Aerosol Science 40 (2009) 563 -- 572

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Aerosol Science

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An improved model for particle deposition in porous foams

Phillip Clark, Kirsten A. Koehler∗, John Volckens

Department of Environmental and Radiological Health Sciences, Colorado State University, 1681 Campus Delivery, Fort Collins, CO 80523, USA

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

Article history:Received 22 January 2009Received in revised form13 February 2009Accepted 19 February 2009

Keywords:Porous foamAerosol samplingAerosol penetration model

Porous foam provides an inexpensive, light-weight and effective medium to capturephysiologically-relevant aerosol fractions. It can be manufactured to have a wide range ofproperties relevant to aerosol deposition. A series of laboratory experiments were conductedto measure particle penetration though porous foam media of varying pore size and foamlength. Both solid and liquid aerosols (0.01–10�m diameter) were tested using a SequenzialMobility Particle Sizer or Aerodynamic Particle Sizer to count and size particles penetratingthe foam. With this data, an existing semi-empirical model was improved upon to predictparticle penetration through a foam of a given fiber diameter, and thickness. The model isbased on three dimensionless parameters (St, Ng, Pe) that account for inertial, gravitational,and diffusive modes of deposition, respectively.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

There is vast epidemiological and toxicological evidence associating particulate matter exposure with disease (Daigleet al., 2003; Davidson, Phalen, & Solomon, 2005; Muhlfeld et al., 2008; Schulz et al., 2005; Timonen et al., 2006). Exposurescan presumably lead to pnemonoconioses, chronic bronchitis, emphysema, cardiac complications, increased hospital admissionsfor asthma, or can initiate other disease states, such as fibrosis or cancer (CDC, 2004; Ibald-Mulli, Wichmann, Kreyling, & Peters,2002). Unprotected individuals who are exposed to a hazardous aerosol will intake a fraction by inhalation, which then leadsto a dose and may ultimately cause an adverse health effect (Crawford-Brown, 1999). The better a measurement represents theactual dose received, the more accurate the estimate of health effect will be.

In recognition of the need to estimate respiratory dose, standards for size-selective sampling were developed to estimateparticle intake (i.e., penetration) into the respiratory tract. The International Standards Organization (ISO), American Council ofGovernmental Industrial Hygienists (ACGIH), andmost recently, Comité Européen deNormalisation (CEN) have adopted samplingcriteria to segregate aerosol into three fractions based on particle penetration into different regions of the respiratory system:inhalable, thoracic, and respirable (ACGIH, 1985; CEN, 1993; ISO, 1983). From these conventions followed the design of personal,penetration-based sampling methods (i.e., personal aerosol samplers with aspiration efficiency equal to the inhalable, thoracic,and respiratory penetration curves).

Penetration-based samplers represent the current state-of-the-art in personal aerosol sampling. Several of these samplertypes employ reticulated polyurethane foam as an upstream size selector to estimate the thoracic and respirable penetrationfractions (Brown, 1980; Chen, Lai, Shih, & Yeh, 1998; Gibson & Vincent, 1981) and semi-empirical models have been developedto predict particle penetration through such foam (Kenny, Aitken, Beaumont, & Gorner, 2001; Kuo et al., 2005; Vincent, Aitken, &Mark, 1993). However, existing models for particle penetration through foam are based solely on particle impaction and settlingtheory (Kenny et al., 2001; Vincent et al., 1993). Kuo et al. (2005), however, reported substantial levels of diffusive deposition

∗ Corresponding author. Tel.: 1 9704916392.E-mail address: Kirsten.Koehler@colostate.edu (K.A. Koehler).

0021-8502/$ - see front matter © 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.jaerosci.2009.02.005

564 P. Clark et al. / Aerosol Science 40 (2009) 563 -- 572

for these foams. Consequently, foam devices designed to meet the thoracic and respirable conventions may introduce bias forsamples where diffusive particle deposition predominates. Therefore, we have generated aerosol penetration data for variousporous foams, as a function of particle size, and modeled the penetration as a function of foam physical properties, incorporatinga diffusive deposition term.

