cfd simulations of the andersen cascade impactor: model development and effects of aerosol charge

Aerosol Science 40 (2009) 807 -- 822

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Aerosol Science

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CFD simulations of the Andersen cascade impactor: Model development andeffects of aerosol charge

Samir Vinchurkara, P. Worth Longesta,b,∗, Joanne Peartb

aDepartment of Mechanical Engineering, Virginia Commonwealth University, Richmond, VA, USAbDepartment of Pharmaceutics, Virginia Commonwealth University, Richmond, VA, USA

A R T I C L E I N F O A B S T R A C T

Article history:Received 5 February 2009Received in revised form20 May 2009Accepted 21 May 2009

Keywords:Andersen cascade impactorComputational fluid dynamicsImage forceElectrostatic chargeAerosol size assessmentMetered dose inhalersDry powder inhalersAerosol characterization

Cascade impactors are commonly used to assess the size characteristics of aerosols in toxi-cology and pharmaceutical applications. These aerosol instruments have been developed andrefined over decades. However, a number of questions remain related to impactor perfor-mance, including the influence of electrostatic charge on measured size distributions. Theobjective of this study was to develop a validated CFD model of the Mark II Andersen cascadeimpactor (ACI) and apply thismodel to evaluate the effects of particle charge ondeposition. Theflow field was simulated using a commercial CFD code for incompressible laminar and transi-tional flows. Particle trajectories and depositionwere evaluated using awell tested Lagrangiantracking approach that accounts for impaction, sedimentation, diffusion, and electrostatic at-traction. Particle charge levels typical of dry powder inhaler (DPI) and metered dose inhaler(MDI) aerosols were considered for a particle size range of 0.3–12�m. As a model validation,computational predictions of cutoff d50 diameters for each of the eight ACI stages were foundto be within 10% difference of existing experimental and manufacturer data. Results indicatedthat charges consistent with DPI and MDI aerosols increased deposition fraction in Stages 0–3by up to 30% and increased deposition fraction in Stages 4–7 by up to an order of magnitude.For Stages 0–3, both DPI and MDI charges reduced the d50 value by approximately 10% or less.In contrast, charged aerosols reduced the d50 values in Stages 4 and 5 by 200% and 60%, respec-tively. All charged submicrometer aerosols considered deposited in Stages 6 and 7. Increasingthe particle charge by an order of magnitude from DPI to MDI values had a relatively smalleffect on further decreasing the cutoff size of each stage. In conclusion, these results can beused to approximate the actual aerodynamic diameter of a charged pharmaceutical aerosolbased on measurements in a standard ACI. Future applications of the developed ACI modelinclude evaluating the influence of space charge on deposition and quantifying the effects ofaerosol condensation and evaporation on size assessment.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Cascade impactors are frequently employed to evaluate the aerodynamic mass-weighted size distributions of aerosols from avariety of sources. For example, cascade impactor testing is the standardpractice for determining the aerosol size distribution fromrespiratory drug delivery devices, such as dry powder inhalers (DPIs), metered dose inhalers (MDIs), nebulizers, and new softmisttechnologies (USP, 2005). Similarly, cascade impactors are frequently used to assess the size distribution of environmental

∗ Corresponding author at: Department of Mechanical Engineering, Virginia Commonwealth University, 601West Main Street, P.O. Box 843015, Richmond, VA23284-3015, USA. Tel./fax: +18048277023.

E-mail address: [email protected] (P.W. Longest).

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808 S. Vinchurkar et al. / Aerosol Science 40 (2009) 807 -- 822

pollutants (e.g., combustion products) and bioaerosols (e.g., airborne viruses and bacteria) (Hinds, 1999; Kittelson, 1998). Anaccurate determination of the size distribution for these aerosols is essential to predict inhalability, the occurrence and site ofdeposition in the respiratory tract, uptake into the tissue and blood, and subsequent drug effectiveness or potential adversehealth effects. High flow rate (Q � approximately 30 L/min) cascade impactors that are frequently implemented in the fields ofinhaled drug delivery and toxicology include the Mark II Andersen Cascade Impactor (ACI) and the Next Generation Impactor(NGI). The NGI was developed specifically for pharmaceutical aerosol testing applications with appropriate stage cut pointsover a wide range of flow rates and minimal overlaps in the collection efficiency curves (Marple et al., 2003). However, the ACIremains widely used for testing aerosol size characteristics in both pharmaceutical and toxicological applications (Dunbar &Mitchell, 2005; Garmise & Hickey, 2008; Holzner & Muller, 1995; Janssens, de Gongste, Hop, & Tiddens, 2003; Longest, Hindle,Das Choudhuri, & Byron, 2007; Marple, 2004; Nichols, Brown, & Smurthwaite, 1998; Nichols & Smurthwaite, 1998; Stein, 1999,2008; Veranth et al., 2000).

Theoretical and numerical studies have been conducted to evaluate the effects of impactor design and flow conditions onthe determination of aerosol size distributions. Several primary studies described the underlying principles governing impactordesign (Andersen, 1966; Cohen & Montan, 1967; Lundgren, 1967). Subsequent studies focused on improving and characterizingthe performance of impactors, aswell as developing impactors for specific applications (Marple, 2004;Marple & Liu, 1974;Marple& Liu, 1975; Marple & Willeke, 1976a; Rader & Marple, 1984; Swanson, Muzzio, Annapragada, & Adjei, 1996; VanOort, Downey,& Roberts, 1996; Vaughan, 1989).

