Silver Nanowire Penetration Through Screen Filter

Abstract

Understanding the filtration characteristics of fibrous particles is important since those particles have caused health and environmental concerns. Due to the straight morphology of metal nanowires, unlike carbon nanotube (CNT) particles nanowires can be considered as appropriate test material to evaluate existing filtration theory for cylindrical particles. We measured the penetration of silver nanowires in the size range of d_m = 200 to 400 nm through screen mesh filter. By using Li et al. (2012)'s theory, we determined the orientation status of silver nanowires inside differential mobility analyzer (DMA) and calculated the dynamic shape factor of nanowires. Theoretical penetration was obtained by using single fiber theory with modified interception parameter including orientation angle between a filter wire and a particle. The orientation angle obtained by fitting experimental data into single fiber theory for the 1 layer of screen mesh filter is found to be close to 40° indicating random orientation of nanowires near filter. However, in the experiments with multi-layers of screen mesh, any tendency related to the orientation angle was not found. We performed numerical simulations for the filtration processes such as impaction, diffusion, interception, and interception of diffusing particles by introducing modified slip correction factor. Overall, when interception of diffusing particles is considered in addition to diffusion and interception, numerically simulation results and theoretical prediction agree better with experimental data regarding the penetration of silver nanowires through the 1 layer of screen mesh filter.

Copyright 2014 American Association for Aerosol Research

1. INTRODUCTION

Particles with high aspect ratio such as nanowires, carbon nanotubes (CNTs), and nanorods have been widely used with various applications because they have unique chemical, mechanical, electrical, and optical properties. But, it is known that those particles have caused health and environmental problems (Ji et al. 2012). Filtration technology for those particles has been used as one of the primary technologies for nanoparticle control. Especially, among fibrous particles, filtration of CNT particles (Seto et al. 2010; Wang et al. 2011a,b; Bahk et al. 2013; Wang and Pui 2013), and asbestos (Cheng et al. 2006; Vallero et al. 2008) have been mainly studied.

There are four main mechanisms for single fiber theory such as inertial impaction, interception, diffusion, and interception of diffusing particles (Hinds 1999). Particle size and morphology determine a dominant filtration mechanism. Diffusion is the most important filtration mechanism for particles below 100 nm (Wang et al. 2007). For the case of agglomerate particles, as the aspect ratio of the particles becomes higher (or the length of agglomerates becomes larger), the influence of interception on the collection efficiency becomes more significant (Kim et al. 2009). Similar to agglomerate particles, fibrous particles with higher aspect ratio can be more collected by the interception mechanism.

Penetration of CNT particles through air filters has been studied (Seto et al. 2010; Wang et al. 2011b; Bahk et al. 2013). In those previous studies, theoretical prediction was conducted based on single fiber theory by modeling CNT as a straight cylinder. However, CNT particles are not appropriate to evaluate existing filtration theory because CNT particles mostly have bents and kinks. Unlike CNT particles, metal nanowires can be considered as appropriate material to compare experimental data with theoretical prediction regarding the penetration of cylindrical particles through air filter since metal nanowires have straight morphology. The penetration of the fibrous particles through the fibrous filter or screen filter was numerically computed through computational fluid dynamics (CFD) simulations (Wang et al. 2007; Kim et al. 2009; Liu et al. 2011). Regarding the penetration of the fibrous particles through filter numerically predicted results were higher than experimental results. There can be two reasons. Commercial filter media is inhomogeneous while the model filter used in CFD simulations homogenous, which can result in discrepancy between the numerical and experimental results (Podgorski et al. 2011). Also, it is difficult to consider orientation angle that is the azimuth between the filter wire and the fibrous particle for each particle in CFD simulations for the prediction of particle penetration. For the reason, there can be deviation of numerical results from experimental data (Wang et al. 2011a).

CNT particles have been used for experiments of fibrous particle filtration with consideration of orientation angle. In Seto et al. (2010)'s study, comparison of single fiber theory related to inertial impaction, interception, diffusion, and gravity with experiments about the penetration of CNT particles through membrane filter was carried out in order to determine orientation angle according to each face velocity. Wang et al. (2011a) carried out numerical simulations related to inertial impaction, interception and diffusion, and experimental filtration study for 1 layer screen mesh filter considering theoretical orientation angle (≈40°). Wang et al. (2011b) compared theoretical prediction related to inertial impaction, interception, diffusion, and interception of diffusing particles with experimental data regarding the penetration of CNT particles through 20 layers of screen mesh filter. Wang et al. (2011b) compared three interception parameter models for theoretical prediction of CNT penetration through screen mesh filter. Bahk et al. (2013) estimated the length of CNT particles from experimental data related to the penetration of CNT particles through 20 layers of screen mesh filter by combining single fiber theory regarding inertial impaction, interception, diffusion, and interception of diffusing particles with the average diameter of CNT particles obtained from scanning electron microscope (SEM) image analysis.