2. Model development

A semi-empirical model estimating particle penetration through porous foam was originally constructed by Vincent et al.(1993) using penetration efficiency data published by Gibson and Vincent (1981) and Wake and Brown (1991). The modelaccounts for particle deposition by impaction and gravitational settling and takes the following form:

ln(P) = − tdf

{54.86St2.382 + 38.91Ng0.880} (1)

where P is the fraction of aerosol penetrating through a foam of thickness, t (in mm), and equivalent fiber diameter, df (in �m).Kenny et al. (2001) later adjusted the model to incorporate SI units and to introduce an alternative method of measuring fiberdiameter. The equivalent fiber diameter of the foam is analogous to the fiber diameter utilized in theoretical treatments of fibrousfilters based on single-fiber efficiency (Kenny et al., 2001). St and Ng, represent the Stokes number and the gravitational settlingnumber, respectively, and they are quantified by the following equations:

St = �0d2aeUCc

18�df(2)

Ng = �0d2aegCc

18�U(3)

where dae is the particle aerodynamic diameter, �0 is the density of water, � is the viscosity of air, U is the velocity of air throughthe foam, Cc is the Cunningham slip correction factor, and g is the acceleration due to gravity. All units are in SI for both equations.

The Peclet number (Pe) describes a particle's tendency to deposit via diffusion and is quantified by the following equation:

Pe = 3��dthdf UkTCc

(4)

where k is Boltzmann's constant, T is temperature in Kelvin, and dth is the thermodynamic equivalent diameter. The thermody-namic equivalent diameter is related to the aerodynamic diameter via the particle density (�p) and the dynamic shape factor (�)(ICRP, 1994):

dth = dae

√��0�p

Cc(dae)Cc(dth)

(5)

We propose an adjusted version of the existing model that incorporates Pewith St and Ng:

ln(P) = − tdf

{aStb + cNgd + ePef } (6)

where the terms a, b, c, d, e, and f are all coefficients with values determined from particle deposition measurements.

3. Experimental method

3.1. Reticulated polyurethane foam

Reticulated polyurethane foam consists of a fiber matrix of porous, interlocking cells in a dodecahedronal skeleton. Foamsare typically characterized by their fiber diameter and percent open area (i.e., the solidity). Fiber diameters are defined as thediameter of a polyurethane fiber taken at the midsection of a fiber linking two adjacent cells; solidity is defined as the ratio offiber volume to total volume occupied by a foam plug.

Four foam types with differing porosities and fiber diameters were tested for this experiment: 45, 60, 80, and 100 pores perinch (PPI). PPI is a term used in the foam industry to describe the approximate porosity of the foam, however, fiber diameter andfoam porosity (defined as one minus the foam solidity) are more accurate descriptors for foam filtration efficiency and are usedin the development of the model. Three foam thicknesses were tested: 5, 10, and 20mm. All of the foam plugs were purchasedfrom and die cut by EN Murray Company (Denver, CO) to the dimensions listed above.

The fiber diameter of each foam was measured by digital microscopy with a Q-Imaging Retiga 2000 R camera (Surrey, B.C.,Canada) mounted on an Olympus IX71 (Tokyo, Japan) microscope. Slidebook Software by 3I (Denver, CO) was used to process theraw images and computer pixels were pre-calibrated to a 10�m primary standard calibration slide. Average fiber diameters are

P. Clark et al. / Aerosol Science 40 (2009) 563 -- 572 565

Table 1Average and standard deviations of fiber diameters and solidity measurements for the four foam types used in the penetration efficiency experiments.

Foam type (PPI) Fiber diameter (�m) Solidity

45 125.5 ± 11 0.025 ± 0.00260 91.8 ± 5.8 0.023 ± 0.00180 55.8 ± 4.7 0.025 ± 0.002100 49.5 ± 5.6 0.025 ± 0.002

Fig. 1. Reticulated polyurethane foam of differing porosities (PPI); magnified 100X.

tabulated in Table 1. Measured fiber diameters were ∼30% larger than predicted by the empirical model relating fiber diameterto manufacturer PPI given in Vincent et al. (1993). Typical images of each foam type can be seen in Fig. 1.

The solidity of a sample was determined by measuring foam plug dimensions with calipers and weighing the foam plugsto the nearest tenth of a milligram (Mettler Toledo XS 104, Greifensee, Switzerland). The density of polyurethane is 1.2 g cm−3,as specified by the manufacturer. Although the higher PPI foams visually appear to have a higher solidity, the measurementsshow this not to be the case. The decrease in pore size is balanced by a decrease in fiber diameter and the solidity was nearlyindependent of foam PPI, as shown in Table 1.

3.2. Aerosol deposition measurements

The experimental variables are summarized in Table 2 and a schematic for the deposition efficiency experiments is shown inFig. 2. In addition to the different porosities and thicknesses of foams examined, deposition fractions for both solid (NaCl) andliquid (oil) aerosols were determined. Experiments were conducted in random order with exception to aerosol type.

