Modeling airborne nanoparticle filtration through a complete structure of non-woven material used in protective apparel

Abstract

Airborne nanoparticles represent a new danger in occupational health. Numerous theoretical and experimental studies have been conducted on the efficiency of filtering media used for respiratory protection, but few have focused on media used for skin protective equipment. Indeed, a significant proportion of airborne nanoparticles can end up on the skin, causing local effects and eventually penetrating the human body. Following experimental data obtained with sodium chloride nanoparticles, the authors propose an empirical model to evaluate the penetration of airborne nanoparticles through medium used in disposable coveralls. This study presents an adaptation of the conventional filtration theory used for filtering media used in respirators. The authors' model is compared with Wang et al.'s and Brochot's models and demonstrates improvements in their descriptive ability. Moreover, a domain of validity of the proposed model was determined that will enable the evaluation of the efficiency of similar protective apparel material structures against airborne nanoparticles.

Keywords

nanoparticle penetration filtration efficiency modeling chemical protective clothing occupational health non-woven materials

The growing interest of manufacturers for engineered nanomaterials (ENM) is resulting in more and more workers having to handle these specific chemical products. By 2018–2020, the number of exposed workers worldwide is estimated to reach more than 6 million.¹ Although inhalation is the most direct exposure pathway for airborne ENMs, dermal contact is also significant. Indeed, recent investigations have measured the penetration of ENM in the different layers of the skin after direct applications on damaged and intact human skin.^2, ³ Gulson et al. applied sunscreens containing zinc oxide nanoparticles to 20 humans. After a five-day application phase, trace levels of zinc were localized in the blood and urine.⁴ Moreover, ENM can cause skin irritation or diseases such as dermatitis.⁵ Given the great reactivity and the potential toxicity of some ENMs, it is imperative that workers wear various protective apparel (PA).

If evaluating the efficiency of PA against ENMs seems relatively straightforward, understanding the mechanisms of penetration is much more complex. A conventional filtration theory was developed on single-fiber collection efficiency based on different mechanisms such as Brownian diffusion, interception, inertial impaction, and also electrostatic forces. However, the major part of these works can be applied for non-woven filtering media.⁶ Givehchi and Tan⁷ have published an overview of airborne nanoparticle filtration. They presented single-fiber efficiency models, proposed since the 60s, mainly as a result of Brownian diffusion and interception.⁷ Unfortunately, these theoretical and empirical models proposed to describe the filtration of micro and sub-micron particles through different standard filtering media did not take into account the homogeneity of the structure of the media.^8–10 Yamada et al. studied the influence of the filter's homogeneity on the air filtration of ENM and proposed a new model to predict collection efficiency.¹¹ The authors concluded that a filter's homogeneity leads to a smaller dependence on the Peclet number, which plays an important role in collection efficiency due to the diffusion phenomenon, which is one of the main mechanisms in the case of particles under 100 nm diameter.

Although numerous models may have been established for filter media used in respirators, to the best of our knowledge, no model has been proposed to predict the collection efficiency of ENM that penetrate through PA materials. Indeed, because of their particular physical form, the majority of studies about filtering media used in protection against airborne particles are focused on respiratory devices. However, as mentioned before, some research has shown the penetration of nanoparticles through the skin. The principle of precaution recommends using chemical protective clothing against nanoparticles without knowing their real efficiency. Specifically, Type 5 chemical protective clothing like those studied in the present work is recommended against airborne solid particulates.¹² The failure to recognize this sooner has led to a lack of knowledge about the filtration mechanisms of airborne nanoparticles and therefore the development of models for the materials used for dermal PA.

Thus, this study presents an empirical predictive collection efficiency model that considers only the collection efficiency due to the mechanisms of diffusion and interception. For this, experimental data were obtained measuring the penetration of sodium chloride (NaCl) airborne nanoparticles through PA materials chosen from the results published by Ben Salah et al.¹³ The authors evaluated the penetration of airborne NaCl nanoparticles through various Type 5 chemical protective clothing materials such as flash spinning, microporous film, and two sorts of laminated materials (three and five layers). They concluded no penetration except for the five layers laminated material (between 8 and 10% penetration). Based on these results, we decided to model the efficiency of three different commercial five-layered laminated materials, taking into account only the three layers involved in the filtering process. The two other layers are only there to maintain the integrity of the structure. Similar to Wang et al.¹⁴ and Brochot,¹⁵ the experimental curves were fitted with semi-empirical adjusted models and the domains of validity were established.