Numerous experimental studies have assessed the performance of the ACI. Mitchell, Costa, andWaters (1988) experimentallystudied the deposition of 10�m particles in a calibrated Mark II ACI impactor attached to a pre-separator. This study concludedthat for particles in the size range of 10�m and above, wall losses could account for up to 20% of the total deposited mass, andthat the wall losses increased significantly with moisture content of the aerosol particles. Vaughan (1989) calibrated the ACI anddetermined that S-shaped size distribution curves for particle deposition on individual stages and wall losses between stagescompared well with the manufacturer's data. This study concluded that removing preceding stages increased wall losses, butnegligibly affected the assessed size distribution. The higher end of wall losses was reported to be in the range of 20–40% ofthe total mass of initial particles. Dunbar, Kataya, and Tiangbe (2005) experimentally analyzed the effects of particle bounce,entrainment, and overload on uncoated impactor plates using large porous placebo particles and concluded that there weresignificant differences between the mass median aerodynamic diameter and geometric standard deviation of the ACI and amultistage liquid impinger. Roberts and Romay (2005) studied the ACI and NGI and recommended regular measurements ofnozzle diameters on each stage of the impactor. Stein and Olson (1997) studied 14 different ACIs to test the reproducibilityof particle size distribution results obtained experimentally and compared the results to theoretically obtained data. The sizedistributions were significantly different for variousMark II ACI impactors because of differences in stage cutoff values associatedwith usage and particle accumulation.

No available CFD study has considered the performance of a high flow rate impactor, such as the widely used ACI. Theonly previous CFD study to evaluate impactor performance was conducted by Swanson et al. (1996) for a low flow rate device(240mL/min) with one orifice per stage, which was referred to as the PC-2 impactor. This analysis included the effects of gravity,inertia and viscous friction. Sticking probability and restitution were defined for the model and S-shaped particle depositioncurves were obtained. Particles within a critical size range were observed to be trapped in recirculation zones close to theimpactor walls. This study illustrates the utility of CFD analysis to evaluate and potentially improve the performance of impactorsand other aerosol characterization devices. However, high flow rate impactors like the ACI and NGI can have on the order of 500nozzles in a single stage resulting in significantly more complex flow patterns compared with a single nozzle design, especiallynear the collection plates (Fang, Marple, & Rubow, 1991). It is expected that interactions among the jets and differences in flowvelocities and system geometries prevent the results of Swanson et al. (1996) from being directly extrapolated to analyze higherflow rate systems with multiple nozzles.

Considering the performance of impactors like the ACI, a number of open questions remain. In the airflow field, unknownsinclude the degree of flow distribution among jets of a single stage, the amount of flow recirculation, and airflow characteristicsresponsible forwall losses. Size change of aerosolswithin the impactor due to hygroscopic growth or evaporation is also known toinfluence impactor performance (Stein, 2008). However, the extent of these effects have not been fully quantified. Furthermore,standard pharmaceutical aerosols from DPI and MDI devices as well as some environmental particles are known to carry asignificant electrostatic charge (Buckley, Wright, & Henshaw, 2008; Byron, Peart, & Staniforth, 1997; Kwok & Chan, 2007; Kwok,Chan, & Glover, 2005; Peart, 2001; Peart & Byron, 1999; Peart, Staniforth, & Meakin, 1995). Aerosol charge is reported to have aneffect on deposition in aerosol generation (Janssens et al., 2004; Mitchell, Coppolo, & Nagel, 2007) and sampling (de Juan et al.,1997) devices, themouth-throat region (Ali, Reddy, &Mazumder, 2007), as well as in the lungs (Balachandran, Kulon, Koolpiruck,Dawson, & Burnel, 2003; Cohen, Xiong, Asgharian, & Ayres, 1995; Cohen, Xiong, Fang, & Li, 1998) based on image and space chargeeffects (Finlay, 2001). However, the extent of aerosol charge on deposition in the ACI has not been quantified. As a result, sizesampling un-neutralized aerosols with an ACI may produce a size distribution that is affected by both the particle aerodynamicdiameter and electrostatic effects in the impactor. These impactor performance issues are difficult to address and quantify usingonly experimental techniques. However, a CFD model of the ACI can readily determine the internal airflow characteristics, theeffects of recirculation on wall losses, and the effects of aerosol charge on deposition.

The objective of this study is to develop a validated CFD model of the Mark II Andersen cascade impactor that can be usedto assess performance and highlight internal transport characteristics. Validation of the CFD model is based on comparisons

S. Vinchurkar et al. / Aerosol Science 40 (2009) 807 -- 822 809

of numerically predicted cutoff diameters at each stage with existing experimental and manufacturer data. To illustrate theutility of this model, the effects of particle charge values consistent with standard pharmaceutical aerosols on deposition areinvestigated. Specifically, charge levels typical of MDI and DPI generated aerosols are considered for a particle size range ofapproximately 0.3–12�m. The effect of aerosol charge is assumed to influence deposition through the interaction of the particleand a neutral conducting wall, i.e., the image charge is considered and space charge effects are neglected. The impactor geometryconsists of the European and United States Pharmacopeia (Ph. Eur/USP) induction port (IP) and eight stages of the ACI. Theflow field is simulated using a commercial CFD code for incompressible laminar and transitional flow. Particle trajectories anddeposition are evaluated using a well tested Lagrangian tracking approach that accounts for impaction, sedimentation, diffusion,and electrostatic attraction and has been corrected for near-wall interpolation effects (Longest et al., 2007; Longest & Vinchurkar,2007b; Longest & Xi, 2007). Results of this study will help to characterize the flow field dynamics inside the ACI and to quantifythe effects of aerosol charge on measured size characteristics. Furthermore, the model developed in this study illustrates theuse of CFD to potentially improve impactor performance and to develop new aerosol characterization devices for a variety ofapplications.

