Chapter 7: Computational fluid dynamics: applications in pharmaceutical technology – Computer-Aided Applications in Pharmaceutical Technology

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Computational fluid dynamics: applications in pharmaceutical technology

Ivana Masic, Jelena Parojcic and Zorica Djuric,     Department of Pharmaceutical Technology Cosmetology, Faculty of Pharmacy, University of Belgrade

Abstract:

This chapter introduces the concept of computational fluid dynamics (CFD) and its applications in pharmaceutical technology. Basic theoretical explanations on the mathematics of fluid flow 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 fluidized bed process simulations are presented.

Key words

Computational fluid dynamics (CFD)

numerical grids

fluid flow

inhalers

dissolution apparatus hydrodynamics

fluid bed processes

7.1 Introduction

Fluid mechanics studies fluid performance at rest and in motion. It can be divided into: fluid statics, the study of fluids at rest; fluid kinematics, the study of fluid in motions; and fluid dynamics, which deals with the effects of forces on fluid motion. With the evolution in computer technology, a branch of fluid dynamics called computational fluid dynamics (CFD) has become a powerful and cost-effective tool for simulating real fluid flow.

The explanations for many natural phenomena, such as river flows, ocean waves, wind currents, functioning of the human body (e.g. cardiovascular and pulmonary system), lie in the field of fluid 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 fluid mechanics in the field of biomedicine. For example, some of the procedures used in treatment of blood vessel obstruction (e.g. stenting, balloon angioplasty, in situ drug delivery for unclotting, bypass surgery, etc.) have statistically significant failure rates, which indicates a need for a patient-specific approach and detailed study of fluid dynamics before and after intervention. The prediction and modeling of flows in vascular and pulmonary systems on a patient-specific basis is still an obstacle, but it is becoming more likely that CFD will find its place in enhanced diagnosis and planning of surgical procedures (Löhner et al., 2003). CFD simulations may give valuable information regarding characteristics of blood flow under complex flow conditions, as well as deformation and flow of erythrocytes in microcirculation (Jafari et al., 2009). In combination with medical imaging techniques, CFD might be a powerful tool for patient-specific simulation of blood flow 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 airflow and particle transport through the asymmetrically branched airways structure (Calay et al., 2002). CFD has also been successfully applied in the study of flow field 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 inflammation that leads to narrowing and obstruction of the airways, which significantly affects the airflow. CFD can serve as an effective tool in clarifying the flow 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 airflow, which may further affect the amount of inhaled gases and particles. Also, certain types of nasal morphology can result in increased flow 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 influence of post-surgical changes of nasal anatomy on airflow characteristics was also investigated numerically using CFD, which might be a relatively fast and efficient 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 scientific results and to give an insight into the possibilities for application in this field. 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 field 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 fluid dynamics that deals with finding numerical solutions to equations describing the fluid flow to obtain a numerical description of the entire flow field. CFD offers significant time and cost savings, as well as comprehensive information about fluid flow 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 difficult to perform experimental tests. In accordance with the applicability and advantages offered by this method, a number of commercial CFD software packages are now available.

CFD is based on the analysis of fluid flow 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 fluid flow 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 flow quantities at the grid points (Sayma, 2009).

CFD software packages are based on highly complex nonlinear mathematical expressions derived from fundamental equations of fluid flow, heat, and mass transfer, and can be solved by complex algorithms built into the program. Fluid flow in a given system can be simulated for defined inlet and outlet conditions (also called boundary conditions). Modeling outputs are usually presented numerically or graphically.

7.2.1 Mathematical description of the fluid flow

The kind of equations describing fluid flow are differential equations, which represent the relationship between flow variables and their evolution in time and space. Basic equations of fluid flow include Euler’s equations for inviscid flow and Navier–Stokes equations for laminar flow of viscous fluid. With appropriate modifications, the Navier–Stokes equations can also be used for turbulent flow. Namely, the variation in time for turbulent flow 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 flow quantity is determined in a time interval that is sufficiently large to neglect small variations, but sufficiently small to take into account large, significant variations. The Reynolds-averaged Navier–Stokes equations are based on this principle, and represent the primary means for describing turbulent flows. 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 flow governing equations and turbulent modeling methods can be found in numerous fluid mechanics textbooks.

7.2.2 Discretization of the flow governing equations

In order to solve the system of differential equations representing the flow, the first step is to define 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 flow at the grid points and interdependency of flow at those points and their neighboring points. The values of the flow 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 finite difference method, the finite element method, and the finite volume method. In unsteady flow, when the solution at a discrete point varies with time, discretization of time dimensions may also be needed (Blazek, 2005; Sayma, 2009).