Experimental details

Three PA materials were selected based on their commercial availability for the workplace and their common design and structure. All the samples were taken from disposable coveralls, discarding the parts with seams (Figure 1).

Figure 1.

Typical photographs of a) the front of SMMMS 1, b) the front of SMMMS 2, and c) the back of SMMMS 3.

The structure of the material consists of five layers hence the name SMMMS: three internal layers of meltblown (M) polypropylene non-woven fabric for filtration, and two external layers of spunbond (S) polypropylene non-woven fabric, to ensure the mechanical resistance and global structure of the material. The structure of the three PA materials was analyzed using scanning electron microscopy (SEM, Hitachi S3600N – V_acc = 5 kV – magnification × 100). Only for the SEM analysis was a 15 nm conductive gold layer deposited by metallization on the external surface of the samples, namely the S-layer to enhance the conductivity of the sample and to obtain better SEM images. The gold layer should not affect the filtration governed only by the internal layers (the M-layers).

Certain specifications and physical characteristics of the selected PA were measured. The thickness (t) was evaluated using standard CAN/CGSB-4.2 No. 37-2002 (Textile Test Methods: Fabric Thickness), which is similar to International Standard ISO 5084.¹⁶ This standard developed for compressible textile fabrics consists in applying an arbitrary pressure between plane surfaces of the tested sample. As the textile fabrics are compressible, the pressure measured was directly linked to the pressure applied. The unit mass (W) was measured according to standard CAN/CGSB-4.2 No 5.1-M90 (R2013) (Textile Test Methods: Unit Mass of Fabrics).¹⁷ Fives specimens of 80-cm² textile fabrics were taken from the protective clothing material conditioned during 24 hours at 21 ± 2 ℃ and 65 ± 2% relative humidity. Each specimen was weighed on a digital balance ( ± 0.1 mg). W was then defined as the mass of the specimen (in grams) divided by its area (in square meters). Finally, the material density (ρ_f) was established using standard ASTM D792-13: Standard Test Methods for Density and Specific Gravity (Relative Density) of Plastics by Displacement.¹⁸ This standard involves weighing a specimen of 1 to 50 g in water, using a sinker with plastics that are lighter than water. Five other specimens were prepared under the aforementioned conditions and weighted. The material density was calculated using a complex formulation described in the standard.

The solidity, α, also defined as 1-porosity of the material, was calculated using unit mass, the material thickness and the fiber density of the medium, as follows:

α = \frac{W}{ρ_{f} t}

(1)

As previously mentioned, the PA materials used in this study consist of a combination of five layers, two S and three M. Although Equation 1 is most commonly employed to calculate solidity (of a homogeneous structure), it is pertinent to think that the solidity of the S-layer is higher than that of the M-layer. Thus, in our case, Equation 1 represents an “average” solidity of our PA materials.

Finally, air permeability was determined using standard CAN/CGSB-4.2 No 36-M89 (R2013).

A polydisperse aerosol of sodium chloride particles (NaCl) was generated from a saline solution (0.05 g/L) using a nebulizer (Collison 3 jets, BGI by Mesa Labs, Colorado, USA). The saline solution was prepared with crystalline NaCl (ACS grade, Fisherscientific, Mississauga, Canada) and MilliQ water (18.2 MΩ cm at 25 ℃, Organic Carbon <2 µg C·L⁻¹). Dry, clean compressed air at 0.69 bar (10 psi) was employed for the nebulizer. Moreover, wet airborne particles passed through a homogenization box with a fan to reduce the humidity rate. The size distribution of the NaCl airborne particles was determined using a Scanning Mobility Particle Sizer spectrometer (SMPS 3936, TSI). It consists in a long differential mobility analyzer (DMA 3081, TSI) and a condensation particle counter (3786, TSI). To neutralize the electrostatic charges, a radioactive source of Krypton 85, used as a particle charge neutralizer, was included. The flow rate was fixed to 6 L·min⁻¹ and the sheath air ratio was maintained at 0.6. For each test, three scans were performed for a total duration of 4.5 min. The size range obtained was from 20 to 250 nm and the size distribution was centered at about 38.5 ± 3.3 nm (Figure 2).