2. Methods

2.1. The Andersen cascade impactor

TheMark II Andersen cascade impactor considered in this study consists of 8 stages and a backup filter. A representative MarkII ACI is shown in Fig. 1 with a standard induction port. The IP is a tubular geometry with a 90◦ bend that is used to direct aerosolsfrom inhalation devices into the impactor (USP, 2005). Each impactor stage consists ofmultiple nozzles that direct air and particlesonto a collection plate. Aerosols are captured on the collection plates by impaction as a function of their aerodynamic size andthe characteristics of the nozzles. Stage 0 is the upper stage of the impactor and is designed to capture particles greater thanapproximately 9.0�m. The remaining stages have progressively smaller diameter jets, which result in higher velocities and theimpaction of smaller aerodynamic particle sizes. Table 1 provides some details of the individual ACI stages including the numberof nozzles, nozzle diameters, and nozzle velocities as provided by the manufacturer (Andersen Inc., 1985). Additional parametersare characterized by the studies of Marple andWilleke (1976b) and Fang et al. (1991). As shown in Table 1, the number of nozzlesper stage ranges from 96 to 400. The use of multiple nozzles in the ACI allows for a high flow rate while maintaining laminar jetconditions. The diameters of the ACI nozzles vary from approximately 2.6mm in Stage 0 to 0.25mm in Stages 6 and 7. The ACI is

Fig. 1. Eight stage Mark II Andersen cascade impactor (ACI), showing Stage 0, Stage 1 and the induction port (IP) separated from the assembly.


Table 1Characteristics of the Mark II Andersen cascade impactor (ACI) based on the manufacturer's data (Andersen Inc., 1985).

Stage No. of nozzles dn (m) Arean (m2) Areatotal (m2) Flow raten (m3/s) veln (m/s) Ren Mach no.

0 96 0.00255 5.1 E−6 4.9 E−4 4.87 E−6 0.955 154 0.0021 96 0.00188 2.77 E−6 2.66 E−4 4.87 E−6 1.758 208 0.0052 400 0.00091 2.62 E−7 2.62 E−4 1.17 E−6 1.8 104 0.0053 400 0.00071 1.59 E−7 1.59 E−4 1.17 E−6 2.939 132 0.0084 400 0.00053 8.9 E−7 8.9 E−5 1.17 E−6 5.246 176 0.0155 400 0.00034 3.67 E−8 3.67 E−5 1.17 E−6 12.72 274 0.0366 400 0.00025 2.02 E−8 2.02 E−5 1.17 E−6 22.94 367 0.0667 201 0.00025 1.01 E−8 1.01 E−5 2.32 E−6 45.49 728 0.132

The subscript n represents the nozzle conditions of each stage.

designed to operate at a flow rate of 28.3 L/min, or 1 ACFM. At this flow rate, the jet Reynolds numbers range from 154 in Stage 0to 728 in Stage 7. Based on Mach number values (Table 1), incompressible flow is expected for all stages (i.e.,M< 0.3); however,the Mach number is above 0.1 in Stage 7 indicating relatively high velocity conditions.

Particles exit the nozzle section of each stage and pass near the collection plates, which are disk-shaped with a diameter of8.255 cm. Particles with sufficient inertia cross the flow field streamlines of the jets and deposit on the collection plates. Themassof particles depositing on each plate is then determined either by weight or by chemical analysis. The heights between the nozzleoutlets and collection plates are 1.02mm for Stages 0 and 1, and 2.15mm for the remaining stages. As a result, very small spacialdistances are required for successful operation of the ACI. Furthermore, particles are in close proximity to the collection plates fora significant fraction of time while in the impactor. The proximity of particles to the collection plate may result in deposition bymechanisms other than impaction and gravitational settling. For example, de Juan et al. (1997) discussed enhanced deposition onimpactor stages arising fromBrownianmotion of ultrafine aerosols and electrostatic charge. Excess deposition due to electrostaticattraction may result in increased mass in the upper impactor stages, and a polydisperse aerosol may be characterized as havinga size distribution different from its aerodynamic distribution based on impaction alone. However, deposition as a function ofboth aerodynamic aerosol size and particle charge has not been quantified.

2.2. Computational geometry and mesh

A computational geometry andmeshwere created for the IP and each impactor stage. As shown in Fig. 2, the IP was generatedwith one plane of symmetry and Stages 1–7 were generated with two planes of symmetry. Stage 0 was constructed with onesymmetry plane to allow for the consideration of the asymmetric inlet profile from the IP. Other than the inclusion of symmetryplanes, the computational models were identical to the Mark II ACI for Stages 0–7. Fig. 2 shows the computational geometry ofthe IP and Stages 0–3. The symmetry planes of each stage indicate the nozzles along the boundary and the thin collection plates.Due to the presence of the symmetry planes, the number of nozzles simulated in each stage is consistent with the values givenin Table 1 divided by 2 (for Stage 0) or 4 (for the remaining stages). It is noted that the collection plates of Stages 0 and 1 in theMark II ACI have large central holes, which are included in the computational geometries (Fig. 2).

Stages of the ACI were simulated independently with only Stages 2 and 3 joined into one mesh. The simulation of individualstages was necessary to avoid generating a domain that was too large for the available computational resources. This approach isalso consistent with some experimental studies of the ACI that consider performance by evaluating individual stages (Vaughan,1989). In each stage of the ACI, air strikes the collection plate, moves outward radially, and then flows between the edge of thecollection plate and the outer wall into the next stage (Hinds, 1999). As a result, the air travels through a 180◦ bend each time itenters a new stage. To simulate inlet conditions, a parabolic velocity profile was assumed to enter the IP. The flow profile exitingthe IP was applied as the inlet condition for Stage 0. Thereafter, a uniform velocity profile was assumed to enter each stageupstream of the 180◦ bend inlet. This approach assumes that the 180◦ inlet controls the flow profile entering each stage beyondthe first. Mass flow outlet boundary conditions were used for all geometries considered.

