The deposition of submicron aerosol particles in model filters consisting of micron-sized fibers containing radial nanowhiskers (needles) on their surfaces is considered. Numerical simulation has been performed for the transverse 3D Stokes flow field in a model filter—an isolated row of whisker-coated parallel fibers taking into account the gas slip effect on their surface. The fiber drag force and the fiber collection efficiency have been calculated as functions of the length and packing density of the whiskers and the distance between the fibers. The dependence of the fiber collection efficiency on the particle radius has been determined.

The external steady flow of a viscous incompressible fluid and the convective-diffusion mass transfer of a solute in an ordered system of parallel hollow fiber membranes located perpendicular to the flow have been calculated in the ranges of Reynolds numbers Re = 0.01–100 and Schmidt numbers Sc = 1–1000. The Navier–Stokes equations and the convective diffusion equation have been solved using computational fluid dynamics methods with the no-slip boundary condition and the condition of a constant solute concentration on the outer surface of the streamlined fiber. Calculations have been performed for one row of fibers and for a system consisting of four and sixteen rows of fibers. The output concentrations and impurity absorption coefficients by the fiber η have been calculated depending on the packing density of the fibers α and numbers Re and Sc . The studies have shown that the absorption coefficient η by the fiber in an isolated row of fibers can be used to calculate the absorption efficiency of a thick fibrous bed.

The deposition of aerosol nanoparticles in a quartz fibrous filter has been studied at a temperature of 700°C. It has been found that nanoparticles with radii larger than 2 nm formed in air from vapors of heavy refractory metals do not rebound from submicron quarts fibers at nanoaerosol flow velocities through the filter below 100 cm/s. It has been shown that the nanoparticles collected on the filter are not desorbed upon air backwash.

Исследовано диффузионное осаждение субмикронных аэрозольных частиц в модельных фильтрах, состоящих из волокон, покрытых пористыми проницаемыми оболочками. В качестве модельного фильтра использована упорядоченная система параллельных цилиндров, расположенных перпендикулярно направлению потока. Приведены результаты расчетов зависимости коэффициента захвата от радиуса оболочек, их проницаемости, плотности упаковки фильтров, а также от радиуса частиц и скорости потока. Расчеты проведены в широком диапазоне чисел Пекле Pe. Показано, что с увеличением диффузионной подвижности частиц и ростом проницаемости оболочек коэффициент захвата и критерий качества фильтра растут, при этом зависимость критерия от радиуса проницаемых оболочек имеет максимум. Показано также, что коэффициенты захвата волокон с пористыми оболочками, рассчитанные с использованием ячеечной модели и для изолированного ряда волокон, практически совпадают.

The deposition of submicron aerosol particles in model fibrous filters consisting of composite fibers coated with coaxial porous permeable shells composed of thin whiskers directed perpendicularly to the fiber surface has been considered. The viscous drag of the composite fibers and the efficiency of the diffusion collection of nanosized (point) and submicron particles from a three-dimensional flow have been calculated taking into account the finite sizes of the latter particles at small Reynolds numbers and Peclet diffusion numbers Pe = 1–106. Filter quality criterion γ, i.e., the ratio between the logarithmic penetration of the particles and the pressure drop across the filter, has been calculated as depending on the particle size and the parameters of the composite fibers. It has been shown that, when filtering aerosols of submicron particles, the γ value of the filters consisting of the composite fibers increases with Pe, markedly exceeds the γ values for point nanoparticles, and may be several times higher than the quality criterion of filters composed of fibers without porous shells.

Inertial deposition of high-density submicron particles in high-performance filters consisting of submicron fibers has been studied. It has been experimentally found that the particles are completely collected by the filters at Stokes numbers substantially exceeding the critical numbers, above which the rebound of the particles from the fibers may take place. It has been assumed that the recorded penetration of radioactivity through analytical high-performance filters in the course of sampling air containing submicron particles of nuclear fuel is due to the penetration of nanoparticles, i.e., so-called “alpha-recoil aggregates” that result from the self-sputtering of α-active materials.