Figure 2.

Size distribution of the NaCl airborne particles.

An experimental apparatus was developed to measure the penetration of airborne NaCl particles through PA material samples (Figure 3). The different parts of this apparatus are minutely presented by Ben Salah et al.¹³ The surface area of the PA samples was 23 cm², which led to a face velocity of 0.435 cm·s⁻¹. The pressure drop (ΔP) between the upstream and downstream sides of the PA sample was measured with a pressure sensor.¹³ The experimental apparatus, apart from the SMPS, was confined in an environmental chamber where the temperature and the relative humidity were maintained at 21 ± 2 ℃ and 55 ± 3%.

Figure 3.

Schematic representation of the experimental setup used by Ben Salah et al.¹³

For each PA sample, five penetration measurements were performed, and for each replicate, three size-distribution scans were performed; before starting to collect data, the system equilibrium conditions (i.e., size distribution and particle concentration) were reached within 5 min.

The measured penetration $(P_{exp})$ of airborne particles through the PA samples was defined as the downstream concentration of particles $(C_{down})$ divided by the upstream concentration of particles $(C_{up})$ .

P_{exp} = \frac{C_{down}}{C_{up}}

(2)

Preliminary useful calculations to apply for the standard filtration theory

According to Hinds,⁶ the total single-fiber efficiency $E_{Σ}$ can be approximated by the sum of the four terms corresponding to different collection mechanisms such as diffusion, interception, inertial impaction, and gravity, labeled as $E_{D}$ , $E_{R}$ , $E_{I}$ , and $E_{G}$ respectively.

E_{Σ} \approx E_{D} + E_{R} + E_{I} + E_{G}

(3)

In the present study, for particle diameters less than 250 nm, we assume after calculations based on Hind's model that diffusion and interception are the dominant filtration mechanisms, as indicated in Equation 4. Moreover, the collection of particles due to electrostatic mechanisms is intentionally discarded to simplify our theoretical approach. However, the effect of the nanoparticle electric charges will be considered in a future work.

E_{Σ} \approx E_{D} + E_{R}

(4)

$E_{Σ}$ can be related to penetration P as shown in Equation 5:

P = exp (- \frac{4 α E_{Σ} t}{π (1 - α) d_{f}})

(5)

where

d_{f}

is the mean fiber diameter from the M-layers. From Equation 5, it is possible to express

E_{Σ}

as:

E_{Σ} = - \frac{π (1 - α) d_{f}}{4 α t} \ln P

(6)

However, the evaluation of $d_{f}$ for these PA fabrics is complicated by electronic microscopy, leading to high variability in the measurements. Indeed, the presence of many deformed fibers (crushed or stretched) due to the manufacturing process was noted. On the basis of this finding, we used Davies' diameter (d_Davies) for calculations instead of $d_{f}$ ¹⁹:

\begin{matrix} d_{Davies} = \sqrt{\frac{η \times U \times t \times f (α)}{Δ P}} \\ with f (α) = 64 α^{3 / 2} \times (1 + 56 α^{3}) for 0.006 \leq α \leq 0.3 \end{matrix}

(7)

where η is the dynamic viscosity of the air, U the face velocity and

f (α)

an empirical correlation including non-ideal effects.⁶

The first step in the theoretical approach of the filtration theory is to determine the flow regime. For this, we need to calculate the Knudsen's number

(K n_{f})

, a non-dimensional number that helps to determine the flow regime (Equation 8). The flow regime is defined as “continuous” if

K n_{f} < 0.001

or “Knudsen flow” if

0.001 < K n_{f} < 0.25

K n_{f} = \frac{2 λ}{d_{Davies}}

(8)

where λ is the mean free path of air molecules, and is 65 nm²⁰ at normal temperature and pressure. In all cases, 0.001 < Kn_f < 0.25, indicating that we are in a Knudsen flow (see Table 2 below). This result also makes it possible to determine the hydrodynamic factor, which will be used in the expression of the collection efficiency due to interception. The hydrodynamic factor (H) is a dimensionless factor that takes into account the effect of the distortion of the flow in the environment of a fiber due to its proximity to other fibers. It is defined as follows ²¹:

\begin{matrix} H = \frac{α}{1 + K n_{f}} - 0, 5 \ln α - 0, 25 α^{2} - \frac{0.75}{1 + K n_{f}} + \frac{{(2 α - 1)}^{2}}{4 (1 + K n_{f})} K n_{f} \end{matrix}

(9)

Table 2.