The computational mesh used to simulate Stages 2 and 3 is shown in Fig. 3. The number of control volumes used for thenumerical model of each stage ranged from approximately 800,000 in Stage 0 to 2.5 million in Stage 7 (Table 2). As illustratedin Fig. 3, a fine mesh was used in the vicinity of the nozzles and near the collection plates. Hexahedral elements were usedin all models to improve the solution quality and reduce the number of control volumes required for grid independent results(Vinchurkar & Longest, 2008). The hexahedral mesh used for the IP geometry was similar to the mesh previously illustrated inLongest and Hindle (2009) and includes sufficient near-wall resolution to maintain wall y+ values less than one as required bythe turbulence approximation that was employed.

Grid convergence was tested for selected stages based on the method described by Longest and Vinchurkar (2007a). For eachstage, grids with low, medium, and high resolutions were considered. Each successive reduction of grid size was based on a gridrefinement factor of 1.5 or larger (Longest & Vinchurkar, 2007a). The criteria for accepting grid performance was defined as avelocity-based grid convergence index (GCI) less than 2.5%, which equates to a relative error less than approximately 1%, and achange in the predicted cutoff diameter of each stage less than 2%. The grid converged meshes were then used in all subsequentsimulations. As an example, the medium resolution grid of Stage 4 met the specified criteria and consisted of approximately 1.4million control volumes.


Fig. 2. Numerical models of (a) IP, (b) Stage 0, (c) Stage 1, and (d) Stages 2 and 3. For impactor Stages 1–7, two planes of symmetry were implemented based onapproximately symmetric flow. The number of nozzles reported is based on the actual ACI without symmetry planes.

2.3. Governing equations

Flow in the IP and ACI was considered to be steady, incompressible, and isothermal at standard laboratory conditions. For aflow rate of 28.3 L/min, the maximum Reynolds number in the IP is approximately 1250. In the impactor, the Reynolds numberdecreases significantly both between stages and in the jets (Table 1). Based on these conditions, flowwas assumed to be laminar ortransitional in the IP and fully laminar in the impactor stages. To simulate conditions in the IP, the lowReynolds number (LRN) k–�model was selected based on its ability to accurately predict pressure drop, velocity profiles and shear stress for transitional andturbulent flows (Ghalichi et al., 1998; Wilcox, 1998). This model was also demonstrated to accurately predict particle depositionprofiles for transitional and turbulent flows in models of the oral airway (Xi & Longest, 2007; Zhang & Kleinstreuer, 2003; Zhang& Kleinstreuer, 2004) and multiple bifurcations (Longest & Vinchurkar, 2007b). The equations governing laminar and turbulentflow based on the LRN k–� model were previously described by Longest and Xi (2007).

One-way coupled trajectories of monodisperse spherical particles ranging in diameter (dp) from 0.3 to 12�mwere calculatedon a Lagrangian basis by directly integrating an appropriate form of the particle trajectory equation. Aerosols in this size rangehave very low Stokes numbers (St = �pdp2CcU/18�D>1), where �p is the particle density, Cc is the Cunningham slip correctionfactor, � is the fluid absolute viscosity, U is the mean fluid velocity, and D is a representative diameter of the system. Othercharacteristics of the aerosols considered include a particle density �p = 1.00g/cm3, a density ratio � = �/�p ≈ 10−3, and aparticle Reynolds number Rep = �|u−v|dp/�>1. The appropriate equations for spherical particle motion under these conditionscan be expressed as

dvidt

= �DuiDt

+ f�p

(ui − vi) + fi,gravity + fi,Brownian + fi,lift + fi,image (1a)

and

dxidt

= vi(t) (1b)


Fig. 3. Numerical model of ACI Stages 2 and 3 illustrating the computational grid. The total number of control volumes for these stages was approximately twomillion cells.

Table 2Number of control volumes used in each geometry considered.

Part No. of control volumes (K)

IP 140Stage 0 800Stage 1 561Stage 2–3 2025Stage 4 1419Stage 5 1909Stage 6 2830Stage 7 2523

In the above equations, vi and ui are the components of the particle and time-averaged local fluid velocity, respectively. Thecharacteristic time required for particles to respond to changes in the flow field, or the particle response time, is �p = Cc�p

dp2/18�. The acceleration term is often neglected for aerosols due to small values of the density ratio (�>1). However, it hasbeen retained here to emphasize the significance of fluid element acceleration in jet systems (Longest, Kleinstreuer, & Buchanan,2004). The drag factor f, which represents the ratio of the drag coefficient CD to Stokes drag, is based on the spherical particleequation of Morsi and Alexander (1972) for aerosols greater than 1�m and includes the Cunningham slip correction factor forsizes less than 1�m. The force per unit particle mass due to gravity was included with the gravity vector oriented in the verticaldirection. Saffman style lift was calculated based on the three-dimensional expression of Longest et al. (2004) for particles greaterthan 1�m. The effect of Brownian motion was considered for particles less than 1�m as a separate force per unit mass term ateach time-step (Li & Ahmadi, 1992; Longest & Xi, 2007).


A charged aerosol near a conducting solid experiences an attractive image force (Hinds, 1999). For a particle with a charge qin Coulombs, the image force per unit mass is

fi,image = 6�d3p�p

q2

16h2��oni (2)

where h is the height of the particle above the conducting surface and �o = 8.854×10−12 C2/Nm2 is the permittivity of free space.The unit vector ni is normal to the surface and points away from the space occupied by the air passage, such that the imageforce always acts in the direction of the wall. Based on the assumption of a dilute aerosol, no particle-to-particle electrostaticinteractions were modeled, i.e., the space charge effect (Finlay, 2001) was not considered.

