Magnetic filtration of an iron oxide aerosol by means of magnetizable grates

The cleaning of gases with low concentrations of small ferromagnetic or paramagnetic particles is a difficult task for conventional filtration. A new alternative procedure, magnetic filtration, is used in this work. Iron oxide aerosol was generated by elutriation of iron oxide particles from a fluidized bed consisting of a mixture of Geldart-C iron oxide powder and large spherical Geldart-B sand particles. The aerosol was filtered by means of a magnetic filter which consisted of one, two or three iron grates staggered to each other. The experimental installation contained also an isokinetic sampling system and a Microtrac SRA 150 Particle Analyser. A theoretical expression for filtration efficiency was deduced from a previous model taking into account the different forces acting on the iron oxide particles. Experimental filtration efficiency matches quite well calculated theoretical efficiency. It was found that an increase in particle size, in thee number of grates or in the applied magnetic field produced higher filtration efficiencies up to 100% in some cases. In all filtration experiments pressure drop through the magnetic filter was very small.     

Penetration of sub-micron aerosol droplets in composite cylindrical filtration elements

Advection-diffusion transport of aerosol droplets in composite cylindrical filtration elements is analyzed and compared to experimental data. The penetration, characterizing the fraction of droplets that passes through the pores of a filtration element, is quantified for a range of flow rates. The advection-diffusion transport in a laminar Poiseuille flow is treated numerically for slender pores using a finite difference approach in cylindrical coordinates. The algebraic dependence of the penetration on the Peclet number as predicted theoretically, is confirmed by experimental findings at a variety of aspect ratios of the cylindrical pores. The effective penetration associated with a composite filtration element consisting of a set of parallel cylindrical pores is derived. The overall penetration of heterogeneous composite filtration elements shows an algebraic dependence to the fourth power on the radii of the individual pores that are contained. This gives rise to strong variations in the overall penetration in cases with uneven distributions of pore sizes, highly favoring filtration by the larger pores. The overall penetration is computed for a number of basic geometries, providing a point of reference for filtration design and experimental verification.     

Coriolis Effects on Filtration Law in Rotating Porous Media

We investigate the filtration law of incompressible viscous Newtonian fluids in rigid non-inertial porous media, for example, rotating porous media. The filtration law is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which gives rigorously the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. For finite Ekman numbers the filtration law is shown to resemble a Darcy's law, but with a non-symmetric permeability tensor which depends on the angular velocity of the porous matrix. We obtain the filtration analog of the Hall effect. For large Ekman numbers the filtration law is a small correction to the classical Darcy's law. The corrector is antisymmetric. In this case we recover a structure of law which is similar to phenomenological laws introduced in the literature, but with a dissimilar effective coefficient.     

Approximate symmetry group classification for a nonlinear fractional filtration equation of diffusion-wave type

A one-dimensional nonlinear fractional filtration equation with the Riemann–Liouville time-fractional derivative is proposed for modeling fluid flow through a porous medium. This equation is derived under an assumption that the fluid has a fractional equation of state in which the fluid density depends on the time-fractional derivative of pressure. The obtained equation belongs to the diffusion-wave type of equations. A case when the order of fractional differentiation is close to an integer number is considered, and a small parameter is introduced into the fractional filtration equation under consideration. An expansion of the Riemann–Liouville time-fractional derivative into the series with respect to this small parameter is obtained. Using this expansion, a first-order approximation of the derived fractional filtration equation is performed. Next, the problem of approximate Lie point symmetry group classification for this approximate nonlinear filtration equation with a small parameter is studied. It is shown that approximate symmetry groups admitted by different realizations of the approximate filtration equation have much more dimensions than the corresponding exact Lie point symmetry groups admitted by unperturbed fractional diffusion-wave equations. Obtained classification results permit to construct approximate invariant solutions for the considered nonlinear time-fractional filtration equations.     