Measured values of the pressure drop and calculated values of Davies' diameter, Knudsen's number and the hydrodynamic factor with U = 0.435 cm/s, λ = 65 nm, and η = 18.1 µPa.s

Sample ID	SMMMS 1	SMMMS 2	SMMMS 3
Pressure drop at 0.435 cm·s⁻¹ (Pa)	27.9 (0.7)	28.1 (0.2)	27.3 (0.7)
Davies' diameter (µm)	2.65	2.01	2.11
Knudsen's number	0.049	0.065	0.062
Hydrodynamic factor	0.285	0.379	0.370

Results and discussion

The structure of the three PA materials was analyzed qualitatively by optical and electronical microscopy. Figure 4a represents an optical image of the surface of SMMMS 1. The calendering observed in this Figure consists to a part of the five layers melted together by welding to ensure the global structure of the material. The calendering occupies 20% of the surface area of the sample. Figure 4b shows a SEM image of the surface of SMMMS 1 and Figure 4c its cross section. In the foreground, the S-layer can be observed and in the background, the M-layer; however, in the cross section, it is very difficult to distinguish the five layers. The two other PA materials were not represented because their structures were similar.

Figure 4.

SMMM1 a) optical image of the surface, b) SEM image of the surface (magnification × 100), and c) the cross section (magnification × 120).

Considering the standard deviations, the thicknesses of the PA material samples are almost the same, as are the values for air permeability (Table 1). On the other hand, the solidity is comparable for SMMMS 2 and SMMMS 3, but is more significant for SMMMS 1. This result is due particularly to the difference in the unit mass.

Table 1.

Specifications of the selected PA: Mean (SD), n = 5

Sample ID	SMMMS 1	SMMMS 2	SMMMS 3
PA thickness (t) (µm)	323 (3)	314 (9)	324 (13)
Unit mass (W) (g·cm⁻²)	57 (1.4)	41.6 (0.6)	42.8 (0.3)
Material density (ρ_f) (g·cm⁻³)	0.910 (0.009)	0.0.867 (0.002)	0.891 (0.006)
Solidity (α)	0.194 (0.005)	0.153 (0.002)	0.148 (0.003)
Air permeability (cm⁻³·cm⁻²·s)	22.1 (1.1)	22.2 (0.9)	23.0 (1.8)

Figure 5 displays $P_{exp}$ of NaCl airborne particles measured for the three PA material samples as a function of the particle diameter. The three PA samples show similar trends in their penetration profiles. As indicated by the manufacturer, the long differential mobility analyzer (DMA 3081, TSI) has a particle size range from 10 to 1000 nm. Thus, the limit of detection of the SMPS is compatible. However, as shown in Figure 5, the experimental penetration was measured only from 25 nm because the penetration rises sharply to reach almost 100%. This phenomenon has been observed by others authors but without offering an explanation.^13,22,23 We think it is a measurement artifact due to SMPS. On the other hand, it is not due to the thermal rebound because the particle size is too big.

Figure 5.

Experimental penetration for the three PA materials as a function of the particle size.

Minimal penetration (3–4%) was observed for particles of a diameter around 30 nm. From 30 nm to 180 nm, $P_{exp}$ increased very quickly from 4–65%. For the 50–200 nm particle range, a significant shift for $P_{exp}$ (4–6%) can be observed between SMMMS 1 and the other two. The standard deviations for SMMMS 1, SMMMS 2, and SMMMS 3 were 1.2%, 3.1%, and 0.7% respectively.

The profiles of our experimental curves were similar to those obtained by Ben Salah et al. for comparable materials.¹³ However, in our case, we observed a maximal penetration of 65% for 250 nm, whereas they measured only 40% for the same particle size.