For fibrous particles, it is important to determine orientation angle in order to calculate the collection of fibrous particles by interception. The fibrous particles can have different interception parameter depending on the orientation angle at every moment because particles rotate in flow field. The angle can be determined by combining theoretical prediction and experiment data (Seto et al. 2010). Seto et al. (2010) experimentally obtained orientation angles according to face velocities. Wang et al. (2011a) computed the average orientation angle based on the ratio of particle rotation time to time for the CNT to pass by the wire.

In this study, we carried out theoretical prediction, numerical prediction, and experimental measurement on the penetration of silver nanowires through a screen filter as a function of electrical mobility diameter. The length and diameter of monodisperse silver nanowires were obtained by image analysis according to their mobility diameters. For the calculation of theoretical and numerical penetration, we determined how silver nanowires were oriented inside DMA based on Li et al.'s (2012) theory. In order to calculate the drag force on silver nanowires outside DMA, the dynamic shape factor of nanowires is considered. Also, the effect of orientation angle on the interception parameter and particle collection by interception was also discussed. By matching experimental data with theoretical prediction regarding the penetration of silver nanowires through screen filter, average orientation angles between screen filter wires and silver nanowires were obtained. For the case of l layer, we also numerically predicted the penetration of nanowires through screen filter considering particle collection mechanisms such as diffusion, interception, interception of diffusing particles, and impaction in CFD simulations. CFD results were compared with theoretical prediction and experimental data.

2. EXPERIMENTAL METHODS

To evaluate existing filtration theory for cylindrical particles, it is necessary to obtain very well defined source material in an unaggregated state suitable for collision atomizer and classify monodisperse particles with DMA. Silver nanowires used in experiments were synthesized in a modified polyol reduction process. 45 mL of Glycerol and 1.83 g of poly vinyl pirrolidone (PVP) were injected to the clean flask, which was then immersed into oil bath to dissolve PVP at 100°C. While dissolving, 1.7 mM NaCl solution in 5 mL of glycerol was prepared and added drop wise into PVP solution after the temperature of the flask dropped to 50°C. After injecting 0.4 g of AgNO₃ into the flask, the solution was gradually heated up to 160°C. The color of the solution turned from pale white into bright orange, red, and finally into gray-green. To control the length of silver nanowires, PVP:AgNO₃ molar ratio was modulated, and silver nanowires synthesized in this way have a length of 1∼2 μm and a diameter of 70 nm. Methanol was added to as-obtained silver nanowire solution with 1:9 volume fraction to remove the PVP residue, and the mixture was centrifuged. After several centrifuge processes, the washed silver nanowires were collected and dispersed into a methanol solution of 0.02 g/mL. The nanowires were synthesized to have a very small distribution of diameter but a wide distribution of length.

In order to determine particle size distribution, silver nanowires in deionized water were generated by atomizer and passed through a diffusion dryer and a neutralizer (Po-210). Mono-disperse particles were classified by DMA (TSI 3081), and the concentration of particles was counted by condensation particle counter (TSI CPC Model 3775). As shown as Figure 1, there are two peaks around mobility diameter d_m = 30 nm and d_m = 168 nm. One peak around 30 nm is attributed to residue in deionized water and the other peak around 168 nm to silver nanowires. Thus, particle size range of silver nanowires to be used in our experiments was determined to be 200 to 400 nm.

FIG. 1 Size distribution of silver nanowires used in experiments.

Figure 2a shows a schematic diagram for set-up for sampling particles. In the set-up, nanowires in the size range of mobility diameter d_m = 200 to 400 nm were classified by DMA where sheath flow rate was set to 6 lpm and then sampled on the silicon substrates using a nanoparticle collector (HCT-4650) where sampling flow rate was set to 1.5 lpm.

FIG. 2 Schematic diagram: (a) set-up for sampling particles and (b) set-up for measuring penetration.

