Absence of any effect of the electric charging state of particles below 10 nm on their penetration through a metal grid

ABSTRACT

The effect of image force on the penetration of nanometer particles through metal grids remains a controversial issue. Experimental evidence of the existence and of the absence of such effect have both been reported in the past. A careful experimental work to measure penetration of particles in the mobility equivalent diameter range between 3.4 and 10 nm has been carried out. The possible particle size change between the aerosol generator and the filter has been considered, as well as the possible effect of particle number concentration on the filtration efficiency. The geometric dimensions of the filter allowed attainment of the fully developed parabolic flow velocity profile upstream the grid. Measurements were done at two values of the fiber Reynolds number, 0.09 and 0.12, much smaller than 1, as demanded by the currently accepted filtration theory. Penetration of charged particles, measured in three alternative ways, has been compared with penetration of uncharged and neutral particles (the latter consisting of a mixture of positive, negative, and uncharged particles). Two main conclusions have been reached: (1) the charging state of the particles does not affect their penetration through the metal grid and (2) the experimentally measured penetrations are fairly well predicted by the fan filter model of Cheng and Yeh.

Copyright © 2018 American Association for Aerosol Research

EDITOR:

• Jing Wang

1. Introduction

Aerosol particle penetration through wire screens has received a relatively large attention in the past, mainly because it constitutes an ideal prototype of a fibrous filter and, as such, has been widely used to develop air filtration theories. Wire screens have also been used to measure aerosol particle size distribution (diffusion battery), although this specific application has lost its former importance in favor of more precise and fast measurements provided by particle electric mobility analyzers.

An important issue is the effect that the presence of electric charges on the particles may exert on the filtration performance of the grids. Electrical effects can appear in two different ways. First, if the aerosol concentration is high enough, mutual repulsion among particles charged with the same polarity, especially in the case of particles with high mobility, can lead to a reduction of the fraction of particles that penetrate the grid. Second, even in the case that the aerosol concentration is low, a charged particle may induce a charge of opposite sign in the fiber, thereby arising an attraction force (image force) between the particle and the fiber, which thus also results in a decrease in penetration.

Experimental studies dealing with the effect of image forces on aerosol penetration through a metal grid in the particle size range below 10 nm are few in number. More important is that contradictory results have been obtained and the topic remains controversial. Scheibel and Porstendörfer (1984) found no difference in the penetration of singly charged and uncharged particles in the particle size range between 3.5 and 100 nm. Otani et al. (1995) did experiments with particles smaller than 10 nm, even with ions, and found no image force effect neither in wire screens nor in laminar flow tubes. The same findings (no image force effects) were reported by Alonso et al. (1997) for particles below 7 nm and air ions. In these three studies, the experimentally measured penetration agreed reasonably well with the fan filter model equation of Cheng and Yeh (1980), which considers diffusion as the only deposition mechanism. Shin et al. (2008) did experiments with (globally) neutral particles with diameter between 3 and 20 nm and found good agreement with the Cheng-Yeh model for temperatures up to 500 K; however, no experiments were done with charged or uncharged particles and, therefore, from their results it is not possible to withdraw any definite conclusion about the effect of image force on filtration. Similar results were reported much earlier by Cheng et al. (1990) also working with neutral aerosols between 4.6 and 20 nm. Note that in this particle size range, the fraction of uncharged particles in a neutral aerosol is quite high, of the order of 90% or more and, therefore, it is difficult to determine whether the presence of <10% charged particles has any effect on the filtration of the globally neutral aerosol.