Two measurement systems were employed to measure aerosol penetration efficiency over approximately three decades ofparticle diameter. Particles with 0.011 � dae � 1.08�m were sized and counted in 44 size channels with a Sequential Mobility

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Table 2The experimental variables used for penetration efficiency tests.

Experimental variable Level of variation

Foam thickness 5, 10, 20mmFoam porosity 45, 60, 80, 100PPIParticle diameter range (SMPS) 0.01–1.08�m (44 size bins)Particle diameter range (APS) 0.52–19.81�m (52 size bins)Aerosol type Solid (NaCl) and liquid (Oil)Foam diameter 17mm (IOM diameter)Air flow rate 2 L/min (IOM flow)

Positive

Pressure Vacuum Valve Flow

Meter

HEPA

Filter

Test Section210Po

SMPS or APS

Hygrometer

Dehumidifier

Nebulizer

Dilution

Chamber

Pressure Gauge

+

+

Fig. 2. The experimental setup used for conducting penetration efficiency experiments.

Particle Sizer (SMPS, GRIMM Technologies, Inc.), consisting of a differential mobility analyzer (DMA) and a condensation particlecounter (CPC). Particles with 0.523 � dae � 19.81�mwere sized and counted with a TSI Aerodynamic Particle Sizer (APS, Model3321) and binned into 52 size channels. The test section was a steel pipe with an inner diameter of 16mm. Test foams wereinserted into the pipe and then maneuvered into the correct position with tweezers. Temperature and humidity were recordedduring each experiment with a NIST-traceable thermometer/hygrometer (Fisher Scientific, Pittsburgh, PA) to ensure aerosol didnot grow hygroscopically during any experiments. Foam diameter (17mm) and air flow rate (2 Lmin−1) were held constant tomatch the geometry and flow rate of the existing IOM sampling cassette.

Solid and liquid test aerosolswere generated in the laboratory using a CollisonNebulizer (BGI,Waltham,MA). The solid aerosolwas generated from a solution of sodium chloride (50g L−1 for SMPS system operation or 60g L−1 for APS system operation)and dried to yield a crystalline polydisperse aerosol. The liquid aerosol was generated from a solution of oil in butanol (4.6 g L−1

for SMPS system operation) or pure oil for APS system operation. The nebulizer generated aerosol for approximately 20minin the dilution chamber prior to the start of each experiment to develop a consistent concentration of aerosol throughouta run. Prior to testing, aerosol output from the nebulizer was evaluated to ensure consistent generation of stable particleconcentration over time. Particle size distributions were also consistent between tests. For the SMPS measurements, the saltaerosol had a count median aerodynamic diameter (CMAD) = 0.166�m and a geometric standard deviation (GSD) = 2.15; thisaerosol had consistent concentrations of particle sizes from 0.038 to 1.0�m. The oil aerosol had a CMAD = 0.150�m and aGSD = 1.90 and maintained consistent concentrations from 0.024 to 1.18�m (dae). The coefficient of variation for repeatedmeasurements of CMAD and GSD was less than 1%. For the APS measurements, the salt aerosol had a CMAD = 0.8�m andGSD = 1.33 and the oil aerosol had a CMAD = 1.05�mand GSD = 1.68. Aerosol that exited the nebulizer was immediately dilutedand dehumidified with approximately 50 Lmin−1 of filtered, compressed air in a 19 L dilution chamber. Excess aerosol wasremoved via a waste outlet air line. For APSmeasurements of the salt aerosol, it was difficult to maintain constant concentrationsin the dilution chamber low enough that coincidence errors in the APS were not significant for particle diameters less than∼5�m. Instead, aerosol was generated in a ∼1m−3 aerosol chamber and air was sampled through the test section from the largechamber. Test aerosol exited the dilution chamber passed through a 210Po neutralizer and into the test section at 2 Lmin−1.Nebulization of the salt solutions produced very low concentrations of aerosol with aerodynamic diameters larger than ∼5�m.Therefore a vibrating orifice aerosol generator (VOAG, TSI #3450) was used to produce a distribution of aerosol with diametersbetween ∼6–9�m.