The finite difference method is the simplest and among the first 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 flow 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 Δx (Figure 7.1). The value of the dependent 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 Δx (Blazek, 2005; Sayma, 2009).

Figure 7.1 Illustration of finite difference grid

The finite element method, as a method for solving partial differential equations, was developed between 1940 and 1960, and its application was later extended to fluid flow problems. Unlike the finite difference method, the finite 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 finite difference method requires only the values of the variables at grid nodes, without information about behavior between the nodes, while the finite element method takes into account variations within each element. The finite element method involves discretization of computational domain and discretization of differential equations. Discretization of the spatial domain considers its subdivision into non-overlapping elements of various shapes. In two-dimensional problems, triangular or rectangular elements are commonly used, while the most common element types for three-dimensional problems are the tetrahedral, hexahedral, and prismatic elements (Figure 7.2). Each element is formed by connecting a number of nodes/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 field 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).

Figure 7.2 Example of: (a) triangular; (b) tetrahedral; and (c) prismatic element

The finite 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 flow 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 flexibility. It can be applied both in the case of structured and unstructured networks, making it suitable for flow 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 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 flows, 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).

Figure 7.4 Illustration of: (a) structured; and (b) unstructured grid

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; 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-dose inhalers (MDIs) have been extensively used in the treatment of respiratory diseases, such as asthma, cystic fibrosis, 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 chlorofluorocarbon (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 airflow, 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 efficiency of DPIs is flow path design. Namely, the main limitation being attributed to these inhalers is pronounced dependence of the dose being delivered on the inspiratory flow 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 airflow through the device, such as on the patient’s inspiration, in order to achieve sufficient turbulence to fluidize 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 influence 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 influence of grid structure and mouthpiece length on device performance (Coates et al., 2004). A flow rate of 60 L/min, which is the flow 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 modified grids were obtained (Figure 7.5). It was shown that grid structure significantly influenced the flow field in the mouthpiece. With the increase of grid voidage, the straightening effect of the grid on airflow decreased (Figure 7.6), leading to an increased amount of powder retained within the device. The mouthpiece length was found to have less significant influence on inhaler performance, with slightly reduced device retention in a shorter mouthpiece.

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)

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)

In one of the studies that followed, Coates et al. (2007) investigated the influence of mouthpiece geometry on the extent of throat deposition and on the amount of drug retained in the inhaler. CFD analysis was performed at flow 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 influence of mouthpiece geometry on flow field in the mouthpiece, which affected the velocity of the exiting airflow. 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 μm. Particles within this size range have a high surface area, which leads to high cohesive and adhesive forces, resulting in a poor aerosolization efficiency. 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 influence of the grid structure on mechanisms of break-up and aerosolization in agglomeration-based DPI systems. The authors designed various grids that differ in wire diameter and aperture sizes, and applied CFD analysis to evaluate the influence of impaction against a grid structure at different flow rates (60, 100, or 140 L/min) on agglomerate break-up and aerosolization efficiency. It was found that impaction against the grid structure is the prevalent break-up 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 (Figure 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 flow rates, agglomerates impact upon the grid structure with greater force, and are re-entrained into higher velocity flow fields, thus encountering stronger turbulent shear flow. The authors emphasized the importance of the optimal balance between aperture size, wire diameter, and grid void percentage, in order to achieve efficient break-up and aerosolization.

Figure 7.7 Turbulence kinetic energy across the center plane of a grid aperture at 140 L/min: (a) 1999 |jm; and (b) 532 jm grid aperture size (reprinted from Wong et al., 2011b; with permission from John Wiley & Sons)

Donovan et al. (2012) investigated the influence of device design, size, and morphology of carrier particles on performance of the carrier-based 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 profiles and particle trajectories (Figure 7.8) within the two inhalers were observed. It was found that fluid flow 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, 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-inhaler 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 influenced by carrier particle morphology, while performance of the Handihaler® was relatively independent of surface roughness. Coupling the CFD simulations with in 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.

Figure 7.8 Carrier particle trajectory inside the inhaler at 60 L/min (from left, dparticle = 32, 108, and 275 μm): (a) Aerolizer®, (b) Handihaler® (reprinted from Donovan et al., 2012; with permission from John Wiley & Sons)

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 field 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, stability testing, obtaining marketing approval for new and generic drugs, testing how the post-approval 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 specific to the selected dissolution apparatus is important, since small differences in hydrodynamic conditions can result in misleading conclusions. However, comprehensive knowledge of hydrodynamics, both in 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-velocity 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 fluid velocity within a distance of approximately 8 to 10 mm. The authors postulated that these pronounced differences in fluid 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, fluid flow was even more complicated (Figure 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 fluid velocity values at certain positions in the vessel.