2.4. Numerical methods

To solve the governing mass and momentum conservation equations in the geometries considered, the CFD package Fluent6 was employed. User-supplied Fortran and C programs were implemented for the calculation of grid converge, initial particleprofiles, particle deposition factors, near-wall particle interpolation (Longest & Xi, 2007), the image force, and post processing.All transport equations were discretized to be at least second order accurate in space. Convergence of the flow field solutionwas assumed when the global mass residual was reduced from its original value by five orders of magnitude and when theresidual–reduction-rates for bothmass andmomentumwere sufficiently small. To ensure that a converged solutionwas reached,residual and reduction-rate factors were decreased by an order of magnitude and the results were compared. The stricterconvergence criteria produced a negligible effect on both velocity and particle deposition fields.

Particle trajectories were calculated within the steady flow fields of interest as a post-processing step. For the larger particlesizes considered, the integration scheme employed to solve Eqs. (1a,1b) was based on the fourth-order Runge Kutta algorithm(Press, Teukolsky, Vetterling, & Flannery, 1996). For particles less than approximately 400nm, extremely small momentumresponse times and time-steps significantly reduced the efficiency of the Runge Kutta algorithm. To evaluate particle trajectoriesfor particles less than 400nm, an analytic integration scheme was employed (Ferziger and Peric, 1999). For both the RungeKutta and analytic integrationmethods, an adaptive step-size control algorithmwas employed to minimize errors (Longest et al.,2004; Press et al., 1996). Due to relatively small response times for all particle sizes, double precision calculations were employed(Longest et al., 2004). Initial spatial concentrations of particleswere defined to be consistentwith the localmass flow rate (Longest& Vinchurkar, 2007a), and initial particle velocities were matched to the local fluid velocity. In order to determine the numberof particles required to produce convergent (i.e., particle number independent) deposition fractions, groups of 10,000 particleswere tested. The number of groups tested for convergence in a geometry was increased until deposition fraction values changedby less than 1% for each stage. The resulting particle counts required to produce convergent deposition fractions were 80,000 fordp < 1�m, 60,000 for 1�m � dp � 4�m, and 40,000 for dp > 4�m.

2.5. Aerosol deposition

In this study, the deposition fraction is defined as the number of particles depositing on a collection plate divided by thenumber of particles approaching the plate. As a result, particles depositing on the impactor nozzles and on the sidewalls are notconsidered. This convention for reporting deposition fraction, also referred to as retention fraction in other impactor studies, isconsistent with the experimental approach of Vaughan (1989).

As described by Hinds (1999), deposition fraction curves for impactors have an S-shape with a large vertical section. Theparticle size consistent with a retention fraction of 50% is defined as the d50 diameter. In an ideal impactor, each stage capturesall particles equal to and greater than the d50 size. As a result, the d50 size is also referred to as the stage cutoff diameter. Knowncutoff diameters will be used to validate the CFD model of the ACI (Andersen Inc. 1985; Vaughan, 1989). The numerical modelwill then be used to predict changes in cutoff diameters for each stage as a function of electrostatic charge.

2.6. Charge on standard pharmaceutical aerosols

A number of studies have measured the charge on standard pharmaceutical aerosols from DPI and MDI devices (Byronet al., 1997; Kwok & Chan, 2007; Kwok et al., 2005; Peart & Byron, 1999). Results of the studies by Kwok et al. (2005) and Kwokand Chan (2007) have been translated to elementary charge units vs. aerodynamic diameter in Fig. 4. Two primary points areobserved from these results. First, pharmaceutical aerosols are charged as a function of size with larger particles holding morecharge. Second, the charge on MDI aerosols is approximately one order of magnitude greater than the charge on DPI aerosols. Inorder to approximate the size dependent charge on DPI aerosols, Fig. 4 indicates that the saturation charge limit (Hinds, 1999)is a reasonable first order approximation. Charge values that are one order of magnitude greater than the saturation limit areobserved to be a reasonable approximation for MDI droplets. As a result, these first order approximations are used in this studyto define the size-dependent charge characteristics of DPI and MDI aerosols.


Aerodynamic diameter (µm)

Ele

men

tary

cha

rge

units

10-1 100 101

101

102

103

104

105

106

Kwok and Chan (2007) DPI Kwok et al. (2005) MDI

DPI

MDI

Saturation charge (DPI approximation) 10x Saturation charge (MDI approximation) Rayleigh limit

Fig. 4. Experimental and approximate charges on standard DPI and MDI aerosols. Charge values are shown to be well below the Rayleigh limit.

Fig. 5. Comparison of CFD predicted aerosol deposition due to the image force with the analytic expression of Chen and Yu (1993) for fully developed laminarflow in a tube. Particle size ranged from 0.5 through 10�m, and 500 elementary charge units were included per particle.

2.7. Validation of electrostatic deposition

To ensure that the electrostatic image force was correctly modeled, predicted deposition in a tubular geometry was comparedwith the analytical expression of Chen and Yu (1993). Characteristics of the tubular flow system were a diameter of 0.45 cm, alength of 5.6 cm, and a Reynolds number of 556, resulting in laminar flow conditions. Fully developed parabolic flowwas assumedat the geometry inlet and the initial particle profile was based on the local fluid velocity field. Approximately 120,000 controlvolumeswere used to discretize the flow field domain. Particles ranging from0.05 to 10�mwere consideredwith 500 elementarycharge units each. The simulation of 10,000 particles was found to produce deposition fraction results that were independent offurther increases in particle number for all sizes considered. Fig. 5 shows good agreement between the theoretical predictions ofChen and Yu (1993) and the CFD model employed in this study for charged aerosol deposition. Therefore, it is concluded that theCFD code is adequately predicting aerosol deposition as a result of the image force.


