Aerosol penetration through fabrics: Experiments and theory

Figures & data

Figure 1. Scanning electron microscope (SEM) picture of (a) 10 oz Denim and (b) A30.

Figure 2. Experimental setup: (a) benchtop and (b) sleeve configurations.

Table 1. Fabric parameters obtained from measurements and optimization.

Media	Parameter	Permeability per unit thickness (m)	Fiber diameter (µm)		Thickness (mm)	Packing density
10 oz denim	Measured	6.06e-9	10.8		0.66	0.31
	Optimized	1.33e-8	1.08		0.11	0.05
A30	Measured	1.51e-8	16.9		0.34	0.37
	Optimized	1.12e-8	0.34		0.14	0.01
A30 + 10 oz denim	Measured	3.91e-9

Table 2. Face velocity and pressure drop across the media.

Parameter	Media	Benchtop (cm s^−1)				Sleeve (m s^−1)
		1.8	6.5	10.4	27	3.0	9.1	18.3	36.6
U0 (cm s^−1)	Denim	–	–	–	–	0.26	2.34	9.49	38.1
	A30	–	–	–	–	0.71	5.57	23.2	94.6
	Denim + A30	–	–	–	–	0.18	1.44	5.89	23.88
ΔP (Pa)	Denim	54.2	195.8	313.2	813.2	7.7	70.5	286.3	1148.3
	A30	21.7	78.3	125.3	325.4	8.4	67.6	280.8	1147.7
	Denim + A30	84.1	303.6	485.7	1260.9	8.64	67.3	275.4	1117.1

Figure 3. Particle penetration over denim under (a) varying face velocity for benchtop test and (b) constant 18.3 m s⁻¹ free stream wind speed with different sampling azimuth during sleeve test.

Figure 4. Maximum penetration particle size (MPPS) vs. face velocity.

Figure 5. The correlation of Lee and Liu (1982) in Equation (3)(3) $$\eta Pe\frac{R}{\sqrt{1+R}}=1.6\left[{\left(\frac{1-\alpha }{Ku}\right)}^{\frac{1}{3}}{Pe}^{\frac{1}{3}}\right]+0.6{\left[{\left(\frac{1-\alpha }{Ku}\right)}^{\frac{1}{3}}{Pe}^{\frac{1}{3}}\right]}^3$$(3) compared with experimental results using denim and optimized fiber parameters.

Table 3. Optimized geometric standard deviation of packing density obtained using inhomogeneous filtration theory.

Media	Benchtop (cm s^−1)				Sleeve (m s^−1)
	1.8	6.5	10.4	27	3.0	9.1	18.3	36.6
10 oz Denim	2.53	2.17	2.13	1.54	1.93	2.35	2.77	1.97
A30	3.92	4.44	2.36	13.47	1.95	2.44	3.10	3.93

Figure 6. Measured and theoretical penetration from benchtop setup: (a) denim 1.8 and 6.5 cm/s; (b) denim 10.4 and 27 cm/s; (c) A30 1.8 and 6.5 cm/s; and (d) A30, 10.4 and 27 cm/s.

Table 4. Weighted error, ${\sum }_{i=1}^N|\left(P_{i,\hspace{0.17em}\text{exp}\hspace{0.17em}}-P_{i,\mathit{predict}}\right)/P_{i,\hspace{0.17em}\text{exp}\hspace{0.17em}}|,$ between the experiment measurements and theoretical predictions.

Media	Benchtop (cm s^−1)							Sleeve (m s^−1)
	1.8		6.5	10.4		27		3.0	9.1			18.3			36.6
	con σg	opt σg	con σg	con σg	opt σg	con σg		0^o	0^o	15^o	30^o	0^o	15^o	30^o	0^o	15^o	30^o
10 oz Denim	7.7	2.5	2.4	3.3	3.3	23.1		10.2	6.6	16.2	11.4	6.6	4.3	16.0	33.1	37.9	80.6
A30	13.2	7.6	12.8	15.9	8.0	10.1		130	13.8	–	–	21.6	–	–	200	–	–
Denim + A30	16.6	–	12.3	46.7	–	13.4		–	58.1	–	–	7.0	–	–	46.7	–	–

Note: “con σ_g” means the prediction obtained from the constant σ_g, and “opt σ_g” means the prediction obtained from the velocity-dependent σ_g.

Figure 7. Measured and theoretical penetration from sleeve setup: (a) denim 3.0 and 9.1 m/s; (b) denim 18.3 and 36.6 cm/s; (c) A30 3.0 and 9.1 cm/s; and (d) A30, 18.3 and 36.6 cm/s.

Figure 8. Measured and theoretical penetration for the combination of denim and A30: (a) benchtop 1.8 and 6.5 cm/s; (b) benchtop 10.4 and 27 cm/s; (c) sleeve 9.1 m/s; and (d) sleeve 18.3 and 36.6 m/s.

Figure 9. Normalized pressure drop for 10 oz denim vs. separation angle.

Figure 10. Measured and theoretical penetration for denim with sleeve setup at 15^° and 30^° under free stream velocity: (a) 9.1 m/s and (b) 36.6 m/s.

Figure 11. Predicted net penetration through 10 oz denim sleeve based on the optimized parameters and inhomogeneous filtration theory.

Lee, K. W., and B. Y. H. Liu. 1982. Theoretical study of aerosol filtration by fibrous filters. Aerosol Sci. Technol. 1 (2):147–61. doi:https://doi.org/10.1080/02786828208958584.

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