faster, but slowed exponentially when
moving away from the spray nozzle. The authors concluded that results
of this study, together with time scale analysis of droplet spreading and
solidifi cation, may improve understanding of the events occurring during
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Computer-aided applications in pharmaceutical technology
Figure 7.17 CFD simulations of the fl ow dynamics in fl uidized bed:
(a) granular temperature; (b) solid velocity magnitude;
and (c) solid concentration (reprinted from Chua et al.,
2011; with permission from Elsevier)
granulation and may be useful for qualitative and quantitative prediction
of aggregation rates.
7.4 Conclusion
With continuous improvements in computing power, CFD techniques are
expected to become a powerful tool used across different branches of
science. CFD is already being used in some industries, such as the
aerospace and automotive industries, but it is still expected to fi nd wide
applicability in the pharmaceutical industry. Some recent studies,
regarding the application of CFD in pharmaceutical technology, have
been presented in this chapter. Benefi ts of applying CFD methods in
pharmaceutical product/process development and optimization are
numerous and doubtless. However, it is worth noting that theoretical
background and experimental validation are prerequisites for reliable
CFD simulation.
7.5 References
Blazek , J . (2 005 ) C omputational Fluid Mechanics: Principles and Application .
Oxford, UK : Elsevier .
Calay , R.K. , Kurujareon, J. , and Holdø , A.E. ( 2002 ) ‘N umerical simulation of
respiratory fl ow patterns within human lung’ , R esp. Physiol. Neurobio. , 1 30 :
201 – 21 .
Chua , K.W. , Makkawi , Y.T., and Hounslow , M.J. ( 2011 ) ‘T ime scale analysis for
fl uidized bed melt granulation I: Granule–granule and granule–droplet
collision rates ’, Chem. Eng. Sci. , 66 : 318 – 26 .
Published by Woodhead Publishing Limited, 2013
256
Computational fl uid dynamics: applications in pharmaceutical technology
Coates , M .S. , F letcher, D .F. , C han , H .K. , and R aper , J .A. (2 004 ) ‘ Effect of design
on the performance of a dry powder inhaler using computational fl uid
dynamics. Part 1: Grid structure and mouthpiece length ’, J. Pharm. Sci., 9 3 :
2863 – 76 .
Coates , M .S. , C han , H .K. , F letcher, D .F. , and Raper , J .A. (2 005 ) ‘I nfl uence of air
fl ow on the performance of a dry powder inhaler using computational and
experimental analyses ’, P harm. Res. , 22 ( 9 ): 1445 – 53 .
Coates , M .S. , C han , H .K. , F letcher, D .F. , and R aper, J .A. (2 006 ) ‘E ffect of design
on the performance of a dry powder inhaler using computational fl uid
dynamics. Part 2: Air inlet size ’, J. Pharm. Sci. , 95 ( 6 ): 1382 –9 2 .
Coates , M .S. , C han , H .K. , F letcher , D .F , and Chiou , H . (2 007 ) ‘I nfl uence of
mouthpiece geometry on the aerosol delivery performance of a dry powder
inhaler ’, Pharm. Res. , 24 ( 8 ): 1450 – 6 .
D’Arcy , D.M. , Corrigan , O.I. , and Healy , A.M. (2 005 ) ‘H ydrodynamic simulation
(computational fl uid dynamics) of asymmetrically positioned tablets in the
paddle dissolution apparatus: impact on dissolution rate and variability ’, J .
Pharm. Pharmacol. , 57 : 1243 – 50 .
D’Arcy , D.M. , Corrigan , O.I. , and H ealy , A.M. ( 2006 ) ‘E valuation of
hydrodynamics in the basket dissolution apparatus using computational fl uid
dynamic – Dissolution rate implications ’, Eur. J. Pharm. Sci. , 27 : 259 – 67 .
D’Arcy , D .M., L iu , B . , B radley , G . , H ealy , A .M., and Corrigan , O .I. (2 010 )
‘ Hydrodynamic and species transfer simulations in the USP 4 dissolution
apparatus: considerations for dissolution in a low velocity pulsing fl ow ’,
Pharm. Res. , 27 ( 2 ): 246 – 58 .