In contrast with the works cited above, there are a number of other experimental works in which image force has been found to increase the filtration efficiency for nanometer-sized particles. Heim et al. (2005) reported a slight increase in the filtration efficiency of charged particles between 2.5 and 20 nm in comparison with that of (globally) neutral particles using nickel and stainless steel meshes. Kim et al. (2006) measured penetration of charged, uncharged, and neutral particles in the size range 2–100 nm and found that the filtration efficiency for charged particles was larger than for uncharged ones, and that the filtration efficiency for neutral particles lied in between the other two, that is, filtration efficiency increased as the fraction of charged particles present in the aerosol increased, a clear indication of the existence of image force effects. In this latter work, it was also observed that electrostatic attraction (image force) was affected by the aerosol face velocity in such a manner that for high velocities particle penetration was not affected by its charging state. Van Gulijk et al. (2009), working with neutral aerosols in the size range 7–20 nm, suggested that the presence of electric charges increased the sticking probability of particles. Finally, Heim et al. (2010) performed penetration measurements for charged particles and ions with mobility equivalent diameters between 1.2 and 8 nm; though they did not do measurements for uncharged particles and, therefore, a comparison cannot be made, these authors found that penetration was smaller than predicted by the Cheng-Yeh theory for very low Peclet numbers and this was attributed to image force between the particles and the grid.

In view of these contradictory results, a careful experimental work has been carried out with the intention to add new light on this controversial topic.

2. Current theory on particle filtration by simultaneous diffusion and image force

The effect of particle charge on filtration was studied experimentally by Lundgren and Whitby (1965) and Yoshioka et al. (1968), using fibrous filters. They found that the single fiber efficiency for the mechanism of image force was proportional to the square root of the image force number, K_IM, defined as[1] $K_{IM}=\left(\frac{{ϵ}_f-1}{{ϵ}_f+2}\right)\frac{C{p}^2{e}^2}{12{\pi }^2\mu u{ϵ}_0{d}_p{d}_f^2},$[1] where ϵ_f is the dielectric constant of the fiber (taken as infinite for metal fibers), ϵ₀ is the dielectric constant of a vacuum, C is the Cunningham slip correction factor, p is the number of charges on the particle, e is the electron charge, μ is the gas viscosity, u is the air flow velocity, d_p is the particle diameter, and d_f is the fiber diameter. K_IM represents the ratio of the particle drift velocity by image force to the fluid flow velocity. In the above cited works, experiments were done with particles between 0.1 and 1 μm in diameter and carrying a large number of charges, up to 320 elementary charges per particle. They proposed the following expression for the single fiber efficiency due to image force:[2] $E_{IM}=a{K}_{IM}^{1/2}.$[2]

The proportionality constant a was 1.5 (Lundgren and Whitby 1965) and 2.3 (Yoshioka et al. 1968).

More recently, Alonso et al. (2007) made experiments with smaller particles (diameter between 25 and 65 nm) carrying up to three elementary charges at most. They found the following expression for the single fiber efficiency:[3] $E_{IM}=9.7K_{IM}^{1/2}.$[3]

Any of these two correlations, (2) and (3), can be added to the single fiber efficiency due to diffusion, to calculate the total single fiber efficiency. According to the fan filter model of Cheng and Yeh (1980), which has been successfully verified in many experimental works, the single fiber efficiency for the mechanism of diffusion is given by[4] $E_D=2.7{\text{Pe}}^{-2/3}.$[4]

In the last expression, Pe is the Peclet number, Pe = ud_f/D, where D is the particle diffusion coefficient (calculated with the Stokes–Einstein equation), and u and d_f have the same meaning as in Equation (1[1] $K_{IM}=\left(\frac{{ϵ}_f-1}{{ϵ}_f+2}\right)\frac{C{p}^2{e}^2}{12{\pi }^2\mu u{ϵ}_0{d}_p{d}_f^2},$[1] ).

If both deposition mechanisms, diffusion and image force, operate simultaneously, the single fiber efficiency can be determined by the approximate expression[5] $E=E_D+E_{IM},$[5] because the cross term containing the product E_DE_IM can be safely neglected (Alonso et al. 2007).

Penetration is finally given by[6] $P=\text{exp}\left(-nSE\right),$[6] where n is the number of screens (one in the present work), and S is the so-called screen parameter (see Table 1 below for its definition).

Table 1. Characteristics of the stainless steel grid used in the experiments.

