Penetration of Monodisperse, Singly Charged Nanoparticles through Polydisperse Fibrous Filters

Figures & data

FIG. 1 An example of estimations based on the classical theory applied to the arithmetic mean fiber diameter for one of the filters (N6) used in experiments. (a) Effect of particle diameter on the single fiber deposition efficiencies of nanoparticles for various deposition mechanisms: Brownian diffusion (E_D ), action of image force for a singly-charged particle and a neutral fiber (E_IF ), and direct interception (E_R ); (b) relative contribution of Brownian diffusion to the overall single fiber deposition efficiency for the range of particle sizes studied experimentally.

FIG. 2 System of fibrous filter production (a), the die structure (b), and single fiber formation (c).

TABLE 1 Summary of filters’ structural parameters

Filter	L[mm]	α [−]	qs [kg/m^2]	dFg [μm]	σ gdF [-]	dFa [μm]	dFmin [μm]	dFmax [μm]
N1	1.00	0.0582	0.0643	4.88	2.24	5.33	2.06	17.64
N6	0.78	0.0171	0.0120	1.66	1.52	1.91	0.87	5.83
F1	1.70	0.0388	0.0593	1.97	1.58	2.55	0.72	11.85
F3	1.58	0.0419	0.0595	2.61	1.68	3.15	0.97	9.98

FIG. 3 SEM images of the tested filters: (a) N1, (b) N6, (c) F1, and (d) F3.

FIG. 4 Normalized cumulative log-normal distributions of fibers’ diameters for investigated filters.

TABLE 2 Materials used for filter penetration measurements (all from Sigma Aldrich)

	Particle type	dP [nm]
Proteins:	Bovine Serum Albumin	6.3
	Enolase	7.2
	Gamma-Globulin	8.2
	Ferritin	12.8
	Thyroglobulin	13.3
Silica Particle:	HS-40	18.2
	AS-40	27.2

FIG. 5 Experimental arrangement.

FIG. 6 Size spectra of Enolase, Ferritin and AS-40 silica particles exiting the classifier DMA – nDMA2.

TABLE 3 Summary of experimentally measured penetrations

	Penetration, P±SD [-]
Particle diameter, dP [nm]	Filter N1	Filter N6	Filter F1	Filter F3
6.3	6.1·10^−4 ± 9·10^−5	1.1·10^−3 ± 1·10^−4	1.7·10^−6 ± 2·10^−7	2.0·10^−6 ± 3·10^−7
7.2	1.6·10^−3 ± 2·10^−4	2.1·10^−3 ± 3·10^−4	1.1·10^−6 ± 2·10^−7	2.8·10^−6 ± 5·10^−7
8.2	4.4·10^−3 ± 6·10^−4	4.5·10^−3 ± 6·10^−4	8.3·10^−6 ± 1·10^−6	7.3·10^−6 ± 7·10^−7
12.8	3.4·10^−2 ± 5·10^−3	3.3·10^−2 ± 3·10^−3	2.5·10^−4 ± 4·10^−5	8.0·10^−4 ± 1·10^−4
13.3	4.6·10^−2 ± 4·10^−3	4.2·10^−2 ± 6·10^−3	7.2·10^−4 ± 7·10^−6	1.2·10^−3 ± 2·10^−4
18.2	1.9·10^−1 ± 2·10^−2	9.4·10^−2 ± 1·10^−2	6.4·10^−3 ± 9·10^−4	8.4·10^−3 ± 9·10^−4
27.2	3.8·10^−1 ± 5·10^−2	2.0·10^−1 ± 2·10^−2	4.8·10^−2 ± 7·10^−3	6.7·10^−2 ± 1·10^−2

TABLE 4 Values of the segregation intensity, s, as a function of the Peclet number, Pe, determined from experimental data using the PSFM

	Filter N1		Filter N6		Filter F1		Filter F3
dP [nm]	Pe	s	Pe	s	Pe	s	Pe	s
6.3	2.34	0.00805	0.837	0.0690	1.12	0.000594	1.38	0.000559
7.2	3.04	0.0161	1.09	0.0958	1.46	0.000341	1.80	0.000459
8.2	3.94	0.0351	1.41	0.152	1.89	0.00140	2.33	0.000759
12.8	9.51	0.149	3.41	0.455	4.55	0.0151	5.62	0.0240
13.3	10.3	0.193	3.67	0.541	4.91	0.0401	6.06	0.0330
18.2	19.0	0.582	6.81	0.741	9.09	0.193	11.2	0.125
27.2	41.6	0.861	14.9	0.973	19.9	0.755	24.6	0.536

FIG. 7 Log-logistic (solid lines) and log-normal (dotted lines) approximations of the segregation intensity, s, versus the Peclet number, Pe, based on the arithmetic mean fiber diameter for four examined filters.

TABLE 5 Parameters of the fitting functions s(Pe) and the coefficients of determination, R²

	Log-normal fit, Equation (23)			Log-logistic fit, Equation (24)
Filter	Pe g	σ gPe	R^2	Pe m	β	R^2
N1	18.36	2.26	0.9841	17.75	2.40	0.9941
N6	3.57	2.55	0.9955	3.58	1.87	0.9940
F1	14.30	1.98	0.9788	14.08	3.26	0.9996
F3	24.17	2.20	0.9890	23.14	2.85	0.9998

FIG. 8 Comparison of experimental data of penetration (points) with PSFM used in line with the log-logistic approximation s (Pe)—solid lines, and with the classical theory applied to the arithmetic mean fiber diameter—dotted lines.

FIG. 9 Analysis of results for the filter N6: (a) an attempt of application of the classical theory for two fitted fiber diameters: d_Ffit = 3.37 μm (dotted line) and d_Ffit = 4.37 μm (dashed line), and for the pressure drop equivalent diameter d _FΔp = 3.64 μm (solid line); (b) interpolation of experimental values of the single fiber efficiency by the power function of the Peclet number: solid line—free exponent of the Peclet number, dotted line—fixed exponent of the Peclet number (=−2/3); (c) comparison of experimental data with the “original” and “modified” Kirsch model; (d) relative errors (indicated by symbols) of calculation of –ln P for various models.