RU2813499C1 - Magnetic-rheological method of determining magnetic susceptibility of particle - Google Patents

Abstract

FIELD: magnetic measurements.

SUBSTANCE: method envisages conducting an experiment on magnetically controlled vertical movement of a particle upward in a liquid column under action of forces, including a magnetic force created by a non-uniform magnetic field. Pole tips of the electromagnetic system used to produce a non-uniform magnetic field are spherical and are placed on both sides of the liquid column. Variation of magnetic parameters of the electromagnetic system is ensured by its current load. Between the tips there are two symmetrical zones of magnetic action on the particle, which are located above and below the axial line of the tips, respectively. Lower zone is used as working zone. In this zone, the downward gravity force and the upward magnetic force oppose each other, causing the possibility of slow upward movement of the analysed particle. During magnetic control of movement of the investigated particle upwards, the current load of the electromagnetic system is varied, causing deceleration in the movement of the particle up to its freezing. Thus, Stokes' force is excluded. Coordinate characteristics of parameters H and/or B and parameters gradH and/or gradB are established. Values of these parameters at the particle hovering point are used to determine magnetic susceptibility χ of particle by an expression obtained from the equation of forces acting on the particle.

EFFECT: reduced number of parameters used to determine magnetic susceptibility χ of a particle, simplification and faster obtaining of values.

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Description

The invention, aimed at obtaining information about the magnetic susceptibility of single particles (small-sized bodies), relates to the field of magnetic measurements. Such information is in demand primarily for making decisions (fundamental) about operating modes and designs of magnetic impact and separation means (separation, magnetophoresis), for example, during ore enrichment, cleaning from magnetically active particles-contaminants of production environments, medical examination and treatment, etc.

There is a known ponderomotive method for determining the magnetic susceptibility of bodies of relatively small sizes [1-7] - according to measurements of the magnetic (ponderomotive) force F _m acting on the body of volume V being studied, placed in a non-uniform magnetic field. This field is created, in particular, between pole pieces of one shape or another [1-7], preferably spherical [5-7], since in this case both obtaining and relatively simple identification of the working area required here is ensured - with practically stable heterogeneity fields (for placing the studied body in it). Using measured and/or calculated values of such parameters as field strength H or its induction B, as well as inhomogeneity gradH or gradB at a particular location of the body under study (of relatively small size), the magnetic susceptibility χ of such a body is determined using known equivalent expressions for magnetic force: F _m = μ ₀ χVHgradH or F _m = χVBgradB/μ ₀ , where μ ₀ = 4π∙10 ^-7 H/m is the magnetic constant. At the same time, in order to have detailed (along a certain section of the line of action of the magnetic force) information about these parameters, they resort to obtaining their coordinate dependencies, most often, starting with the coordinate dependence of parameter B [6, 7] - through the corresponding step-by-step movement of the Hall sensor of the teslameter ( Additionally, the coordinate dependence of the parameter H can also be obtained by simple calculation, taking into account the known relationship H = B/μ ₀ ). Next, by differentiating the coordinate dependence of the parameter B or H, the coordinate dependence of the parameter gradB or gradH is obtained.

However, in cases where the body to be studied is so small (it is a small particle) that measuring the magnetic force F _m acting on it becomes problematic, the ponderomotive method is hardly applicable in such cases.

There is a known magnetic-rheological method for determining the magnetic susceptibility χ of a small-sized body (particle) through its magnetically controlled movement in a liquid column vertically downward [8, 9] under the influence of gravity (gravitational) _Fg , Archimedes F _A , Stokes F _S , as well as magnetic forces F _m . The latter manifests itself due to the inhomogeneous magnetic field created by the electromagnetic system between the spherical pole pieces located on both sides of the liquid column. The necessary information about the generated field, including at a particular current load of the electromagnetic system, is illustrated by specially obtained coordinate (according to the coordinates of the particle movement - along the action of the magnetic force) characteristics of such magnetic field parameters as strength H and/or induction B, gradient gradH and /or gradB. When carrying out each experiment to implement the method, the time of limited fixed (within a zone of practically stable field inhomogeneity located above the center line of the pole tips) movement of the particle under study is determined. The desired magnetic susceptibility χ of the particle is determined based on the condition of the balance of these forces.