Fiber diameter, df (μm)	66^1
Thickness, h (μm)	120^2
Opening (μm)	103^1
Open area fraction (%)	37^1
Surface density, ρs (g/cm^2)	0.031^2
Volume density, ρv (g/cm^3)	7.96^1
Solid volume fraction, α (-)	0.324^3
Screen parameter, S (-)	1.110^4

¹ Datum provided by the manufacturer (Goodfellow).

² Measured.

³ Calculated from α = ρ_s/hρ_v.

⁴ Calculated from S = 4αh/πd_f(1 − α).

3. Experimental method

Penetration through a metal grid was measured for three different electric charging states of the aerosol: (1[1] $K_{IM}=\left(\frac{{ϵ}_f-1}{{ϵ}_f+2}\right)\frac{C{p}^2{e}^2}{12{\pi }^2\mu u{ϵ}_0{d}_p{d}_f^2},$[1] ) positively charged particles; (2[2] $E_{IM}=a{K}_{IM}^{1/2}.$[2] ) uncharged particles; and (3[3] $E_{IM}=9.7K_{IM}^{1/2}.$[3] ) a globally neutral aerosol containing positive, negative, and uncharged particles, with a roughly zero net charge.

Figure 1 shows the general experimental setup employed for the measurement of penetration of aerosols in the three charging states. An evaporation-condensation NaCl aerosol was charged in a circular tube containing two thin foils of ²⁴¹Am, each with an activity of 0.9 μCi, and size-classified with a differential mobility analyzer (TSI NanoDMA, length = 4.987 cm; electrodes radii = 0.937 and 1.905 cm). The DMA was operated in open mode, i.e., no sheath recirculation, at aerosol (= sampling) flow rate of 2 l/min, and sheath (= excess) flow rate of 20 l/min. The singly charged monodisperse particles, with mobility-equivalent diameter selected between 3.4 and 10.0 nm, leaving the DMA were then passed through one of the two routes, A and B in the drawing, in order to preserve or modify their charging state. Route A contains another ²⁴¹Am neutralizer, with the same characteristics as the former, and an electrostatic precipitator (ESP). The ESP consisted of a circular grounded tube made of copper, 10 mm ID and 10 cm in length, with a coaxial metal wire 2 mm in diameter to which a DC voltage, high enough to remove all the charged particles, was supplied. When the ESP is turned on, the particles coming from route A are all uncharged; when the ESP voltage is turned off, the aerosol sent to the filtration unit is neutral, i.e., it contains uncharged particles and roughly the same amount of positive and negative particles giving a zero net charge. Note that since the particles are very small (≤10 nm), the fraction of uncharged particles in the neutral aerosol is rather high, above 90% for 10 nm particles, and about 99% for the smallest particles tested. On its part, route B is a bypass route, a conductive tube carrying directly the positively charged particles from the DMA to the filtration unit.

Figure 1. Setup for the measurement of particle penetration through the metal grid contained inside the filter. NaCl = polydisperse sodium chloride aerosol generated by evaporation-condensation; DMA = differential mobility analyzer; 3WV = three-way valve; ²⁴¹Am = cylinder containing two small circular foils of ²⁴¹Am, each with an activity of 0.9 μCi; ESP = electrostatic precipitator; T = metal T-junction; MF = mass flowmeter; dummy = cylinder of same dimensions as the filter but with no metal grid inside; CPC = condensation particle counter.

The filter efficiency measuring system consisted of two geometrically identical holders made of brass and electrically grounded, one containing one metal grid (‘‘filter” in route C in Figure 1), the other empty (‘‘dummy” in route D). Each holder consisted of a central tube, 80 mm long and 36 mm ID, and two conical ends 40 mm in length and an inside diameter linearly changing between 4 and 28 mm. The central tubes of the holders were equipped with a series of rings, each 5 mm long, 36 mm OD, and 28 mm ID. The grid was placed near the holder outlet, between the two last rings and in contact with them. The wire screen exposed to the aerosol flow was thus a circle of 28 mm in diameter. The length of the straight central tube assured the attainment of a fully developed parabolic flow velocity profile upstream of the grid if the aerosol flow rate is kept below 1.2 l/min. The test particles, either charged, uncharged, or neutral, were alternately passed through the filter and the dummy unit. Penetration through the grid was determined from comparison of the particle concentrations measured at the outlet of the holders. In general, particle number concentrations were measured with a condensation particle counter (CNC, TSI model 3786).