Asymptotics for filtration of polydisperse suspension with small impurities

A model for deep bed filtration of a polydisperse suspension with small impurities in a porous medium is considered.Different suspended particles move with the same velocity as the carrier water and get blocked in the pore throats due to the size-exclusion mechanism of particle retention.A solution of the model in the form of a traveling wave is obtained.The global exact solution for a multiparticle filtration with one high concentration and several low concentrations of suspended particles is obtained in an explicit form.The analytic solutions for a bidisperse suspension with large and small particles are constructed.The profiles of the retained small particles change monotony with time.The global asymptotics for the filtration of a polydisperse suspension with small kinetic rates is constructed in the whole filtration zone.     

Existence and uniqueness of the solution of the boundary-value problem for a parabolic equation of unsteady filtration

The problem of the motion of a filtration front in a zero background in the case of a power-law dependence of the filtration coefficient on gas density is considered, and the existence and uniqueness theorem for solutions in the class of analytic functions is proved. The solution is constructed in explicit form, recurrence formulas for computing the coefficients in the series are obtained, and the convergence of the series is proved by the majorant method. The filtration front construction procedure is proposed.     

Magnetic filtration with magnetized granular beds： Basic principles and filter performance

This study is devoted to the explanation of different characteristics of magnetic filtration and the way these characteristics affect the important filtration parameters. Magnetic fields in pores and the force effect of these fields on magnetic particles and the magnetization properties of packed beds composed of ferromagnetic spheres and metal chips are evaluated. The profile of accumulation and capture regions of the particles, the variation of the fluid velocity in these regions and analytic expressions of particle capture radius are presented. The effects of filtration regime parameters on magnetic filter performance were investigated. An analytical expression has been obtained for the dependence of the logarithmic efficiency coefficient on filtration velocity, the geometry of filter elements, the particle size and other parameters of filtration. The stationary and non-stationary equations of the magnetic filtration processes are given. An expression of magnetic filter performance is shown with dimensionless parameters obtained from the filtration system. These relations are useful for calculations in engineering practice, including the design of magnetic filters, provision of suggestions on construction, and optimization and control of filter operation.     

Plane filtration in a laminar medium in the presence of imperfect reservoirs

Exact and approximate solutions were obtained describing filtration flow in a plane region in sectors corresponding to imperfect reservoirs and suction gaps. These equations make it possible to obtain an approximate solution to the three-dimensional problem of the filtration of ground waters by solution of the two-dimensional problem; imperfect reservoirs are permitted in the filtration region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 76–83, May–June, 1973.     

Shock tube study of the dynamical behavior of granular materials

The purpose of the present study is to clarify both the compression phenomenon and the gas filtration effect that take place inside a granular medium when it is dynamically loaded by a shock wave. In order to measure the pore pressure and the total stress at different locations along the granular medium, pressure transducers were placed along the side-wall and at the end-wall of the shock tube test section, which was filled with the granular material. In order to elucidate the gas filtration effect, the results of two experiments with identical granular media but with and without filtration were compared. The gas filtration was eliminated by means of a thin plastic film, which was placed at the front edge of the granular medium. Based on this comparison quantitative information on the gas filtration and its role in the stress formation inside granular media of different material and length was obtained. Furthermore, curves of the dynamic compression and the Young moduli of the granular medium for the range of the operating conditions were reconstructed.     

Charged ultrafine particle filtration through vehicular cabin air filters

Understanding the effectiveness of cabin air filters is important for assessing human exposure to ultrafine particles (UFPs) of vehicular origin. The filtration efficiency of vehicular UFPs with electric charges was investigated for different electric charge characteristics (charge state, charge polarity). The average filtration efficiency increased ∼10% as the electric charge state on the particles changed in distribution from lightly charged to highly charged. The enhancement of filtration efficiency due to electric charge was different at various filter-face air velocities. As electric charges increased, the filtration efficiency increased 12% and 9% at low air velocity (0.1 m/s) and high air velocity (0.5 m/s), respectively. The filter fiber material poses somewhat effect on the filtration efficiency change due to the electric charge. The effects of filter usage and charge polarity on filtration efficiency due to the electric charge were negligible. A coefficient was empirically derived and successfully accounts for the electric charge effect on UFP filtration efficiency.     