3. Results

3.1. Flow field conditions

Velocity fields in Stages 1 and 4 are displayed as three-dimensional contour plots in Fig. 6. Conditions at the symmetry planeare shown on the right-hand-side of each figure. Where wall boundaries exist, the velocity values at the first internal controlvolume center are shown. In Stage 1, the flow is observed to strike the collection plate of the preceding section (Stage 0), movethrough the 180◦ bend, and enter the connection section leading to the nozzle plate (Fig. 6a). As the flow leaves the 180◦ bend,significant recirculation zones are created along the outer impactor wall and within the central region of the connection section.These recirculation regions may increase deposition on the impactor sidewalls and entrain aerosols. Furthermore, the flow isobserved to be unevenly divided among the nozzles of Stage 1. Specifically, the difference in maximum velocity values betweenthe outer and inner nozzles is greater than 50%. This variability in nozzle conditionsmay reduce impactor performance and resultin less sharp impactor deposition curves. In Stage 4, a similar recirculation pattern is observed in the connecting section upstreamof the nozzle plates (Fig. 6b). However, the maximum velocity in the nozzles of Stage 4 is observed to be more uniform.

3.2. Neutral aerosol deposition

Deposition of uncharged 8, 3.5 and 0.6�mparticles in Stages 0, 2 & 3, and 6 is shown in Fig. 7. Aerosolswere assumed to depositat initial wall contact on all surfaces except inside the nozzles. Due to expected high shear stress values, aerosols contacting theinternal nozzle walls were assumed to bounce back into the flow field with a restitution coefficient of 1.0. Considering thelocation of particles, significant deposition is observed to occur on the upper nozzle plates in all stages. Significant deposition isalso observed on the sidewalls of the 180◦ bend transition sections. Deposition on the sidewalls in these locations is expecteddue to particle inertia and curved flow streamlines. As shown in Fig. 7, wall losses were greatest in the upper stages, e.g., 0 and2, and were reduced by Stage 3. The wall loss deposition in Stage 6 was less than approximately 3%. On the collection plates,particle deposition patterns were observed to localize below the nozzle orifices, as observed experimentally (Vaughan, 1989).These localized deposition patterns were less pronounced for Stage 0 and much more apparent for Stages 2 & 3, and Stage 6.The collection plate deposition pattern in Stage 3 indicates that the particles are relatively well distributed among the availablenozzles.

To validate the performance of the computational model, deposition fractions across a range of particle sizes were comparedwith S-shaped deposition curves from the experiments of Vaughan (1989) and the ACI manufacturer (Andersen Inc., 1985). Asdescribed, deposition fractions in the impactor were based on the number of particles approaching each collection plate to thenumber deposited, which was the convention implemented by Vaughan (1989). For all stages considered, the CFD results areconsistent with the deposition curves of both Vaughan (1989) and themanufacturer (Fig. 8). Discrepancies with the experimentaldata are greatest for Stage 0 (Fig. 8a). These differencesmay be the result of including transitional flow in the IP withoutmodelingthe turbulent dispersion of particles. Nevertheless, the agreement between the model and experimental results is good for allstages considered. In Stage 6, there is a relatively large difference between the experimental results of Vaughan (1989) and themanufacturer data (Fig. 8d). However, the CFD results generally fall between these two existing data sets. Experimental data wasnot available from Vaughan (1989) for Stage 7. However, Stage 7 CFD results are in good agreement with the manufacturer data(Andersen Inc., 1985).

Fig. 6. Contours of velocity magnitude for ACI: (a) Stage 1 and (b) Stage 4. The location of the collection and nozzle plates are indicated.


Fig. 7. Visualization of predicted monodisperse wall losses and collection plate deposition patterns for (a) Stage 0, (b) Stages 2 and 3, and (c) Stage 6. The threeparticle sizes considered were 8.0, 3.5, and 0.6�m.

Based on the results of Fig. 8, numerically predicted cutoff diameters are compared with the manufacturer data (AndersenInc., 1985) and experimental results of Vaughan (1989) in Table 3. As described, these cutoff values are based on a depositionfraction of 50%. Based on the manufacturer data (Andersen Inc. 1985), numerical predictions are within approximately 10% errorfor all stages except 2 and 6. In these stages, the percent errors are within 20% of the manufacturer's data (Andersen Inc., 1985).Considering the data of Vaughan (1989), percent errors of the numerical predictions compared with the experiments are lessthan 10% for all stages considered. Numerical predictions are within 5% error of the experiments in Stages 0, 2, and 6. Consideringthe range of reported differences between the experiments of Vaughan (1989) and the manufacturer data, it is concluded thatthe CFD model is accurately predicting the d50 cutoff diameters of each stage considered.

It is interesting that the cutoff diameters predicted by CFD increased from Stage 1 to 2 (Table 3). This increase results in thelarge percent difference from the reported manufacturer d50 values observed in Stage 2 (i.e., approximately 20%). However, thepredicted d50 value is within 0.52% difference of the Vaughan (1989) experimental data. Stage 2 is the first stage with 400 nozzles(cf. Table 1). Numerically, a reduction in accuracy is expected due to the simulation of additional nozzles compared with Stage 1.However, the numerical predictions are very close to the experimental results of Vaughan (1989). As a result, the CFD simulationssupport the observations of Vaughan (1989) that the cutoff diameters between Stages 1 and 2 are very close, i.e., within 0.3�m.In fact, the CFD predicted difference in cutoff diameters between Stages 1 and 2 is approximately 0.25�m. The minor increase inpredicted cutoff size at Stage 2 can be explained by considering the expected numerical inaccuracies, which for the other stagesappear to be 10% or less compared with experimental results, and the significant increase in solution complexity associated withincreasing the number of nozzles to 400.