Modeling of single-fiber efficiency

As indicated in the “Preliminary useful calculations to apply for the standard filtration theory” section, certain parameters needed to be determined in order to apply filtration theory. Thus, according to equations 7, 8, and 9 and the values summarized in Table 1, the Davies' diameter, the Knudsen's number and the hydrodynamic factor were calculated for all PA materials, using the experimental values of the pressure drop and solidity (Table 2).

Many researchers have proposed theoretical and empirical models for collection efficiency due to diffusion.^24,25 For example, Lee and Liu validated their model with a fiber diameter from 11 to 12.9 µm and a face velocity between 1 and 300 cm·s⁻¹ ²⁶; Hinds proposed another model with different values of fiber diameter and face velocity, 0.1 to 50 µm and 0.1 to 200 cm·s⁻¹ respectively.⁶ However, all these models are valid only in a specific field of study, particularly with regard to the particle size, fiber diameter, solidity, and face velocity.

Initially, the experimental data were compared with the experimentally derived equations from Wang et al.¹⁴ and Brochot.¹⁵ Both proposed expressions, displayed in Equation 10 (Wang et al.) and Equation 11 (Brochot), where Pe is the dimensionless number of Peclet.

E_{D - Wang} = 0.84 P e^{- 0.43}

(10)

E_{D - Brochot} = 0.976 P e^{- (1.525 α - 0.506)}

(11)

The empirical models (Wang et al. and Brochot) were chosen because some of their PA material parameters were compatible with ours (Table 3). The fiber diameters, particle diameters, and thicknesses are not exactly the same, but their magnitudes are similar. However, solidity is higher for our PA materials, and the face velocity is at least 10 times less than for Wang et al. and Brochot.

Table 3.

Physical characteristics of the studied filtered material and experimental inputs used by Wang et al.¹⁴ and Brochot.¹⁵

	Present study	Wang et al.	Brochot
Solidity	0.153–0.194	0.039–0.050	0.055–0.091
Fiber diameter (µm)	2.0–2.7*	1.9–4.9	1.34–5.02*
Thickness (µm)	314–324	530–740	336–502
Particle diameter (nm)	25–250	<100	<100 and <400
Face velocity (cm·s⁻¹)	0.435	5.3–15	5.3

Note: * Davies diameter

In equations 10 and 11, the coefficients 0.84 and 0.976 are empirically determined, as well as the power of the number of Pe 0.43 or the function dependent on α for Brochot. The negative powers in the equations (10 and 11) indicate that the collection efficiency increases as Pe and d_p decrease.

Pe is a function of Davies' diameter, face velocity, and the diffusivity of particles D (Equation 12). The latter is defined from k, the Boltzmann constant; T, temperature; d_p, the particle diameter; η, the dynamic viscosity of the air; and finally C_c, the Cunningham slip correction factor (Equation 13).

Pe = \frac{d_{Davies} U}{D} with D = \frac{kT C_{c}}{3 π η} d_{p}

(12)

C_{c} = 1 + (\frac{2 λ}{d_{p}}) (1.257 + 0.4 e^{- 0.55 (\frac{d_{p}}{λ})})

(13)

As shown in Figure 6, none of the proposed models can satisfactorily represent the experimental penetration obtained with our materials. Both empirical models of Wang et al. and Brochot underestimate our level of penetration. In addition to the difference in experimental parameters and physical characteristics, these two models studied different filtering medium, used mainly in respiratory protection, which does not correspond in terms of structure to our PA materials.

Figure 6.

Comparison between the experimental penetration (for SMMMS 2) and Wang et al.'s and Brochot's models of the collection efficiency.

In light of these findings, an optimized model was developed in this study suited to our PA materials. The first step in our approach was to consider that $E_{Σ} \approx E_{D}$ , which is correct for particle diameters under 100 nm.¹⁴ Indeed, the effect of the interception efficiency is remarkable for particles bigger than 100 nm. However, this simplification is valid for standard filter media (homogeneous structure, monosized fibers, etc.). In the present case, the most penetration particle size may be shifted due to calendering or electrostatic charges. Thus, the experimental single-fiber efficiency ( ${E_{D}}_{exp}$ ) due to diffusion can be expressed as a rearrangement of Equation 6 considering the experimental penetration.