Figure 2b shows a set-up for the measurement of experimental penetration of silver nanowires through screen mesh filter. Silver nanowires generated by the atomizer are classified depending on mobility diameter by the DMA and their penetration through a screen filter is defined as the ratio of particle concentration of nanowires through filter holder chamber to that through dummy chamber:

[1]

where P _exp. is experimental penetration, N _filter is number concentration passing through a filter chamber with screen filter made of 300-mesh type 304 stainless steel (Manufacturer: Ehwa wire, Co., Ltd.) and N _dummy is number concentration passing through a dummy chamber. The concentrations N _filter and N _dummy were by a CPC for 90 seconds, respectively. DMA sheath flow rate was set to 6 lpm and flow rate through filter holder set to 1.5 lpm by the CPC. Thus, the filter section face velocity was set to 5 cm/s. Experiments were conducted with screen filter with different layers, that is, 1 layer, 10, 20, and 30 layers, respectively.

For the determination of particle morphology such as the diameter and length of silver nanowires, SEM images analysis was conducted for polydisperse (unclassified) and monodisperse silver nanowires (d_m = 200 nm, 250 nm, 300 nm, 350 nm, 400 nm) using Image J s/w. As shown in Figure 3, nanowires have straight shape unlike CNT particles with bents and kink. Thus, it is advantageous to use nanowires for a comparison between theoretical and numerical predictions and experimental data for the penetration of nanowire through filter. In Figure 4, histograms of average length and diameter of monodisperse silver nanowires are plotted. The average diameter is 70 nm and the average length is from 1005 to 2169 nm.

FIG. 3 SEM images: (a) polydisperse (unclassified) silver nanowires, (b) monodisperse silver nanowire (d_m = 200 nm), (c) monodisperse silver nanowire (d_m = 250 nm), (d) monodisperse silver nanowire (d_m = 300 nm), (e) monodisperse silver nanowire (d_m = 350 nm), and (f) monodisperse silver nanowire (d_m = 400 nm).

FIG. 4 Histograms: (a) silver nanowire length (d_m = 200 nm), (b) silver nanowire length (d_m = 250 nm), (c) silver nanowire length (d_m = 300 nm), (d) silver nanowire length (d_m = 350 nm), (e) silver nanowire length (d_m = 400 nm), and (f) silver nanowire diameter.

3. DETERMINATION OF CYLINDRICAL PARTICLE ORIENTATION

Li et al. (2012) proposed an analytical model that can determine the orientation status of cylindrical particles from relation between the geometrical length and electrical mobility diameter. The average electrical mobility in DMA is defined as (Li et al. 2012):

[2]

where q is the free charge on the particle, K _⊥ is the principal component of the friction coefficient tensor perpendicular to the axial direction, K _∥ is the principal component of the friction coefficient tensor parallel to the axial direction, and θ is the angle between the axis of an axially symmetric particle and the electric field direction. ⟨cos²θ⟩ becomes 1 when particle is fully aligned and becomes 1/3 when particle is fully random.

Li et al. (2012) developed an orientation-averaged electrical mobility theory for rigid axis symmetric particles undergoing Brownian motion by considering the electrical polarization of the particles in an electric field. The theory was validated by experimental results of monodisperse gold rods (Li et al. 2013). Since silver nanowires are conducting rod like gold rods, we considered only the induced dipole polarization energy in present study. ⟨cos²θ⟩ can be calculated from complicated equation (Equation (22) in Li et al. [2012]). |Z_p −Z _p,random|/Z _p,random of silver nanowire according to their morphology can be calculated by combining Equation (2) and Equation (22) in Li et al. (2012) using Mathematica as shown in Figure 5. In the calculation of |Z_p −Z _p,random|/Z _p,random, we considered the average length and diameter of silver nanowires obtained from SEM images analysis. From Knutson and Whitby's (1975) expression for the mean electrical mobility of particles exiting a DMA, the size-selecting voltage of DMA is expressed as:

[3]

where μ is the gas viscosity, Q_s is sheath flow rate, r ₁ is the radius of inner electrode of DMA, r ₂ is the radius of outer electrode of DMA, C_c is the slip correction factor, e is the elementary charge, and L is the length of DMA electrode. We can obtain the detection voltage from Equation (3) and then the electric field strength, E=V/(r ₂−r ₁), equal to 3045 V/cm, 4245 V/cm, 5499 V/cm, 6787 V/cm, and 8098 V/cm for mobility diameter d_m = 200 nm, 250 nm, 300 nm, 350 nm, and 400 nm, respectively. As the electric field strength inside DMA increases, the nanowires in DMA tend to be more aligned parallel to the axial direction. In other words, if |Z_p −Z _p,random|/Z _p,random reaches a constant value, the orientation of particle can be determined to the fully aligned orientation. As shown in Figure 5, the value of |Z_p −Z _p,random|/Z _p,random for nanowires in range of 200 to 400 nm reach a constant value equal to 0.27 approximately as electric field strength increases to larger than 3000 V/cm. Thus, the nanowires in range of 200 nm to 400 nm used in our experiments can be assumed to be fully aligned with the electric field inside the DMA.