Filtration of fine aerosols with model filters formed from composite fibers coated with porous permeable shells (layers) of a discrete structure consisting of finer parallel fibers has been considered. Drag forces and efficiencies of diffusion collection of submicron particles have been calculated as depending on the porosity of the filters, parameters of the shells, and the Peclet diffusion numbers at which the filter performance is substantially increased.

The diffusion deposition of point particles from a Stokes–Brinkman transverse stationary flow in a model monolayer membrane composed of contacting spherical hollow grains (capsules) with porous permeable shells formed from nanoparticles, is calculated. Monolayers with square and hexagonal packings of the grains are considered. Approximation equations are constructed for the dependences of grain drag force on shell thickness, Brinkman permeability parameter S, and internal shell radius ξ. Efficiencies of point particle collection on the grains are calculated as depending on the Peclet number, S, and ξ, and it is shown that layers of hollow permeable grains possess the highest filtration performance criterion among layers of impermeable and permeable uniform porous grains provided that the zero-concentration boundary condition is fulfilled at the outer radius of the grain.

A numerical simulation of a three-dimensional Stokes–Brinkman flow in the model filtering membranes, the role of which is played by a monolayer of the contiguous porous permeable homogeneous spherical granules and a monolayer of the granules coated with porous permeable shells, has been performed. Approximation formulas for calculating the resistance forces of the permeable granules to the flow in a layer with square and hexagonal packing have been obtained. The applicability limits of the solutions obtained within the cell model for the evaluating the resistance and permeability of a layer of porous granules have been shown. The diffusional deposition of point particles from the flow in the monolayer of porous granules with a square structure has been studied. The nanoparticle collection efficiencies by granules in a broad range of Péclet diffusion numbers depending on the permeability of granules are calculated.

The influence of the inertia of a viscous incompressible liquid flow on the viscous drag and diffusion deposition of particles in model granular filters at Reynolds numbers higher than unity, Re > 1, has been considered. The granule drag forces and particle-collection efficiencies in isolated layers with square and hexagonal packings of granules have been calculated. The influence on each other of approaching monolayers of granules on pressure drop and nanoparticle deposition has been studied. It has been shown that, at Re > 1, the collection efficiency dramatically increases due to the effect of interception.

Diffusion deposition of nanoparticles in model granular filters with different structures has been considered at low Reynolds numbers. On the basis of a three-dimensional flow field calculated for layers of granules, nanoparticle-collection efficiences have been determined for the granules in a wide range of the Peclet diffusion numbers. The interference of the layers has been studied, and approximation equations have been derived for calculating the pressure drop and the nanoparticle-collection efficiency.

The effect of gas slip at fibers on the drag to a flow and the deposition of submicron particles in model filters with a tree-dimensional flow field has been considered. The average values of the drag force and the efficiency of diffusion collection of particles with finite sizes in a double hexagonal three-dimensional model filter taken as a standard uniform filter have been calculated as depending on the packing density of fibers and the Knudsen number. It has been shown that, in the region of the sizes of the most penetrating particles, under preset conditions, and at specified filter parameters, the obtained collection efficiency values agree with the results of calculations performed by empirical formulas for a model fan filter. Moreover, formulas derived for a planar flow taking into account the slip effect are applicable to highly porous filters.

The Stokes–Brinkman flow field has been calculated in a model deposit, i.e., a row of parallel chains formed from porous spherical clusters of nanoparticles and oriented perpendicularly to the gas flow direction. The force of drag to an air flow has been calculated for the row of chains taking into account their permeability and the distance to neighboring chains. The drag forces have been found for nanodendrites composing clusters with allowance for the gas slip effect. Corresponding approximation formulas have been derived. A method has been proposed for calculating the pressure drop across a highly porous deposit of clusters of aerosol nanoparticles deposited onto a filter.