Figure 7.9 CFD simulations of fluid flow: (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)

In the study that followed, McCarthy et al. (2004) applied CFD to simulate the influence of paddle rotational speed on hydrodynamics in a dissolution vessel. It was found that the magnitude of both axial and 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-dimensional mixing route throughout the paddle apparatus, which has not been possible to achieve with velocimetry measurements. Path-lines of fluid mixing from a plane 0.5 mm above the 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 (Figure 7.10). They also simulated the fluid flow around a cylindrical compact positioned at the base of the vessel. It was found that fluid flow above the planar surface of a compact undergoes solid body rotation. Fluid flow 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.

Figure 7.10 Path-lines of fluid flow 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)

D’Arcy et al. (2005) investigated the influence 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 fixed 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 from compact with all surfaces exposed. A significantly 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 fixed during testing than in compacts that were fixed 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 influenced 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)

The basket dissolution apparatus (Apparatus 1) was the first official 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 clarified. D’Arcy et al. (2006) used CFD to simulate fluid flow within the basket dissolution apparatus at different stirring speeds. Results obtained by CFD simulations were compared with results from flow visualization techniques and with published ultrasound-pulse-echo velocity data. It was shown that CFD can give good predictions of fluid flow 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 (Figure 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.

Figure 7.12 Contours of velocity magnitude around the basket at 50 rpm (reprinted from D’Arcy et al., 2006; with permission from Elsevier)

D’Arcy et al. also successfully applied CFD simulations for the analysis of the hydrodynamics in flow-through apparatus (USP apparatus 4), effects of hydrodynamics on mass transfer in a low velocity pulsing flow, and the effects of the dissolved compounds on local hydrodynamics in flow-through apparatus (D’Arcy et al., 2010, 2011).

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 fluid bed processors are fluidized, 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 fluidized particles. There are different types of fluid 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 fluidized bed. The main advantage of the fluid 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 fluid flow, distributor plate design, processing chamber geometry, type and position of nozzle, etc.), process (fluidizing air flow rate, fluidizing air temperature and humidity, atomizing air pressure, liquid flow 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 fluid 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 efficiency of the fluid bed process is the air flow 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 airflow in a top-spray fluid bed processor. CFD simulations were verified by experimental methods, using air mass flow rate, pressure drop, and inner wall temperature recordings. CFD modeling revealed that the lateral air inlet results in a non-homogeneous airflow towards the distributor, and possible configuration changes that might improve airflow 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 airflow conditions (Figure 7.13).

Figure 7.13 CFD simulations of the airflow 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)

The Wurster processor is a type of bottom-spray fluid bed processor with characteristic design, making it suitable for tablet and pellet coating, or it can be used for production of fine agglomerates (Figure 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 fluidized 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 fluidizing chamber (Fukumori and Ichikawa, 2006; Dixit and Puthli, 2009).

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 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 influence 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 flow and granule growth within a Wurster fluid 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 fitting to experiments, but can provide useful information that can be used for development of simplified models.

Figure 7.15 Moisture content after 50s simulation in: (a) particle phase; and (b) gas phase (reprinted from Karlsson et al., 2009; with permission from John Wiley & Sons)

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 influence of the apparatus geometry (Wurster vs. top-spray fluid 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 (Figure 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-spray granulator was random. The average air velocity was lower in the top-spray granulator then in the Wurster granulator. In order to investigate the effects of particle and fluid 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 fluid and particle dynamics.

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)

Chua et al. (2011) used theoretical analysis coupled with CFD simulations to predict granule–granule and droplet–granule collision rates of fluidized bed melt granulation in a top-spray 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 flow 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 solidification, may improve understanding of the events occurring during granulation and may be useful for qualitative and quantitative prediction of aggregation rates.

Figure 7.17 CFD simulations of the flow dynamics in fluidized bed: (a) granular temperature; (b) solid velocity magnitude; and (c) solid concentration (reprinted from Chua et al., 2011; with permission from Elsevier)

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 find wide applicability in the pharmaceutical industry. Some recent studies, regarding the application of CFD in pharmaceutical technology, have been presented in this chapter. Benefits 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.

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