D’Arcy , D .M. , L iu , B . , and C orrigan , O .I. (2 011 ) ‘ Investigating the effect of
solubility and density gradients on local hydrodynamics and drug dissolution
in the USP 4 dissolution apparatus ’, Int. J. Pharm. , 419 : 175 – 85 .
Depypere , F ., P ietersb , J .G. , and D ewettincka , K . (2 004 ) ‘ CFD analysis of air
distribution in fl uidised bed equipment ’, Powder Technol. , 145 : 176 – 89 .
Dixit , R. and P uthli , S. ( 2009) ‘F luidization technologies: aerodynamic principles
and process engineering ’, J. Pharm. Sci. , 98 : 3933 – 60 .
Donovan , M .J. , K im , S .H. , R aman , V . , and S myth , H .D. (2 012 ) ‘D ry powder
inhaler device infl uence on carrier particle performance ’, J. Pharm. Sci., 101 :
1097 – 107 .
Dressman , J . and K rämer, J . (eds) (2 005 ) P harmaceutical Dissolution Testing .
Boca Raton, FL : Taylor & Francis .
Fay , J.A. ( 1994 ) Introduction to Fluid Mechanics . Cambridge, MA : MIT Press .
Fries , L . , A ntonyuk , S . , H einrich , S . , and P alzer, S . (2 011 ) ‘ DEM–CFD modeling
of a fl uidized bed spray granulator’ , Chem. Eng. Sci. , 66 : 2340 – 55 .
Fukumori , Y. and Ichikawa , H. ( 2006 ) ‘ Fluid bed processes for forming functional
particles ’, in J. S warbrick (ed.) Encyclopedia of Pharmaceutical Technology ,
3rd edition. pp. 1773 – 9 . New York : Informa Healthcare .
Ghalati , P.F., Keshavarzian, E. , Abouali, O., Faramarzi , A. , Tu , J. , and Shakibafard ,
A. (2 012 ) ‘N umerical analysis of micro- and nano- particle deposition in a
realistic human upper airway ’, C omput. Biol. Med., 42 : 39 – 49 .
Healy , A .M. , M cCarthy , L .G. , G allagher, K .M., and C orrigan , O .I. (2 002 )
‘ Sensitivity of dissolution rate to location in the paddle dissolution apparatus ’,
J. Pharm. Pharmacol. , 54 : 441 – 4 .
Published by Woodhead Publishing Limited, 2013
257
Computer-aided applications in pharmaceutical technology
Jafari , A . , Z amankhan , P ., M ousavi , S .M. , and K olari, P . (2 009 ) ‘N umerical
investigation of blood fl ow. Part II: In capillaries ’, C ommun. Nonlinear Sci.
Numer. Simulat. , 14 : 1396 – 402 .
Karanjkar , A . (2 003 ) ‘ Design, development and optimization using computational
fl uid dynamics ’, Pharm. Technol. Europe , 15 ( 3 ): 42 – 4 .
Karlsson , S . , R amsuson , A . , v an Wachem, B. , and Björn , I .G. (2 009 ) ‘C FD
Modeling of the Wurster bed coater ’, A IChE J. , 55 ( 10 ): 2578 – 90 .
Kukura , J. , Arratia , P.E. , Szalai , E.S., Johnson , K.E. , and M uzzio , F.J.
( 2003 ) ‘ Experimental and computational methods for understanding
pharmaceutical fl ows, Part I: Laboratory scale devices ’, P harm. Technol.
Europe , 15 ( 3 ): 23 – 31 .
Löhner , R . , C ebral, J . , S oto , O . , Y im, P ., and B urgess , J .E. (2 003 ) ‘ Applications of
patient- specifi c CFD in medicine and life sciences’ , Int. J. Numer. Meth. Fluids ,
43 : 637 – 50 .
Makris , E . , N eofytoua , P ., T sangarisb, S . , and H ousiadas, C . (2 011 ) ‘ A novel
method for the generation of multi-b lock computational structured grids from
medical imaging of arterial bifurcations ’, M ed. Eng. Phys., doi:10.1016/j.
medengphy .12.004.
McCarthy , L.G. , Kosiol , C . , Healy , A.M. , Bradley , G., Sexton , J.C., and Corrigan ,
O.I. ( 2003 ) ‘S imulating the hydrodynamic conditions in the United States
Pharmacopeia paddle dissolution apparatus ’, A APS PharmSciTech, 4 ( 2 )
Article 22.