Particles were diverted to routes A or B, and C or D, by means of three-way valves provided by a local manufacturer and operated manually. Three metal T-junctions, shown as T-1, T-2, and T-3 in Figure 1, completed the general experimental setup. All the connecting tubes were made of conductive plastic.

Since penetrations were measured by comparison of the number concentration of particles coming from two alternative routes, C and D, one has to be sure that the two routes are perfectly identical, so that the presence of valves, T's, and tubes does not have any effect on the measurements. The best way to assure the correctness of the measurements is to follow the methodology proposed by Alonso and Borra (2016). This method consists in performing a measurement with, say, the setup shown in Figure 1, yielding a penetration P₁. A second measurement is carried out after exchanging the filter and dummy units, so that the filter is now placed in route D and the dummy unit in route C, keeping the rest of the setup unchanged. With this second arrangement a penetration P₂ is obtained. Penetration should finally be determined as the geometric mean of P₁ and P₂. This method is admittedly tedious and time consuming, but it guaranties that the experimental measurements are not affected by the possible asymmetry of the line accessories (valves, T's, connections, etc.).

The metal grid, provided by Goodfellow, was made of stainless steel. Its characteristics are listed in Table 1.

Two evaporation-condensation polydisperse aerosols differing in their particle size distribution were generated. One, obtained with the furnace operated at 560ºC, had a mean diameter of about 4.5 nm; from this aerosol, particles with diameters of 3.4, 4.1, and 5.1 nm were selected with the nanoDMA. From the other polydisperse aerosol, generated at 600ºC and which peaked at 8.2 nm, particles of diameters 5.8, 7.2, 8.8, and 10.0 nm were selected. In this manner, the test monodisperse aerosols used for penetration measurements were selected from near the peak of the particle size distribution of the polydisperse aerosol in order to reduce the extent of sizing errors (Alonso et al. 2014).

Experiments were carried out with two aerosol flow rates through the filter/dummy system, 0.8 and 1.0 l/min, giving aerosol face velocities of 2.17 and 2.71 cm/s, and fiber Reynolds numbers of 0.09 and 0.12, respectively. To attain these flow rates, part of the incoming aerosol was purged just before the second three-way valve (see Figure 1).

For each aerosol flow rate, each particle diameter selected with the nanoDMA, and each electric charging state of the aerosol, 10 penetration measurements were done by shifting consecutively the three-way valve 3WV-2 between routes C and D, and using the setup shown in Figure 1, i.e., with the filter placed in route C and the dummy unit in route D. Subsequently, the filter and dummy units were exchanged, as described above, and 10 additional penetration measurements were done. Finally, the geometric average of the two values thus obtained was calculated. These, the geometric averages, are the penetration values reported in the sequel. It must be pointed out that the values of the two penetrations measured, before and after filter/dummy exchange, were very similar and, therefore the arithmetic mean practically coincides with the geometric mean (Alonso and Borra 2016).

Additional experiments were also carried out to test possible sources of errors. First, the possibility of a change in particle size as the aerosol travels through the charge conditioning routes A and B was examined. For this, the setup shown in Figure 2 was used. The second DMA was also a TSI nanoDMA operated under the same conditions as the first one.

Figure 2. Setup for measuring the diameter of the particles at the end of the two alternative routes A and B.

Second, penetration of positively charged particles was measured in two additional ways, besides the one performed with the setup of Figure 1. For these additional experiments, the three-way valve 3WV-1 and route A altogether were omitted (see Figure 3). Furthermore, since in this case the aerosol only contains unipolarly charged particles, an aerosol electrometer (EM) can be used instead of the CPC for concentration measurements.

