Darya Sandulyak

On the Issue of Choosing the Measuring Zones in a Faraday Balance When Studying Magnetic Susceptibility of Small Samples

By the example of polar pieces of spherical, conical and truncated conical shape, we substantiate and implement the approach to identifying a local, spatially limited, working zone (to position and examine magnetic susceptibility of ‘microsamples’) for the Faraday balance, viz. the zone with stable inhomogeneity of the field. It involves obligatory obtaining and analyzing coordinate characteristics of induction (intensity) in the interpolar area, at this, sinuous characteristics, i.e. the ones with an inflexion, should be give preference to out of the traditional nonlinear characteristics. Then, the well-linearized zone near the inflexion point (the corresponding derivative here demonstrates an extremum) most fully satisfies the requirement (to a working zone) for preserving the field inhomogeneity constancy. It is established that in comparison with the spherical polar pieces, the conical ones provide a working zone that is closer to the axial line, whereas the truncated conical polar pieces ensure the zone farther from their axial line.

Ferrous Material Fill: Magnetization Channels, Layer-by-Layer and Average Permeability, Element-to-Element Field

For the magnetic samples of heterogeneous (including bulk) ferrousmaterials, a qualitative, and according to the data on the demagnetization factor N of finely dispersed samples quantitative assessment of the volume fraction is provided for the characteristic intervals γ of the ferrous component. There are three intervals: the first one is γ ≤ 0.2, the second one is 0.2 0.4–0.45 (up to \( \gamma \cong 0.6 \) for a material filled with “densely packed” granules or grains). It should be noted that samples of heterogeneous ferrous materials within the third interval γ, according to the stabilization of N and its proximity to the N-value for a uniform sample (which indicates a “magnetic splicing” of the ferroelements in the heterogenous material), possess the features of a uniform magnetic sample and, therefore, they fully correspond to the notion of a quasi-uniform object. Special attention is paid to filling of granules or grains (with their inherently stable value of γ) as a completely independent class of heterogeneous ferrous materials.

An Approach to Employing Speed Dependences of the Pressure Loss in Filter-Matrixes to Diagnose the Transitional Regime of the Flow

The paper analyses the data on pressure differential p in a layer of balls loading (of the matrix), the statistics varying with the speed of filtration and the balls diameter. Employing the solid approach to generalization, we obtained explicit reference to critical (transition) value of the Reynolds number (Re=60-80). Alternatively to the recognized universal expression for p, the article provides individual expressions of p fair for laminar and post-laminar flow regimes respectively. The paper features a comparative analysis of different options for considering the filtering media porosity impact.

Functional Validation of Demagnetizing Factor of Quasi-Solid and Solid Magnets (Phenomenological Approach)

We managed to get the following results: we have confirmed the commonality of the functional view of the demagnetizing factor for quasi-solid and solid ferromagnetic cylindrical samples dependence on their relative dimension; the view is exponential with the radical of the relative dimension being the argument. Also the second argument is in addition revealed is a weak power function of magnetic permeability of substance of a magnetic. Expanded functional dependence for the demagnetizing factor which it is possible to use at the solution of a wide range of scientific and practical tasks is received. It is noted that for rather narrow range of values of magnetic permeability, for example, characterizing quasisolid “substance” of a matrix magnetic, the functional coefficient degenerates in a constant.

Granular Material (of Commeasurable and Multi-Dimensional Granules) Properties

The paper analyses the data on measuring the packaging density γ and porosity ω of the medium-loading of balls with d diameter and the loading tank of D diameter, as well as the compound of balls of diameters d1 and d2 ≤ d1. The stabilization of γ and ω was observed with D/d≥4-5: γ=0.61-0.63, ω=0.37-0.39, which allows evaluating the medium-loading of the commensurable granules as a conditionally orderly structure with cells, on average close to square-rhombic ones. As to the compound of the granule-balls in the range of d2/d1=1-0.5, judging by the data on γ and ω variance with d2/d1<0.4-0.5 (up toγ=0.85-0.87 and ω=0.13-0.15 with d2/d1→0), the media-loadings of multi-dimensional granules with characteristic γ and ω values can be considered as provisionally ordered structures with corresponding cells. We provide the expression for defining averaged values of the coordination number of the granule.

About Transition Reynolds Number of Filtration Magnetophoresis Process

In this present work, the approaches providing establishment of transitional value of Reynolds number when filtering liquids in the magnetized granulated (polyspherical) matrix are considered. It is shown that value of transitional number of Reynolds by flow through the granulated matrix is not crisis for process of a magnetophoresis. It is confirmed on the example of magnetophoresis of ferroparticles in water suspension, thermal power plant condensate, liquid ammonia. It is established that the effective of magnetophoresis could be performed also in case of Reynoldss values much more than determined hydrodynamic Reynolds number. It significantly expands idea of the beginning of crisis of the magnetophoresis regime and allows to receive the limiting filtering speed for any media passed through a zone of a filter magnetophoresis.

Phenomenological Interpretation of Classical Expression for Force Affecting a Ferroparticle in the Magnetic Field

The unprecedented attempt has been made to fully expand classical and often quoted (above all by magnetic separation regimes and conditions analysis) expression for the force affecting the ferroparticle in magnetic field with the functional character of the following parameters of this expression being taken into account: magnetic induction, magnetic gradient and ferroparticle magnetic susceptibility. For this purpose a particular case of force impact has been analyzed in field approximating one-dimensional field. This field is produced in module of two distantly oriented magnetic elements. The obtained dependences for magnetic induction, magnetic gradient and ferroparticle magnetic susceptibility (according to distance x to polar surface one of the magnetic elements) have been used. By the analysis the fact has been taken into account that ferroparticle magnetic susceptibility depends on its shape as well as substance magnetic susceptibility depends, in its turn, on magnetic field intensity around ferroparticle. In other words, magnetic susceptibility of material depends on distance x to polar surface usually being ignored. The analysis of the following expanded variant of magnetic force expression allows to determine that phenomenological dependence (on parameter x) which has a very simple exponential form can be an alternative to this expression. Such dependence can be reasonably used by decision-making in theoretical and practical tasks of magnetic separation. The undertaken attempt to specify the role of another parameter B0 – magnetic induction on polar surface (that is often considered as the most essential) – shows the power (approximating square) character of magnetic force concerning this parameter.