On the determination flow rates for the compressible and immiscible viscous filtration fluids

The object of this paper is to treat the mathematical problem of the determination of flow rates for compressible and immiscible viscous filtration filtration with a free surface.     

Free-Boundary Problems for Nonlinear Models of Fluid Filtration in Inhomogeneous Porous Media

Existence theorems are proved for solutions of problems of nonlinear gravity fluid filtration in regions with specified boundaries of complex geometry. The theory developed can be used to design the underground flow net of a hydraulic structure with specified filtration characteristics.     

Filtration of a wet gas

The equations of filtration of a wet gas are derived. The numerical solution is also considered, concerning the filtration to a well from a circular seam, taking account of condensation (evaporation) of moisture.     

Unsteady-state filtration of a liquid to a rectilinear gallery in a two-layer fractured porous stratum

In connection with investigations of the filtration of a liquid in oil-bearing strata with fractured and fractured-porous types of collectors, the article discusses the unsteady-state filtration of a homogeneous liquid in a two-layer stratum of great extension, with different values of the permeabilities of the system of fractures of the intercalations.     

Steady filtration through foam

The process of filtration of a liquid through a deformable porous medium with the structure of a gas-liquid foam is considered. A basis is provided for a model of fluid flow through foam. Expressions are obtained for the differential law of steady filtration and the integral laws of filtration through a vertical column of foam under the influence of body and surface forces.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 98–103, May–June, 1986.     

Steady-state filtration of gas-condensate mixtures

In the present article, in an analysis of the results of an investigation of gas-condensate wells by the method of steady-state samples, use is made of known solutions to the problem of the steady-state filtration of a stratified liquid (gas) with constant properties [1, 2]. However, the filtration of a gas-condensate mixture to a well with the reduction of the pressure below the pressure of the start of condensation p₊ is accompanied by considerable changes in the composition and properties of the gas and liquid phases which, in turn, have an effect on the filtration characteristics of a porous medium. Among the many communications devoted to this problem (see, for example, the reviews [3, 4]), there are investigations which take account of the effect of a change in the composition and properties of the phases on the characteristics of steady-state filtration [5–7]. Here, it is proposed to model real gas-condensate mixtures by pseudobinary or pseudoternary systems with experimentally determined phase ratios. However, there are still no sufficiently well-justified examples of the reduction of multicomponent mixtures to the above-mentioned model systems. The present article, within the framework of the theory of the filtration of multicomponent systems, discusses the problem of the steady-state filtration of a real gas-condensate mixture to a central well in a round stratum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 69–75, September–October, 1973.The authors thank V. N. Nikolaevskii for his invaluable evaluation of the work, and R. G. Zotov for his aid in making the calculations.     

A two-parameter model for three types of nuclepore filtration of leukocytes

I.Intr0ductionWhenbloodcellspassthr0ughthefiltermembraneorthecapillaries,theypresentsimilarcharacteristicsIl'l,sothetechniqueofthenucleporefiltrationofcel1suspensionshasbeenextensivelyappliedtothestudyofbloodcellrheology.Therheologicalpropertiesofleuk0cy…     

Development of complex analysis methods in filtration theory problems

This paper is a review of studies carried out on the basis of two-dimensional boundary-value problems of filtration theory. The role of critical regimes determining the specifics of filtration flows with moving boundaries is noted.     

A law of filtration with limiting gradient

Two-dimensional steady filtration of an incompressible fluid with limiting gradient is considered. A special filtration law is assumed, and this makes it possible to employ the formalism of the theory of functions of a complex variable in the solution of the problems. For this law, a solution is obtained to the well-known problem [1] of motion in a strip from a plane point source.