FIG. 5 Theoretical calculations of |Z_p −Z _p,random|/Z _p,random vs. electric field inside DMA for d_m = 200 nm, 250 nm, 300 nm, 350 nm, and 400 nm.

4. THEORY FOR FILTRATION

One can theoretically compute the penetration of the nanowires using single fiber filtration theory (Hinds 1999).

[4]

where P _th is theoretical penetration, α is solidity of the filter, L is filter thickness, n is the number of the stacked screen meshes, d_f is average diameter of filter wire, and E_T is total efficiency by diffusion, interception, inertial impaction, and interception of diffusing particles.

[5]

Equation for the efficiency by inertial impaction, E_I , is shown in Table 1 where

[6a]

[6a]

TABLE 1 Equations depending on deposition mechanism (see Bahk et al. 2013)

Deposition mechanism	Equation
Inertial impaction
Diffusion	ED =2.7Pe ^−2/3,
Interception
Interception of diffusing particles

is Stokes number, is Kuwabara hydrodynamic parameter, ρ _p is the density of silver, d_w is the diameter of the silver nanowire, and R _ae is the aerodynamic radius of fibrous particle depending on aspect ratio defined by Equation (14) in Bahk et al. (2013).

Equation for the efficiency by diffusion, E_D , is also shown in Table 1 where (Peclet number) is defined as:

[7]

where U ₀ is face velocity (Wang et al. 2011a).

FIG. 6 Screen filter made of 300-mesh type 304 stainless steel: (a) SEM image and (b) modeled screen filter.

Filtration efficiency by interception of spherical particles onto filter fiber is expressed as a function of interception parameter, R=(d_p /d_f ) like Equation (6c). However, for the case of silver nanowires, the filtration efficiency by interception is obtained with corrected interception parameter R' expressed as (Bahk et al. 2013):

[8]

where L_w is the length of silver nanowire and θ′ is the orientation angle between the filter wire and the silver nanowire. Equations for the filtration efficiency by interception and interception of diffusing particles, E_R and E _DR, are expressed as a function of R′ in Table 1.

5. NUMERICAL METHOD

Figure 6(a) shows the SEM image of screen filter used in our experiments. The thickness of filter was measured to be 95 μm using a micrometer and the weight of screen filter per 100 cm² to be 2.17 g using a micro balance. From SEM image analysis the average diameter of wires on screen filter is measured to be 37.5 μm. The solidity (α) of screen filter is defined as (Cheng and Yeh 1980):

[9]

The solidity of screen filter used in our experiments is equal to 0.288. As shown in Figure 6(b), the screen filter is modeled for CFD simulations by placing two perpendicular cylinders with the diameter of 37.5 μm and a gap of 27 μm between those two cylinders to satisfy the solidity of 0.288 following Wang et al.'s (2011a) approach. We used commercial CFD code FLUENT solver (steady-state and laminar flow) to obtain the flow field and particle trajectories around the screen mesh filter. For simulation of the flow field, boundary conditions are face velocity 5 cm/s at inlet, symmetry on four sides of the domain and outflow at outlet. We checked the grid convergence by comparing pressure drop Δp after passing by the screen mesh filter from CFD simulations with that from experimental model by Davies (1973):

[10]

When we used 0.78 million grids for CFD simulations, the value of Δp is 1.20 Pa, which is close to 1.29 Pa from Equation (10).

Mechanism of particle capture from filter is inertial impaction, diffusion, interception and interception of diffusing particles. Particle collection by diffusion can be obtained by solving the convection diffusion equation defined as:

[11]

where u_i is the ith component of the flow velocity and C is particle concentration. User Defined Scalar of FLUENT is used for applying the convection diffusion equation. For solving the equation, boundary conditions are C=1 at the inlet, C=0 on the filter surface and ∂C/∂x=0 at the outlet (Wang et al. 20011a).