3.3. Effects of electrostatic charge

The effects of electrostatic charge on deposition for DPI representative aerosols are shown in Fig. 9. For each stage, numericalpredictions of neutral and charged particles are compared across a range of aerosol sizes. As described, the approximate DPIcharge level was selected as the saturation charge limit, which is illustrated in Fig. 4. To illustrate the changes in deposition as afunction of aerosol diameter, linear best fit curveswere used to represent the numerical data for charged and uncharged particles.


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Fig. 8. Predictions of deposition fractions for Stages (a) 0 and 1, (b) 2 and 3, (c) 4 and 5, and (d) 6 and 7 compared with the experimental results of Vaughan (1989)and the manufacturer's data (Andersen Inc., 1985).

These lines are most accurate in the range of the cutoff diameters for each stage, which appear as linear sections of the S-shapedcurves seen in Fig. 8. Considering Stages 0 and 1, the DPI level of charge is observed to increase the deposition fraction for allparticle sizes considered by a small amount (Fig. 9a). For Stages 2 and 3, a more significant increase in deposition for the chargedaerosols is observed (Fig. 9b). In general, charge increases the deposition fraction up to approximately 30% in Stage 3, which hasa manufacturer stated cutoff diameter of 3.3�m. A more significant increase in deposition fraction as a result of DPI charge isobserved in Stages 4–7. In Stages 4 and 5, DPI level charges increase deposition by a factor of 10 or greater for some aerosol sizes(Fig. 9c). Considering Stages 6 and 7, nearly all charged aerosols in the submicrometer range are deposited (Fig. 9d).

The effect of charge on MDI aerosols is illustrated in Fig. 10. In general, the deposition results for approximate MDI chargevalues are similar to DPI conditions. Specifically, relatively small increases in deposition are observed in Stages 0–3. For theseupper stages, themaximum increase in depositionwith a charged aerosol is approximately 35%, based on the particle sizes shown(Fig. 10b). In Stages 4–7, charge is again observed to significantly increase deposition by up to an order of magnitude (Fig. 10c andd). As with the DPI conditions, all submicrometer MDI charged aerosols are observed to deposit in Stages 6 and 7 (Fig. 10d). Forall stages, MDI charge levels are observed to increase deposition compared with DPI values. However, this increase is relativelyminor compared with the order of magnitude increase in charge held by the MDI aerosols.

Numerical predictions of cutoff diameters for neutral and charged aerosols are presented in Table 4. These d50 values areestimated based on the linear curve fits presented in Figs. 9 and 10. Percent difference in d50 values as a result of charge wascalculated as the difference between the neutral and charged values divided by the neutral value. For all cases considered,increasing the aerosol charge reduced the cutoff diameter of each stage. For Stages 0–3, both DPI and MDI charges reducedthe d50 value by approximately 10% or less (Table 4). In contrast, charged aerosols reduced the d50 values in Stages 4 and 5 byapproximately 200% and 60%, respectively. As observed above, all submicrometer aerosols simulated in Stages 6 and 7 deposited.Therefore, d50 values could not be computed for these stages. Surprisingly, increasing the charge from the DPI level to MDI


Table 3Numerical predictions of stage cutoff diameters (d50) in micrometers compared with the manufacturer's data (Andersen Inc., 1985) and the results of Vaughan(1989).

Stage no. 0 1 2 3 4 5 6 7

Predicted neutral d50 (�m) 8.79 5.43 5.67 3.3 1.86 1.00 0.59 0.44Manufacturer d50 (�m) 9.0 5.8 4.7 3.3 2.1 1.1 0.7 0.4% Error for CFD vs. Manufacturer 2.3 6.3 20.6 0 10.9 9.0 15.7 10.0Vaughan (1989) d50 (�m) 9.0 6.0 5.7 3.1 2.06 0.9 0.6 –% Error for CFD vs. Vaughan (1989) 2.3 9.5 0.52 6.4 9.2 11.1 1.6 –

All predictions are within approximately 10% of the experimental study of Vaughan (1989).

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Fig. 9. Comparison of predicted deposition fractions for neutral and DPI-charged aerosols in Stages (a) 0 and 1, (b) 2 and 3, (c) 4 and 5, and (d) 6 and 7.

values had a relatively small effect on further decreasing the cutoff sizes. Therefore, it appears that once an aerosol is sufficientlycharged, further increases in the charge level will have a diminishing effect on deposition in the ACI.

Based on the results of Table 4, it is observed that as the stage number increases, which is consistent with decreasing cutoffsizes, the percent difference between neutral and charged d50 values increases to a maximum of approximately 200% at Stage 4.However, the percent difference in d50 values decreases at Stage 5 to approximately 60%. This reverse in trend may be due to thefact that electrostatic deposition is time dependent. Jet velocities significantly increase in Stage 5 comparedwith the upper stages(Table 1). This increasing jet velocity will reduce the time available for electrostatic attraction to occur and thereby diminishelectrostatic deposition effects. As a result, it appears that deposition of charged particles in the ACI depends on an interactionamong aerosol aerodynamic diameter, charge, and the residence time in each stage.

Fig. 11 plots “predicted aerodynamic diameters” vs. “ACI measured diameters” for neutral and charged aerosols. The ACImeasured diameter is the MMAD that would be determined in a laboratory experiment using a neutral or charged aerosol.The predicted aerodynamic diameter is the aerodynamic size predicted by CFD calculations correcting for charge effects in


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Fig. 10. Comparison of predicted deposition fractions for neutral and MDI-charged aerosols in Stages (a) 0 and 1, (b) 2 and 3, (c) 4 and 5, and (d) 6 and 7.

Table 4Predicted stage cutoff diameters (d50) in micrometers for neutral, DPI, and MDI aerosols.