{E_{D}}_{exp} \approx - \frac{π (1 - α) d_{Davies}}{4 α t} \ln P_{exp}

(14)

Firstly, ${E_{D}}_{exp}$ has been plotted as a function of theoretical Pe (Figure 7) for a size range from 25 to 250 nm. The shape of the curve suggests that for the three PA materials, a power regression can be used to model collection by diffusion mechanism, as used by Wang et al.¹⁴ (Equation 15). While the diffusion was preponderant in the filtration mechanisms for particles smaller than 100 nm, it was still present for larger sizes up to 250 nm. The fit curves were also performed for 25–100 nm particles and the expressions of the power regressions obtained were strictly the same.

{E_{D}}_{exp} = AP e^{- m}

(15)

Figure 7.

SMMMS 2 typical experimental single-fiber efficiency due to diffusion as a function of the theoretical number of Peclet and fit curve (dash line) using power regression ( $AP e^{- m}$ ) for a size range from 25–250 nm.

The following expressions were obtained for each PA sample (Equation 16):

\begin{matrix} E_{D} (SMMMS 1) = (0.157 \pm 0.004) P e^{- (0.524 \pm 0.045)} \\ E_{D} (SMMMS 2) = (0.124 \pm 0.003) P e^{- (0.528 \pm 0.012)} \\ E_{D} (SMMMS 3) = (0.134 \pm 0.004) P e^{- (0.502 \pm 0.012)} \end{matrix}

(16)

Equation 16 shows that m-powers (as defined in Equation 16) are comparable for all PA materials. On the other hand, A-factors (also defined in Equation 16) obtained are significantly different. A for SMMMS 1 is higher than SMMMS 3 and higher even than SMMMS 2. In comparison with Equation 10 and Equation 11, the A-factors are 6–8 times smaller than those proposed by Wang et al. or Brochot. As previously mentioned, the solidity is higher for our PA materials and the face velocity is at least 10 times more important than for Wang et al. and Brochot. These parameters greatly influence the single-fiber efficiency due to diffusion. This could explain the difference observed for the m-powers and the A-factors between their models and our proposed models.

In 1988, Rao and Faghri presented a theoretical model of particle diffusion where A can be expressed as a function of the solidity α.²⁷ For Pe < 50 (corresponding to our case), they proposed the following expression (Equation 17):

E_{D - Rao} = 4.89 (\frac{1 - α}{H})^{0.54} P e^{- 0.92}

(17)

In light of these findings, the authors tried to link A-factors with the solidity of the materials using a similar expression. Figure 8 displays the variation of the A-factor as a function of the ratio $(1 - α) / (1 - α) H H$ for the three PA materials. The A-factor values increase as a power fit with $(1 - α) / (1 - α) H H$ with a good correlation coefficient (R² = 0.95). Finally, in our study, it was possible to obtain an optimized model of the collection efficiency due to diffusion where the m-power is constant (an average of the three models) and the A-factor is a function of the solidity of the filtering medium (Equation 18). Comparing this with Rao and Faghri's expression, the $(1 - α) / (1 - α) H H$ -power was higher in our case and the factor before was much smaller. These results could be attributed to the difference in materials studied, particularly as to their solidity.

E_{D - proposed} = 0.06 (\frac{1 - α}{H})^{0.9} P e^{- (0.52 \pm 0.01)}

(18)

Figure 8.

Determination of the correlation between the A-factor and the solidity using Rao and Faghri's formalism.²⁷

As to the contribution of the interception collection (from 100 nm), the model of Lee and Liu was chosen because the domains of their study were similar to ours.²⁶ Effectively, except for face velocity (parameter non-significant for the collection due to interception), the fiber diameter and solidity were comparable. Lee and Liu proposed the following expression (Equation 19):

E_{R - Lee & Liu} = 0.6 (\frac{1 - α}{H}) (\frac{R^{2}}{1 + R})

(19)

where R is defined as follows:

R = \frac{d_{p}}{d_{Davies}}

(20)

In the present study, it appeared that the collection efficiency due to the interception mechanism remained low compared with the diffusion mechanism, even for particles larger than 100 nm, therefore we had to adapt Lee and Liu's model. Thus, the proposed model for the interception mechanism became (Equation 21):

E_{R - proposed} = 0.06 (\frac{1 - α}{H}) (\frac{R^{2}}{1 + R})

(21)

Finally, according to Equation 5, the adjusted model for the total single-fiber efficiency is the sum of the diffusion contribution and the interception contribution. The complete expression is presented in Equation 22.