FIG. 7 Particle trajectories of silver nanowire (d_m = 200 nm): (a) P_DR with Brownian diffusion and (b) P_R without Brownian diffusion.

Particle collection by inertial impaction, interception, and interception of diffusing particles can be obtained from discrete phase model (DPM) by solving equation of the particle motion defined as:

[12]

where m_p is the particle mass, v is the drift velocity of the particle, t is the time, and F_d is the drag force on the particle. Like Wang et al. (2011a), if we assume that the nanowire and a spherical particle pass through the DMA with the same electrical charges on them, then the drag on the nanowire in the DMA is the same as that on a sphere with equivalent mobility size. The drag (F_d ) on the nanowire in DMA can be computed as:

[13]

As earlier mentioned, the silver nanowires in the range of d_m = 200–400 nm under our experimental condition are fully aligned with the electrical field inside DMA. However, in the filter section, the silver nanowire can freely rotate. Thus, following Wang et al.'s (2011a) approach the drag force in the filter section should be recalculated considering the effective dynamic shape factor of silver nanowires. The effective dynamic shape factor x is defined as (Li et al. 2012):

[14]

where x _⊥ is the dynamic shape factor when particle travels perpendicular to the axial direction and x _∥is the dynamic shape factor when particle travels parallel to the axial direction. In the calculation of the dynamic shape factor, we considered the average length and diameter of silver nanowires obtained from SEM images analysis. Thus, the corrected drag force is defined as:

[15]

However, drag force per particle mass is considered in DPM to compute particle trajectory with Stokes-Cunningham drag law. For spherical particle, particle trajectory is calculated by solving Equation (16) as defined as:

[16]

For silver nanowires, the drag force F′ _d should be divided by actual mass reflecting the cylindrical morphology. Thus, Equation (16) is modified as:

[17]

where the modeled mass and actual mass equal to and , respectively. From Equations (17), one should note that the modified slip correction factor C′ _c should be considered for the case of silver nanowires in DPM instead of C_c (d_m ). The value C′ _c is expressed as

[18]

By considering particle length in user-defined function (Wang and Pui 2009), interception effect can be taken into account. Wang et al. (2011a) obtained the theoretical value of θ′. equal to 40°. But, in Wang and Pui 2009, Wang et al.'s (2011a) study, the orientation angle θ′ was not considered in numerical simulations. On the other hand, in our study, the particle length in DPM trajectories is assumed to be L_w sin θ′. We uniformly injected 22,500 particles over the inlet surface. The inertial impaction effect was found to be negligible. The total penetration obtained from numerical simulations, P _nu is defined as (Hinds 1999):

[19]

where P_D is the penetration by diffusion, P_R is penetration by interception, and P_DR is penetration by interception of diffusing particles. Brownian diffusion effect was not taken into account in the calculation of P_R while Brownian diffusion effect was considered in the calculation of P_DR . In Figure 7, particle trajectories of d_m = 200 nm are plotted. Particle trajectories in Figure 7a are related to P_DR with Brownian diffusion and particle trajectories in Figure 7b related to P_R without Brownian diffusion. The blue, green, and red solid lines represent trajectories of noncaptured particles, particles captured by right filter wire, and particles captured by left filter wire, respectively.

FIG. 8 Ratio between T_r and T_t according to the number of layers.

FIG. 9 Experimental data for penetration of nanowires through screen mesh filter.

6. RESULTS AND DISCUSSIONS

While silver nanowires pass through the screen mesh filter, the distance between filter wire and silver nanowire can be affected by the orientation angle θ′ in the filter section. In other words, the penetration characteristic of silver nanowires can be affected by the orientation angle . Thus, it is important to determine the orientation angle for the silver nanowire. For determination of orientation angle, the relation between the time to pass 1 layer of screen filter (T_t ) and the particle rotation period (T_r ) is compared. T_t and T_r are defined by approximating the silver nanowires using ellipsoids and given by the formula (Jeffery 1922):

[20a]

[20a]

[20a]