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The DMA measures the mobility diameter (dm), as opposed to the aerodynamic diameter (dae) of a particle. Eq. (7) was usedto convert dm to the volume equivalent diameter, dve, and Eq. (8) was used to convert dve to dae (DeCarlo, Slowik, Worsnop,Davidovitz, & Jimenez, 2004):

dmCc(dm)

= dve�t

Cc(dve)(7)

�p

�d2veCc(dve) = �0d

2aeCc(dae) (8)

where �t is the dynamic shape factor in a transition regime, Cc is Cunningham's slip correction factor, � is the dynamic shapefactor in any regime. The SMPS used in this experiment was calibrated against a SMPS from a separate lab and was found to bewithin 5% of the CMD determined from the other SMPS. The APS measured aerodynamic diameter directly (no corrections wereperformed to the data) and its calibration was verified with nebulized solutions of polystyrene latex spheres (Duke ScientificCorp.).

Penetration efficiencies were calculated by comparing aerosol concentrations measured downstream of the test section withand without the foam plug using the following equation:

Pi =Ci foam+housing

Ci housing(9)

where Pi represents the aerosol fraction penetrating through the foam, Ci housing is the aerosol number concentration after passingthrough the test section without foam, and Ci foam+housing is the aerosol number concentration after passing through the testsection with foam in place; all values are specific to `i', which denotes the particle size of interest. Three consecutive scansof aerosol concentration for foam in and foam out were averaged together for each measurement of penetration fraction. Anunweighted, iterative, nonlinear least squares regression was used to construct the penetration model (Eq. (6)) using the SASsoftware package (Cary, NC). Specific foam characteristics were analyzed for their associationwith particle penetration efficiency.One-way andmultivariate ANOVA tests were conducted comparing four parameters to particle penetration: fiber diameter, foamthickness, particle size, and aerosol type. A p-value of 0.05 was selected to define significance.

4. Results

Foam penetration fractions for salt particles are shown in Fig. 3 and for oil droplets in Fig. 4. Penetration is shown as afunction of foam fiber diameter, aerodynamic particle diameter, and foam thickness. Generally, penetration fraction was directlyproportional to fiber diameter and inversely proportional to foam thickness. Smaller fiber diameters and pores (for a givensolidity) tend to increase particle collection through enhanced diffusion and impaction. However, between 0.1 and 1.1�m nomechanism efficiently influences particle deposition as seen in Figs. 3 and 4. For dae > 1.1�m, deposition is controlled primarilyby inertial deposition and only modestly by gravitational deposition at the flow condition used. Measured penetration fractionsfor dae > 0.5�m were in reasonable agreement yet somewhat smaller than those predicted using the existing model describedby Eq. (1) (dashed lines) for dae > 1�m. This is not surprising since the existing model was developed with foam samples ofgenerally higher porosity than studied here and intended to capture a 50% deposition fraction around 10�m.

The variability in measured penetration fraction tended to be highest for the 45PPI foam. The 45PPI foam is less rigid than the100PPI foam and may have had a tendency to compress or twist during insertion of the foam plug into the housing. The 5mmfoam plugs also had more scatter in measured penetration fractions than the 20mm plugs, likely due to the difficulty in properlyaligning the 5mm plugs in the housing.

Much of the uncertainty in penetration fraction associated with the upper and lower limits of reported particle diameters foreach system is due to poor count statistics. During SMPS measurements, an insufficient number of particles were generated forsizes smaller than 0.04 (0.02)�m and larger than 0.42 (0.37)�m (dae) for salt (oil) aerosol. For measurements performed withthe APS, it is very difficult for particles larger than ∼5�m to exit the Collison nebulizer, yielding larger variability in measureddeposition fractions for larger particle diameters, particularly with the salt aerosol. Using the VOAG to generate salt aerosol, wewere better able to constrain the penetration curves up to ∼10�m.

Additional variability in the measured penetration fractions is attributed to variations in the aerosol concentration overtime. If the aerosol number concentration entering the test section varies with time, a bias is introduced into Eq. (9). Aerosolconcentrations generated for this experiment were stable within 10% of the average. However, even such small variations likelyintroduced some variability in the measured penetration fraction.

Particle size, fiber diameter, and foam thickness were found to be significant predictors of particle penetration. Tukey testsshowed that penetration fraction differed significantly (p< 0.05) between foams of 45, 60 and 100PPI, with few exceptions.However, the fiber diameters for the 100 and 80PPI foams used in these experiments were not significantly different from oneanother and, as such, penetration efficiencies did not differ significantly between the two foams (p> 0.05). Penetration fractionswere only determined in the SMPS size range for the 80PPI foam. Penetration data for the 80PPI foam are not shown in Figs. 3and 4, however, they were included in model development, where available.