Figure 3. Setup for two additional ways to measure penetration of charged particles. The two ways differ in the apparatus used to measure particle concentrations, a condensation particle counter (CPC) in one case, and an aerosol electrometer (EM) in the other. In comparison with the setup of Figure 1, note that one three-way valve and one T-junction have been eliminated (3WV-1 and T-1, respectively).

4. Results and discussion

4.1. Particle size downstream the DMA

In the first place, the possible effect of the differences between routes A and B of the general setup (Figure 1) on the particle size was assessed. The results of these experiments, carried out with the setup shown in Figure 2, are presented in Table 2. The first column in the table represents the mobility-equivalent particle diameter inferred from the fixed voltage applied to the first DMA using the standard Knutson–Whitby equation. For a fixed voltage applied to DMA-1, the voltage in the second DMA was scanned and particle concentration measured with the CPC. From the arithmetic mean voltage, almost coincident with the peak voltage, resulting from DMA-2 measurements the corresponding mobility-equivalent particle diameter was calculated. The thus measured particle diameters of the aerosols coming from routes A and B are listed in the second and third columns, respectively. It is first observed a slight increase of particle size for both routes in comparison with the nominal particle diameter inferred from DMA-1. However, this does not mean a real, ‘‘physical” growth of the particles themselves by, say, condensation or coagulation. Condensation can be neglected because the two air streams, the one serving as sheath air and that use to generate the NaCl aerosol were previously dried by passing them through silica gel beds. Likewise, coagulation can be ruled out because particle number concentrations were below 5⋅10⁴ cm⁻³. Note also that for the two largest particles there is even a slight decrease of the particle diameter. The observed mismatch between the DMA-1 fixed voltage and the DMA-2 peak voltage is actually typical of tandem DMA experiments; these so-called voltage shifts have been observed quite frequently in the past. Nevertheless the differences are very small and should not deserve any further consideration.

Table 2. Comparison between particle diameters of the aerosols coming from routes A and B (setup of Figure 3).

	dp measured with DMA-2 (nm)
dp measured with DMA-1 (nm)	Route A	Route B
3.4	3.6	3.6
4.1	4.2	4.2
5.1	5.2	5.3
5.8	5.8	5.8
7.2	7.4	7.4
8.8	8.7	8.8
10.0	9.8	9.8

The important point is that the particle diameter of the test aerosols supplied to the filter/dummy system is independent of whether the aerosol has passed through route A (neutralizer plus ESP) or through route B (directly from DMA-1). Indeed, the second and third columns in Table 2 are practically coincident.

4.2. Penetration of positively charged particles measured in three different ways

Penetration measurements for positively charged particles were, in comparison with the other two charging states, the most difficult of all. The concentration of the aerosols entering the filter/dummy system depended on the polydisperse aerosol from where they were generated and also on the specific size of the particles under considerations. For the higher concentrated aerosols, concentrations were reasonably constant during the first 5–7 min or so and penetration measurements could be done with confidence; after that, concentrations underwent large and erratic, non-periodic fluctuations with no definite tendency and measurements could not be done. In these circumstances, the DMA voltage was set to zero, so that only clean air passed through the experimental line. After half an hour or so, measurements could be done again for another 5–7 min. For lower concentrated aerosols, stable concentrations lasted for longer periods of time, about 10–15 min, after which clean air was passed through the system to let the accumulated charges dissipate away. All the conductive parts of the experimental line were grounded; the only dielectric parts where charges can accumulate are the o-rings present in the three-way valves to prevent leakage. In contrast, experiments with uncharged and neutral particles did not give any trouble at all.

Table 3 shows that there are no significant differences in the penetrations of positive particles measured in the three different manners explained in the Experimental Method and also in the table caption. The reported values of penetration are the geometric means of the two penetrations measured before and after exchange of the filter and dummy units; in turn, each of these two penetrations are the arithmetic averages of 10 measurements. The standard deviations of the 20 measurements are also reported in Table 3. These values of standard deviation are the largest obtained in this work: the corresponding standard deviations for neutral and uncharged particles were smaller, possibly because concentrations were more stable than for positive particles.