McCarthy , L.G. , Bradley , G. , Sexton , J.C. , Corrigan , O.I., and Healy, A.M.
( 2004 ) C omputational fl uid dynamics modeling of the paddle dissolution
apparatus: agitation rate, mixing patterns, and fl uid velocities’ , A APS
PharmSciTech , 5 ( 2 ): Article 31.
Na , Y., Chunga , K.S. , Chungb , S.K. , and Kim , S.K. ( 2012 ) ‘E ffects of single- sided
inferior turbinectomy on nasal function and airfl ow characteristics’ , R esp.
Physiol. Neurobi. , 180 : 289 – 97 .
Olivieri , L.J. , de Zelicourt, D.A. , Haggerty , C.M. , Ratnayaka , K., Cross , R.R. ,
and Yoganathan , A .P. (2 011 ) ‘H emodynamic modeling of surgically repaired
coarctation of the aorta ’, Cardiovasc. Eng. Technol. , 2 ( 4 ): 288 – 95 .
Pordal , H .S. , M atice , C .J. , and F ry , T .J. (2 002 ) ‘ Computational fl uid dynamics in
the pharmaceutical industry ’, Pharm. Technol. N. Am. , 26 ( 2 ): 72 – 9 .
Prime , D . , A tkins, P .J., S later, A . , and Sumby , B . (1 997 ) ‘ Review of dry powder
inhalers ’, Adv. Drug Deliv. Rev. , 26 : 51 – 8 .
Rajniak , P. , Stepanek , F. , D hanasekharan , K. , Fan , R. , Mancinelli, C. , and
Chern , R .T. (2 009 ) ‘A combined experimental and computational study of
wet granulation in a Wurster fl uid bed granulator ’, Powder Technol., 1 89 ( 2 ):
190 – 201 .
Sayma , A. ( 2009 ) Computational Fluid D ynamics, 1st edition. D enmark :
Abdulnacer Sayma & Ventus Publishing ApS .
Segal , R.A. , Kepler, G.M. , and K imbell , J.S. ( 2008 ) ‘E ffects of differences in nasal
anatomy on airfl ow distribution: a comparison of four individuals at rest’ ,
Ann. Biomed. Eng. , 36 ( 11 ): 1870 – 82 .
Sforza , D.A., Putman , C.M. , and Cebral , J.R. ( 2012 ) ‘C omputational fl uid
dynamics in brain aneurysms’ , I nt. J. Numer. Meth. Biomed. Engng., 28 ( 6 – 7 ):
801 – 8 .
Published by Woodhead Publishing Limited, 2013
258
Computational fl uid dynamics: applications in pharmaceutical technology
Summers , M .P. and A ulton , M .E. (2 007 ) Granulation, in: Aulton’s Pharmaceutics
– The Design and Manufacture of Medicines, 3rd edition. pp. 4 10 – 24 .
Edinburgh, UK : Churchill Livingstone Elsevier
Wong , G .K.C. and Poon , W .S. ( 2011 a) ‘C urrent status of computational fl uid
dynamics for cerebral aneurysms: the clinician’s perspective’ , J. Clin. Neurosci. ,
18 : 1285 – 8 .
Wong , W ., F letcher, D .F. , T raini, D . , C han , H .K. , C rapper , J ., and Young , P .M.
( 2011 b) ‘P article aerosolisation and break-u p in dry powder inhalers:
evaluation and modelling of the infl uence of grid structures for agglomerated
systems ’, J. Pharm. Sci. , 100 : 4710 – 21 .
Wong , W ., F letcher, D.F. , T raini , D . , C han , H .K., and Young , P .M. (2 012 ) ‘T he
use of computational approaches in inhaler development ’, A dv. Drug Deliv.
Rev. , 64 : 312 – 22 .
Yang , X .L. , L iu , Y ., and L uo , H .Y. (2 006 ) ‘ Respiratory fl ow in obstructed
airways ’, J. Biomech. , 39 : 2743 – 51 .
Young , P.M. , Traini , D. , and Edge , S. ( 2007 ) ‘ Advances in pulmonary therapy ’, in
R.O. Williams , D.Y. Taft , and J .T. McConville (eds) A dvanced Drug
Formulation Design to Optimize Therapeutic Outcomes. pp. 1 – 51 . New
York : Informa Healthcare .
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