[20a]

where β is the aspect ratio of silver nanowire, L_w /d_w and G is the constant velocity gradient on ellipsoid in the flow field (Wang et al. 2011a), L_m is L_w /2 and Ra is the ratio of T_t to T_r as the layer of filter is stacked. In case of single screen filter, T_t is smaller than T_r . Thus, particle rotation can be neglected and the average orientation angle θ′ equals to the specific value 40° (Wang et al. 2011a). However, in case of multiple layers of screen mesh filter, the relation between T_r and T_t can be different from the case of single layer. As shown in Figure 8, as the screen filter is stacked, the ratio Equation (20d) is too large for the particle rotation to be neglected. Thus, in case of multiple layers of the screen filter, it is difficult to determine the specific orientation angle value. Figure 9 shows experimental penetration according to the number of stacked layers. Table 2 summarizes the orientation angles obtained by fitting experimental data shown in Figure 9 into theoretical penetration by single fiber theory. In the case of 1 layer, the orientation angles are in the range of 33° to 51.9°, which is good agreement with the specific value 40° from Wang et al.'s (2011a) study and the orientation angle in the range of 47° to 59° from Seto et al.'s (2010) study. Seto et al. also set the face velocity to 5 cm/s, which is the same as in our study. In the case of multiple layers, as shown in Table 2, it seems that there is no tendency regarding the orientation angle. This phenomenon might be explained by further study on filtration characteristic of stacked screen mesh filter.

TABLE 2 The orientation angle depending on the number of layers (obtained by fitting the experimental data)

	The orientation angle (°)
dm (nm)	1 layer	10 layers	20 layers	30 layers
200	34.1	25.6	31.4	16.0
250	51.9	22.5	30.4	19.0
300	41.6	22.8	30.2	20.0
350	41.2	26.6	29.7	21.0
400	33.0	26.6	29.7	21.9

TABLE 3 The penetration of silver nanowire by theoretical and numerical method according to deposition mechanisms

	Theoretical penetration			Numerical penetration
Mobility
diameter (nm)	PD	PR	P DR	PD	PR	P DR
200	0.991	0.998	0.997	0.990	0.999	0.993
250	0.993	0.996	0.997	0.992	0.998	0.995
300	0.994	0.994	0.997	0.993	0.998	0.994
350	0.995	0.992	0.997	0.994	0.997	0.992
400	0.996	0.991	0.997	0.995	0.997	0.992

We obtained the penetration of nanowires through the 1 layer of screen mesh filter with theoretical prediction and numerical simulations with the orientation angle 40°. Penetration results for 1 layer of screen mesh filter from theoretical prediction, numerical simulations, and experiments are plotted together in Figure 10. Figure 10 shows that the magnitude of penetration does not decrease as mobility diameter increases similar to Wang et al. (2011a). It is expected that as mobility diameter increases, the value of P_R decreases in both theoretical and numerical predictions because the magnitude of interception parameter increases with the length of nanowires. However, for silver nanowires used in our experiments, P_R through theoretical and numerical methods decreases only by 0.1–0.2% as the mobility diameter increases by 50 nm like Table 3. It is because the average length of silver nanowires increases only by 300 nm as the mobility diameter increases by 50 nm, which is not helpful to advance the interception effect. It should be noted that in both theoretical prediction and numerical simulation results, taking into account of the interception of diffusing particles effect P _DR shows a better agreement with experimental results compared to when P _DR is not considered.

FIG. 10 Theoretical prediction (θ' = 40°) vs. numerical simulation (θ' = 40°) vs. experimental data for the penetration with the 1 layer of screen mesh filter.

7. CONCLUSIONS

We carried out theoretical, numerical and experimental study related to fibrous particle filtration by using the silver nanowires, which are more favorable for evaluating the filtration theory for cylindrical particles than CNTs because the shape of silver nanowire is not bent and curled but stiff and straight. In experiments, we measured the penetration of silver nanowires in the size range of d_m = 200 to 400 nm through screen mesh filter. According to Li et al.'s (2012) theory, silver nanowires inside DMA were found to be fully aligned to the electric field and the dynamic shape factor for silver nanowires was obtained. In case of 1 layer of screen mesh filter, we obtained the orientation angle between the filter wire and the particle by fitting experimental results into filtration theory and the value is very close to 40°, which is the average orientation angle Wang et al. (2011a) theoretically predicted. Thus, in theoretical prediction and numerical simulation for the 1 layer of screen mesh filter, the orientation angle is assumed to be equal to 40°. In our numerical simulations, the interception of diffusing particles was also investigated in addition to diffusion, impaction, and interception. From numerical simulation results, it was found that impaction is negligible. Overall, theoretical and numerical predictions by filtration mechanisms including inertial interception, diffusion, and interception of diffusing particles with the orientation angle 40° agree very well with experimental results. For multiple layers of the screen mesh filter, any tendency regarding orientation angle was not found and this tendency would be proved out by further study.

FUNDING

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2011-0014649).