Table 3. Penetration of positively charged particles measured in three different ways: (a) with the setup shown in Figure 1, using the particles coming from route B; (b) with the setup shown in Figure 3 using the condensation particle counter (CPC) to measure concentrations; and (c) with the setup of Figure 3 using the aerosol electrometer (EM). Flow rate through the filter (or dummy) unit: 1.0 l pm.

dp (nm)	Pe (-)	(a)	P (-) (b)	(c)
3.4	3.8	0.28 ± 0.03	0.25 ± 0.04	0.26 ± 0.03
4.1	5.6	0.36 ± 0.04	0.37 ± 0.04	0.37 ± 0.04
5.1	8.5	0.50 ± 0.03	0.47 ± 0.03	0.51 ± 0.03
5.8	11.2	0.55 ± 0.03	0.55 ± 0.02	0.56 ± 0.03
7.2	16.9	0.64 ± 0.06	0.65 ± 0.03	0.67 ± 0.02
8.8	25.3	0.72 ± 0.04	0.74 ± 0.03	0.74 ± 0.02
10.0	32.8	0.76 ± 0.03	0.78 ± 0.03	0.77 ± 0.03

4.3. Effect of concentration on penetration of positively charged particles

Penetration of positively charged particles through the metal grid was measured at two levels of particle number concentration. In these experiments, a dilutor was inserted in the general setup shown in Figure 1, between T-2 and 3WV-2. In the dilutor, a certain fraction of positive particles coming from route B was diverted toward a bypass route in which a HEPA filter was placed. The two streams, the one with particles and the clean one, merged in an additional T-junction located just before the three-way valve 3WV-2.

The results of these experiments are shown in Table 4. The number concentrations appearing in the third and fifth columns are those measured for the route containing the filter, C in the first series of 10 measurements, and D in the second series after exchanging of the filter and dummy units. Penetrations in the fourth column correspond to the low concentration level (i.e., third column), and penetrations in the last column are those obtained for the high concentration aerosol (fifth column). It is seen that up to 3⋅10⁴ cm⁻³, particle concentration does not have any effect on penetration. For the aerosol concentrations attained in this work (high level, no dilutor), space charge effects can be safely neglected.

Table 4. Effect of particle number concentration on penetration (positively charged particles).

dp (nm)	Pe (-)	N (cm^−3)	P (-)	N (cm^−3)	P (-)
3.4	3.8	280	0.26 ± 0.04	2520	0.28 ± 0.03
4.1	5.6	675	0.35 ± 0.04	5040	0.36 ± 0.04
5.1	8.5	1280	0.50 ± 0.04	9530	0.50 ± 0.03
5.8	11.2	930	0.57 ± 0.03	9100	0.55 ± 0.03
7.2	16.9	1690	0.62 ± 0.03	15300	0.64 ± 0.06
8.8	25.3	3150	0.71 ± 0.04	32700	0.72 ± 0.04
10.0	32.8	2110	0.75 ± 0.03	24100	0.76 ± 0.03

A more detail examination of the effect of concentration on the penetration of positively charged particles is presented in Figure 4, which shows the raw data (particle number concentration at the outlet of the filter and of the dummy unit) obtained for 8.8 nm particles. The plotted data are the averages of 20 measurements, 10 in a first series, and the remaining 10 after exchanging the filter and the dummy unit. The data points lie in a straight line, the slope of which is the particle penetration, and this means that the aerosol concentration has no effect on filtration, i.e., space-charge effects (mutual repulsion between the unipolarly charged particles) are completely negligible, at least up to the highest concentration achieved in this work, about 5⋅10⁴ cm⁻³. For the rest of the particle sizes tested, the concentrations were significantly lower than for 8.8 nm and, as shown in Table 4, no concentration effect was observed either.

Figure 4. Effect of particle number concentration on the penetration of positively charged 8.8 nm particles at face velocity of 2.71 cm/s.