E_{Σ} = 0.06 (\frac{1 - α}{H})^{0.9} P e^{- 0, 52} + 0.06 (\frac{1 - α}{H}) (\frac{R^{2}}{1 + R})

(22)

Figure 9 compares the experimental penetration and our proposed model and the models of Wang et al. and Brochot. Our proposed model presents a good correlation with the experimental data. However, for the smaller particles, under 30 nm, a divergence can be observed, as noted by other authors. ^9, ¹³ More investigations are needed to explain this phenomenon.

Figure 9.

Comparison between a typical experimental penetration (SMMMS 1 in this case) and the proposed model for the collection efficiency due to diffusion.

After determining a new expression of the total single-fiber efficiency for PA materials, a domain of validity for our proposed model was proposed as a function of α, d_f, and U ranges. Using MATLAB, we arbitrarily set a 10% domain of validity. A comparison for $25 nm \leq d_{p} \leq 250 nm$ was performed between the experimental data and the proposed model. For each values of $25 nm \leq d_{p} \leq 250 nm$ (incrementation step of 5 nm), of $0.050 \leq α \leq 0.300$ (incrementation step of 0.010), of $1 μ m \leq d_{f} \leq 10 μ m$ (incrementation step of 1 µm) and $0.001 m \cdot s^{- 1} \leq U \leq 0.01 m \cdot s^{- 1}$ (incrementation step of 0.0005 m·s⁻¹), the absolute value of the difference between the experimental data and the proposed model, must not exceed 10% as follows in Equation 23.

| P_{exp} - P_{model} | \leq 10 %, for 25 nm \leq d_{p} \leq 250 nm

(23)

Table 4 summarizes the different domains of validity obtained for each parameter indicated above. These domains of validity will enable the study of other materials employed in the manufacturing of PA, particularly chemical protective clothing (CPC), using the optimized proposed model. Although the range of particle diameter is narrow, those of solidity and fiber diameter include a large number of protective non-woven materials.

Table 4.

10% domain of validity for the proposed model

Parameters	Domain of validity
Particle diameter (nm)	25–250
Solidity, α	0.060–0.250
Fiber diameter, d_f (µm)	2–5
Face velocity, U (cm·s⁻¹)	0.350–0.900

Conclusion

For the first time, to the best of our knowledge, an optimized empirical model on the penetration of nanometric airborne particles (25–250 nm) through non-woven PA and CPC materials based on the conventional filtration theory has been presented. The single-fiber efficiency was computed using the experimental results and compared with the well-known theoretical or empirical expressions found in the literature. For example, the power law model chosen for its single efficiency due to diffusion and depending on the Peclet number led to satisfactory agreement with the experimental data. However, some coefficients were adapted to enhance the fit applying mathematical regressions. It has also been shown that A-factors encountered in the efficiency due to the diffusion could be linked to the solidity of the materials.

The determination of a domain of validity for our proposed model could make it possible to simulate the efficiency of other materials used in PA manufacturing. Indeed, the solidity domain includes a lot of protective non-woven materials having an SMMMS structure.

We are aware that the electrostatic effect has not been taken into account as in the majority of work found in the literature. Moreover, the face velocity factor is more important than that encountered in the workplace. Work is in progress to address these issues.

However, considering the large number of different media used in PA and the inhomogeneity of their manufacturing processes, chemical composition, and design, it would be very difficult, to the best of our knowledge, to develop a single penetration model for airborne nanoparticles through all sorts of CPC without considering certain parameters such as the random orientation of the fibers or the tortuosity of the PA material.

To enhance our knowledge about the filtration of airborne nanoparticles through PA, work is underway to take into consideration the electrostatic charges of the particles and the PA materials, and also the different structures encountered in the PA. Moreover, the effect of temperature and the humidity rate, the main parameters in the filtering mechanisms, will be investigated.

Footnotes

Acknowledgement

The authors wish to thank Prof. Maximilien Debia (University of Montréal) for the SMPS.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and /or publication of this article.

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