568 P. Clark et al. / Aerosol Science 40 (2009) 563 -- 572

Fig. 3. Penetration fraction as a function of foamPPI and aerosol aerodynamic diameter for salt particles. Error bars represent one standard deviation of penetrationfraction. Foam thickness is represented by colorwith 20mm thickness in light grey (green online), 10mm thickness in dark grey (blue online), and 5mm thicknessin black (red online). The converged model represented by Eq. (6) is shown in solid lines and the model described by Eq. (1) (Vincent et al., 1993) is shown indashed lines for comparison. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)

One-way ANOVA found that particle type (solid or liquid) was a statistically significant predictor of penetrationfraction (p = 0.03). However, for 0.05< dae < 5�m, the salt penetration was found to be less than 1% larger than theoil penetration, on average. Therefore, the oil and salt data were combined into one dataset for the modelregression.

P. Clark et al. / Aerosol Science 40 (2009) 563 -- 572 569

Fig. 4. Penetration fraction as a function of foam PPI and aerosol aerodynamic diameter for oil particles. Error bars represent one standard deviation of penetrationfraction. Foam thickness is represented by colorwith 20mm thickness in light grey (green online), 10mm thickness in dark grey (blue online), and 5mm thicknessin black (red online). The converged model represented by Eq. (6) is shown in solid lines and the model described by Eq. (1) (Vincent et al., 1993) is shown indashed lines for comparison. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)

5. Discussion

The determined coefficients for the Combined Model (Eq. (6)) are given in Table 3 and the model is shown as solid lines foreach foam porosity and thickness in Figs. 3 and 4. The penetration data used for model convergence was restricted to particleaerodynamic diameters between 0.02 and 0.37�m for the oil aerosol and between 0.04 and 0.42 for the salt aerosol from the

570 P. Clark et al. / Aerosol Science 40 (2009) 563 -- 572

Table 3Converged coefficients for Eq. (6) using measured penetration fractions for both salt and oil aerosol.

ln(P) = − tdf

{aStb + cNgd + ePef }

(where t is in mm and df is in �m)Model coefficient Combined

a 40.7b 1.90ca 38.9da 0.880e 84.36f −0.747

aModel coefficients for the gravity term, Ng, were taken from Vincent et al. (1993).

Fig. 5. Scatter plot of all measured penetration fractions to the modeled penetration fractions predicted using Eq. (6).

SMPS and between 0.54 and 9.65 �m for the APS with oil aerosol and between 0.54 and 5.83�m from nebulized salt solutions.Due to the large variability in measured penetration fractions using the VOAG generated salt aerosol, these fractions were notincluded in the model convergence, but were in reasonable agreement with the Combined Model, as seen in Fig. 3. Any negativedeposition fractions (usually about −1 to −10%) were altered to reflect a value of zero; this correction is justified as foam did notproduce particles, and particle re-entrainment was negligible. Both of these assumptions were confirmed through independenttests. Similarly, any deposition fractions greater than one were altered to reflect a value of one. The source of these negative andgreater than unity deposition fractions is unclear, but may be due to variations in SMPS and APS counting efficiency or instabilityin generated aerosol concentrations.

Wewere unable to adequately constrain the gravitational component of Eq. (6) firstly, because we only had reasonable countsfor particles smaller than ∼10�m and secondly, because the residence time through the foam at 2 Lmin−1 was on the order oftenths of a second. This can be expressed mathematically through the Froude number: the ratio of St to Ng. Froude numbers forour work ranged from 23–59, indicating the importance of impaction over gravity in the deposition of aerosol. Therefore, we setthe values of the coefficients for the gravitational term to those determined by Vincent et al. (1993), assuming that the gravityand inertial depositionmechanisms are independent. In that study, larger particle diameters and lower face velocities were used,better constraining the gravitational coefficients. New coefficients were found for the inertial term.

Eq. (6) closely predicts penetration of particles in porous foam media. Fig. 5 shows a scatter plot of the modeled to measuredpenetration fractions. There is generally good agreement between the data and the model with a squared Pearson correlationcoefficient of 0.93.

Model residuals (actual minus predicted penetration) were compared to foam thickness, fiber diameter, and aerodynamicdiameter. The residual data appeared normally distributed and homoscedastic when compared to foam thickness, fiber diameter,and aerodynamic diameter.