4.4. (Absence of any) effect of particle charging state on penetration

Figures 5 and 6 show the experimental results obtained for positively charged particles at two different face velocities, along with the theoretical curves calculated with the equations described above in Section 2. The full line represents the prediction of the fan filter model, i.e., assuming that diffusion is the only deposition mechanism operating in the filter. The dashed and dashed-dotted lines were calculated with the full Equation (5[5] $E=E_D+E_{IM},$[5] ), i.e., considering particle deposition by image force in addition to diffusion. The curve corresponding to the correlation of Lundgren and Whitby (1965) is very close to that of Yoshioka et al. (1968) and has not been plotted to preserve clarity. The curve D + IM including the correlation of Yoshioka et al. is also very close to the curve for diffusion alone and, because of the experimental errors (given by the standard deviations appearing in Tables 3 and 4), it is difficult to make a definite conclusion about the presence or absence of image force effects in our experiments. In contrast, the curve D + IM using the correlation of Alonso et al. (2007), which was obtained for particles much smaller than those used by Lundgren and Whitby and Yoshioka et al., is certainly far from the experimental points and can be discarded.

Figure 5. Experimental penetrations obtained for face velocity of 2.17 cm/s, along with theoretical curves. D = Cheng-Yeh fan filter model considering diffusion alone; D + IM = diffusion plus image force using two different correlations, those of Alonso et al. (2007) and Yoshioka et al. (1968).

Figure 6. Experimental penetrations obtained for face velocity of 2.71 cm/s, along with theoretical curves. D = Cheng-Yeh fan filter model considering diffusion alone; D + IM = diffusion plus image force using two different correlations, those of Alonso et al. (2007) and Yoshioka et al. (1968).

From Figures 5 and 6, one is tempted to conclude that image force has no effect on the penetration of particles under 10 nm through metal grids. This conclusion appears more strongly justified by Figure 7, in which the results obtained for positively charged particles (+) are accompanied by those obtained for uncharged (0) and neutral (+0-) particles. Indeed, no significant difference among the three charging states can be observed in this plot. Furthermore, the data points are fairly well reproduced by the fan filter model, considering diffusion as the only particle deposition mechanism, i.e., assuming E_IM = 0 in Equation (5[5] $E=E_D+E_{IM},$[5] ).

Figure 7. Experimental penetrations for three particle charging states and two face velocities. +: positively charged particles; +0-: globally neutral aerosol (i.e., containing positive, negative, and uncharged particles, and zero net charge); 0: uncharged particles. The curve represents the prediction of the fan filter model, i.e., assuming that diffusion is the only deposition mechanism operating.

5. Conclusions

A careful experimental investigation has been carried out to examine the effect of the charging state of particles with diameter below 10 nm on their penetration through a grounded metal grid. From a source of positively, singly-charged particles withdrawn from a DMA, three aerosol populations were generated, one consisting of 100% uncharged particles, a second one containing a large fraction of uncharged particles and small amounts of positive and negative particles (neutral aerosol), and a third population consisting entirely of positive, singly-charged particles. First, experimental measurements have shown that the presence of a neutralizer and an electrostatic precipitator does not modify the particle size, so that the three aerosols undergoing filtration had essentially the same mean diameter. Second, it has also been shown that space charge effects are negligible at the particle number concentrations attained in this work. And third, penetration of positive particles has been measured using three slightly different methods that gave essentially the same results.

After these preliminary and essential checks, penetration experiments of charged, uncharged, and neutral particles were performed. The main results can be summarized thus: (1[1] $K_{IM}=\left(\frac{{ϵ}_f-1}{{ϵ}_f+2}\right)\frac{C{p}^2{e}^2}{12{\pi }^2\mu u{ϵ}_0{d}_p{d}_f^2},$[1] ) the experimentally measured particle penetration through the metal grid agrees fairly well with the fan filter model equation of Cheng and Yeh (1980) for diffusional deposition and (2[2] $E_{IM}=a{K}_{IM}^{1/2}.$[2] ) image force can be safely neglected for singly-charged particles having mobility equivalent diameter smaller than 10 nm. These results are in agreement with those obtained in the past by some groups, but are at odds with the results reported by other groups.