Stage no. 0 1 2 3 4 5 6 7

Predicted neutral d50 (�m) 8.79 5.43 5.67 3.3 1.86 1.00 0.59 0.44CFD DPI d50 (�m) 8.29 5.30 5.38 3.05 0.14 0.56 NAa NAa

% Difference 5.9 2.4 5.2 7.9 172 56.4CFD MDI d50 (�m) 8.19 5.20 5.26 2.97 0.03 0.53 NAa NAa

% Difference 7.1 4.3 7.5 10.5 194 61.4

aCutoff diameter could not be computed because all particle sizes considered deposited above 50%.

the impactor. The charged aerosol results reported in Fig. 11 are based on the neutral and charged cutoff diameters shown inTable 4. For neutral particles, this figure shows that the ACImeasured diameter and predicted aerodynamic diameter are the same,i.e., charge has no effect on deposition. The curves for DPI and MDI charged aerosols represent corrections for ACI measurementsin order to predict the aerodynamic size. For example, a charged MDI aerosol measured to have a mass median aerodynamicdiameter of 3�m in an ACI is predicted to have an aerodynamic diameter of 2.4�m (see dark arrow in Fig. 11). Similarly, acharged DPI orMDI aerosol with a known aerodynamic size of 4�mwill deposit in the ACI like a 4.3�maerosol (see light arrow inFig. 11).

4. Discussion

CFD can be used as an effective analysis and design tool for the evaluation of aerosol instruments, like the ACI. For thefirst time, detailed flow field conditions inside the widely used ACI were reported in this study. Significant recirculation zones


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Fig. 11. Correction curves relating ACI measured particle sizes with predicted aerodynamic diameters. The ACI measured diameter is the result of particle sizeand charge. The predicted aerodynamic diameter is the corrected size after removing charge effects.

and unevenly divided nozzle flow rates were observed, especially in the upper stages. Deposition patterns on collection platesrevealed that particles are relatively well distributed among the nozzles beyond the first two impactor stages. For unchargedaerosols, predicted cutoff diameters were in excellent agreement with existing experiments and manufacturer data. Therefore,the numerical model was considered to be sufficiently accurate for predicting factors affecting aerosol deposition and sizemeasurements. The developed ACI model can now be applied to evaluate the effects of variables other than aerosol size ondeposition. Furthermore, the CFD approach illustrated in this study can be implemented to design future aerosol samplinginstruments like small scale assessment devices for environmental monitoring and bioterrorism preparedness.

The numerical ACImodelwas employed to determine the effect of expected charge values on the deposition of pharmaceuticalaerosols. Pharmaceutical inhalationdevices areoften testedusinghigh flowrate impactorswithout chargeneutralizing theaerosol(USP, 2005). However, aerosol charge is known to affect deposition in impactors (de Juan et al., 1997). Results of this study quantifythe effect of approximate charge on the deposition of pharmaceutical aerosols in the ACI. Specifically, the particle d50 valuesin Table 4 can be used to define new cutoff values for each ACI stage when charged pharmaceutical aerosols are considered.Moreover, Fig. 11 provides a graphical representation of the shift in measured aerosol sizes resulting from particle charge inthe ACI. As indicated in these results, standard pharmaceutical charge values can result in a significant change in the measuredaerosol size, especially for particles less than approximately 3�m.

Further evidence of the importance of charge on deposition within cascade impactors is provided in the form of the recentrecalibration of the Electrical Low Pressure Impactor (ELPI) (Kotian, Peart, Bryner, & Byron, 2009). The ELPI was originallycalibrated with the use of corona-charged aerosols, but it has found extensive use for the characterization of pharmaceuticalaerosols in amodified “charger-free” configuration (Glover & Chan, 2004; Kwok et al., 2005; Kwok & Chan, 2008; Telko, Kujanpaa,& Hickey, 2007). In this charger-free setup, the ELPI has been reported to `undersize' the particle size distribution of aerosol cloudsgenerated by MDIs (Kotian et al., 2009). Kotian et al. (2009) recalibrated the modified ELPI using four independent, polydispersepharmaceutical aerosols with different median diameters in the range of 0.9–3.7�m, following their characterization in anACI. The mean d50 values obtained following recalibration of the modified ELPI were found to deviate increasingly from themanufacturer-supplied values as aerodynamic diameter decreased.

Limitations of the current study include simplifying assumptions related to the ACI geometry, CFD model, and aerosolconditions. To reduce the number of control volumes required for each stage, two planes of symmetry were implemented inmost cases. This approach neglects the potential for axisymmetric swirl conditions in the angular coordinate direction of theimpactor. Furthermore, most stages were simulated separately, which neglects the exact airflow and particle profiles enteringthe 180◦ inlet bend. Considering the CFD model, a two-equation turbulence approximation was used to simulate transitionalflow in the IP as an inlet condition for Stage 0. Turbulent quantities were neglected in Stage 0 and laminar flow was assumedthroughout the impactor. Considering the dispersed phase, the aerosols were assumed to be non-evaporating particles. Dropletevaporation is expected tobe significant for thedepositionof liquidbasedpharmaceutical aerosols as a functionof the surroundingrelative humidity (Longest et al., 2007; Stein, 2008). Finally, only effects of the image charge were considered for dilute aerosolconditions.


In conclusion, the current study illustrates the utility of a CFDmodel to evaluate the performance of aerosol testing equipment.Results of this study can be used to better analyze the aerodynamic size of charged aerosols that are evaluated in the ACI withoutcharge neutralization. Future applications of the developed ACI model include evaluating the space charge effect on depositionand quantifying the effects of aerosol evaporation on size assessment at different relative humidity conditions. Furthermore,the CFD approach illustrated in this study can be used to design and develop the next generation of aerosol assessment andcharacterization devices.

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cfd simulations of the andersen cascade impactor: model development and effects of aerosol charge

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