Kuo et al. (2005) generated penetration fractions of submicron particles for a range of porosity, face velocity, and compressionconditions. However, none of the measurements presented here are repetitions of their conditions. The model was used to

P. Clark et al. / Aerosol Science 40 (2009) 563 -- 572 571

Fig. 6. Comparison of the ACGIH thoracic or respirable penetration fraction to the modeled penetration fraction through the foam insert used in the personal IOMsampler (left panels). Bias map of the measured mass (middle panels) or number concentration (right panels) when using the IOM foam insert against the ACGIHconvention for penetration to the thoracic region (top panels) or respirable (bottom panels) of the respiratory tract.

predict the only reported penetration fractions for which the foam was not compressed (60PPI, 0.15ms−1 face velocity and50mm thickness) and reasonable agreement was obtained.

We also employed the model to predict the penetration of aerosol through an IOM sampler operating with standard foaminserts (model #225-772, SKC, Inc.) designed to match the thoracic or respirable penetration conventions. The thoracic foaminsert is a 45PPI foam plug with a diameter of 1.75 cm, has a thickness of 1 cm, and operates at 2 Lmin−1. The respirable foaminsert is a 85PPI plug with a 1.65 cm diameter, 1.2 cm thickness and also operates at 2 Lmin−1. The left panels of Fig. 6 comparethe fraction of aerosol penetrating through the IOM foam insert for collection onto the filter to the thoracic (top) or respirable(bottom) penetration conventions given by the ACGIH. While previous studies of the IOM foam insert have only determined thepenetration for particles larger than 1�m, the model developed here allows comparison between the sampler and thoracic orrespirable conventions for the fine and ultra-fine mode aerosol. The IOM foam inserts indeed agree well with the thoracic andrespirable conventions for supermicron aerosol, yet our model shows that these inserts will capture a fraction of the particleswith dae < 0.1�m, leading to an underestimate of the exposure.

We have constructed bias maps to test the performance of the IOM aerosol sampler with foam inserts given myriad possibleaerosol size distributions. The mass of aerosol collected on the filter for 550 lognormal size distributions with mass mediandiameters (MMD) between 0.05–20�m and geometric standard deviations (GSD) between 1 and 4 was calculated and comparedto the mass penetrating the thoracic or respirable regions predicted by the convention. The percent difference between the IOMestimated masses and masses penetrating to the thoracic (top) or respirable (bottom) regions is presented in isopleth maps asa function of MMD and GSD in the middle panels of Fig. 6. For 0.1<MMD< 5�m and 1< GSD< 4, the IOM with foam insertsprovides a good estimate of the thoracic and respirable exposures, within ± 10%. Most ambient aerosol size distributions willfall within this range and these exposures can be adequately estimated using the IOM with foam inserts.

However, the emergence of engineered nanoparticles as an occupational health concern has led some researchers to suggestthe use of conventional filter based aerosol samplers to estimate nanoparticle exposure levels. A scanning electron microscopehas been suggested for use in determining nanoparticle number concentrations on filter media (NIOSH, 2008; Peters et al., 2009).To assess exposure accurately, it is necessary that an aerosol sampler adhere to the conventions for exposure within a regionof the respiratory system. In the right panels of Fig. 6, bias maps have been constructed in terms of number concentration forthe IOM with foam inserts against the thoracic (top) and respirable (bottom) penetration conventions. Since the foam insertremoves a portion of the nano-sized particles in the airstream, their concentration will be underestimated on the filter. This biasis substantial for ultrafine particle size, where number concentration can be more than 40% (90%) negatively biased for aerosolswith count median diameter (CMD) less than 0.01�m, as compared to the thoracic (respirable) convention.

6. Conclusion

Penetration fractions over three decades of particle aerodynamic diameter have been measured. This penetration data wasused to improve upon the existing semi-empirical foam penetration model for aerodynamic diameters ranging from 0.01 to

572 P. Clark et al. / Aerosol Science 40 (2009) 563 -- 572

10�m and to account for diffusive deposition, which is important for particles with dae < 1�m. The new model was used totest the performance of the IOM with foam insert to capture the thoracic exposure. Our model shows that while the foam insertprovides good size selection for dae > 1�m, the exposure will be underestimated for dae < 0.1�m. This may be important if theIOM inserts are used in determining the exposure to engineered or incidental nano-sized aerosols. The shape of the penetrationcurves generated, however, also suggests that a foammay be engineered tomimic the deposition of aerosol into a healthy, humanlung. Future work will investigate this possibility.

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