Deposition of submicron aerosols in filters from fibers coated with layers of nanowhiskers

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Abstract

The deposition of submicron aerosol particles in model filters consisting of micron fibers with radial nanowhiskers on the fiber surface is considered. Numerical modeling of a 3D Stokes transverse flow field was performed in a model filter – an isolated row of parallel fibers with whiskers, taking into account a gas slip effect on their surface. The dependencies of the fiber drag force and the fiber collection efficiency on the length and packing density of the whiskers and on the distance between the fibers are calculated. The dependence of the fiber collection efficiency on the particle radius was determined.

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About the authors

V. A. Kirsh

Институт физической химии и электрохимии им. А.Н. Фрумкина РАН

Author for correspondence.
Email: va_kirsch@mail.ru
Russian Federation, Ленинский проспект, 31, корп. 4, Москва, 119071

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Supplementary files

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2. Fig. 1. Scheme of the calculation cell (a): (b) – section transverse to the grain.

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3. Fig. 2. Dependences of the resistance force of a fiber with needles on the length of the needles hw at different distances between the layers of needles along the fiber axis ξ = 0.2 (1), 0.4 (2), 1 (3); 4 is the resistance force of an impermeable fiber with an equivalent radius of 1 + hw, according to formula (14): the number of needles in the cross section N = 8, the dimensionless radius of the needle aw = 0.025, Kn = 0.

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4. Fig. 3. Dependences of the resistance forces of a fiber with a “fur coat” of needles (1, 2) and fiber rods shielded by a layer of needles on hw: (1, 1') – N= 8, (2, 2') –N = 4; ξ = 1, b = 0.3.

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5. Fig. 4. Dependences of the resistance forces of fibers with “coats” of radial needles (1–3) on the length of the needles for different fiber packing densities b = 0.2; 2 – rod fiber shielded by a layer of needles, 3 – equivalent impermeable fiber with a radius of 1 + hw; ξ = 1, aw = 0.025, N = 4.

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6. Fig. 5. Dependences of the drag force of a fiber with needles on the Knudsen number Kn, obtained by linear extrapolation of the calculated dependences 1/F (flow model with a slip boundary condition, Kn << 1, curves 6) to the region of intermediate Kn numbers: hw = 0.5 (1), 1 (2), 1.5 (3), 2 (4), 0 (5); a0 = 1.5 μm, aw = 0.025, b = 0.2, ξ = 1, N = 8.

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7. Fig. 6. Dependences of the diffusion coefficient of capture of point particles by a fiber with a “fur coat” of needles taking into account the gas slip effect (solid lines) and without taking it into account (dashed lines) on the Peclet number, where hw = 0 (1), 0.1 (2), 0.5 (3), 1 (4), 2 (5): a0 = 1.5 μm, aw = 0.025, Kn = 0.043 (λ = 0.065 μm), ξ = 0.2, N = 8, b = 0.2, U = 10 cm/s.

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8. Fig. 7. Quality criterion of the filter γ = γ∗/2a0 made of fibers with needles of length hw = 0.5 depending on the Peclet number: 1 – direct modeling taking into account gas slip at Kn = 0.043, 2 – Kn = 0, 3 – fiber without a “coat” of nanowhiskers. The remaining parameters are the same as in Fig. 6.

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9. Fig. 8. Dependences of the collection coefficients (a) and quality criteria (b) of model filters made of fibers with needle “coats” on the particle radius: (1–3) – calculation for a composite fiber with hw = 1, (4–6) – for a fiber without needles, solid lines – taking into account the gas slip effect at Kn = 0.043, dashed lines – without taking into account, Kn = 0: b = 0.1 (1), 0.2 (2), 0.3 (3); (c) – the ratio of the quality criteria on rp at b = 0.1 (1), 0.2 (2), 0.3 (3) at Kn = 0.043; aw = 0.025, hw = 1, a0 = 1.5 μm, ξ = 1, N = 4, U = 10 cm/s.

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10. Fig. 9. Dependences of the capture coefficients on the particle radius at hw = 1 (a), 3 (b), where ξ = 1 (1), 0.4 (2), 0.2 (3); 4 – rod without a layer of needles, 5 – impermeable fiber of equivalent outer radius, Kn = 0, b = 0.2, the parameters are the same as in Fig. 8.

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11. Fig. 10. Dependences of the capture coefficients of a fiber with a “fur coat” of needles on the particle radius for hw = 1.5 (1, 1'), 1 (2, 2'), 0.5 (3, 3'), 0 (4) without taking into account (1 – 4) and taking into account the gas slip effect at Kn = 0.043 (1'–3') b = 0.2, ξ = 1, a0 = 1.5 μm, aw = 0.025, U = 10 cm/s, N = 8.

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12. Fig. 11. Dependences of the capture coefficients of a fiber with a “fur coat” of needles on the particle radius for hw = 1 (1, 1'), 0.5 (2,2') taking into account the gas slip effect at N = 8 (1, 2), 4 (1', 2'): b = 0.2, ξ = 1, a0 = 1.5 μm, aw = 0.025, U = 10 cm/s, Kn = 0.043.

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13. Fig. 12. Dependences of the quality criteria of a filter made of fibers with needles (1 – 6) on the particle radius at hw = 0.2 (2), 0.5 (3), 1 (4), 1.5 (5), 2 (6), 3.5 (7), 1 – hw = 0, Kn = 0.043; 2' – hw = 0.5, Kn = 0. The remaining parameters are the same as in Fig. 11.

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