The disadvantage of this method is the following. Due to the vertical movement of the particle under study in the liquid column downwards (within the working zone located above the center line of the pole tips), in the force balance condition necessary to determine the magnetic susceptibility χ of the particle under study, such significant forces as gravitational and magnetic coincide in direction. In this regard, the particle under study moves relatively quickly, the time of such particle movement is very short, which causes difficulties in its registration and negatively affects the accuracy of measurements of this time and, ultimately, the accuracy of determining the values of χ.

There is a known magnetic-rheological method for determining the magnetic susceptibility χ of a particle (small-sized body), which involves conducting an experiment on its magnetically controlled vertical movement upward in a liquid column [10]. The particle is acted upon by the following forces: gravity (gravitational) F _g , Archimedes F _A , Stokes F _S , as well as magnetic force F _m created by a non-uniform magnetic field (as in the previous analogue - with the resulting coordinates, according to the coordinates of the particle’s movement, characteristics of such magnetic parameters fields as intensity H and/or induction B, gradient gradH and/or gradB). The pole pieces (spherical in shape) of the electromagnetic system used to obtain this field, which makes it possible to change the magnetic parameters of its current load for each of the subsequent experiments, are located on both sides of the liquid column. Of the two symmetrical zones of magnetic influence on the particle located vertically between the pole pieces, located respectively above and below the axial line of the tips, the lower zone is used as the working zone. In it, the force of gravity directed downward and the magnetic force directed upward, being mutually competitive, counteract each other, making it possible for the particle under study to move slowly upward. When implementing the method (using the magnetic influence zone located below the center line between the pole pieces), the magnetic susceptibility χ of the particle under study is determined based on the equation of the forces acting on it.

The disadvantage of this method is the following. According to [10], to implement it, it is necessary to have data (obtained empirically) of a significant number of parameters. These include, in addition to the time of fixed movement of a particle in a liquid (upward, within the zone of stable field inhomogeneity), also the viscosity of the liquid, the equivalent diameter of the particle, the coefficient taking into account the difference in the shape of the particle under study from the model spherical one (or its inverse value - the ratio of the speeds of movement in the liquid the particle under study and a spherical particle equivalent in diameter to it). This complicates the implementation of the method and reduces the efficiency of obtaining the desired values of the magnetic susceptibility of the particle to be studied.

The objective of the invention is to reduce the number of parameters used (due to those mentioned above) necessary to determine the magnetic susceptibility χ of the particle being studied, simplifying and increasing the efficiency of obtaining χ values.

The expected technical result is achieved in a magnetic-rheological method for determining the magnetic susceptibility χ of a particle, which involves conducting an experiment on its magnetically controlled vertical movement upward in a liquid column. This movement is carried out under the influence of the forces of gravity (gravitational) F _g , Archimedes F _A , Stokes F _S , as well as magnetic force F _m on the particle under study, created by a non-uniform magnetic field with coordinate, according to the coordinates of the particle movement, characteristics of such magnetic field parameters as strength H and/or induction B, gradient gradH and/or gradB. The pole pieces of the electromagnetic system used to obtain this field, which provides the ability to change the magnetic parameters of its current load for subsequent experiments, of which it is preferable to use spherical tips, are located on both sides of the liquid column. Considering that between the pole pieces there are two vertically symmetrical zones of magnetic influence on the particle, located respectively above and below the axial line of the tips, it is the lower zone that is used as the working zone. In this zone, the force of gravity directed downwards and the magnetic force directed upwards, being mutually competitive, counteract each other, causing the possibility of a slow upward movement of the particle being studied, and the magnetic susceptibility χ of the particle is determined based on the equation of the forces acting on it. According to the method, with magnetic control of the upward movement of the particle under study, the current load of the electromagnetic system is varied directly during the experiment, causing inhibition in the movement of the particle until it freezes (in this case, the speed of movement of the particle will become υ = 0). This eliminates the Stokes force (F _S = 0) in the compiled equation of forces acting on the particle. From the established coordinate characteristics of the parameters H and/or B, the values of these parameters at the hovering point of the particle are used. In addition, the values of these parameters at the same point are used from the coordinate characteristics of the parameters gradH and/or gradB (obtained on the basis of the mentioned characteristics H and/or B). The desired magnetic susceptibility χ of the particle under study is determined based on the narrowed (without force F _S ) equation of the forces acting on it according to any of two expressions:

$$\chi =\frac{g(\rho -{\rho }_{\eta })}{{\mu }_0\cdot HgradH}$$ or $$\chi =\frac{g(\rho -{\rho }_{\eta })}{\mathrm{IN}grad\mathrm{IN}}{\mu }_0$$ ,

depending on which of the parameters is selected by the operator to obtain the coordinate characteristics of the magnetic field between the pole pieces, namely intensity H or induction B = μ ₀ H, where g is the acceleration of gravity (9.8 m/s ² ), μ ₀ - magnetic constant (4π·10 ^-7 H/m), ρ and ρ _η - density of the particle and liquid being studied.

The magnetic parameter included in one of the indicated calculation expressions for χ, namely the field induction B at the hovering point of the particle under study, is found from a pre-established coordinate characteristic of the parameter B - through step-by-step measurements with a Teslameter with a Hall sensor, in particular, mounted on a coordinate table. In this case, the coordinate characteristic of the field strength H = B/μ ₀ and its value at a specified point become available by simple calculation.

The magnetic parameters included in the indicated calculation expressions for χ, such as gradB and/or gradH at the hovering point of the particle, are found from the coordinate characteristic of the parameter gradB and/or gradH, obtained after approximating the coordinate characteristic of the parameter B and/or H, for example, using the Excel program with a polynomial no less than the fourth degree, and subsequent differentiation of this characteristic (which is the dependence of the parameter B and/or H on the coordinates of the real and potential magnetically controlled movement of the particle being studied).

The implementation of the proposed magnetic-rheological method for determining the magnetic susceptibility χ of a particle is illustrated using the example shown in Fig. 1 of the diagram of a variant of the executive body of this method - with an electromagnetic system, the magnetic circuit of which has spherical pole pieces 1; between them there is a column of liquid 2 with the studied particle 3 located in it. In the initial stage of the experiment, i.e. when this particle (volume V and density ρ) moves vertically, it is acted upon by four forces: gravity (gravitational) _Fg , Archimedes force _FA , Stokes force _FS and magnetic force _Fm . By varying the current load of the winding of the electromagnetic system, the operator must, when carrying out this experiment, achieve braking in the movement of the particle until it freezes, i.e. when the speed υ of its movement becomes υ = 0 and, therefore, the Stokes force disappears: F _S = 0. Then from the condition of the balance of forces acting on the particle when it hangs, namely F _g = Vρg (g is the acceleration of free fall), F _A = Vρ _η g (ρ _η - fluid density), F _m = μ ₀ χVHgradH = χVBgradB/μ ₀ (μ ₀ = 4π⋅10 ^-7 H/m - magnetic constant) the previously indicated expressions will follow to determine the magnetic susceptibility χ of the studied particles. The magnetic parameters of the inhomogeneous (between the pole pieces) magnetic field at the place where the particle hangs, required here, namely the values of the field strength H and/or its induction B, as well as the values of gradH and/or gradB are set as follows. Thus, the coordinate dependences of H and/or B are obtained by measurements, and the coordinate dependences of gradH and/or gradB are found by differentiation.

The inventive step of the proposed method is confirmed by the distinctive part of the claims.

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[10]. Patent RU 2805765. Method for magnetic-rheological diagnostics of the magnetic susceptibility of a particle during its magnetically controlled movement in a liquid (Sandulyak A.A., Sandulyak D.A., Polismakova M.N., Sandulyak A.V., Kharin A.S., Soloviev I.A.).

Claims (5)

1. Magnetic-rheological method for determining the magnetic susceptibility of a particle, which involves conducting an experiment on its magnetically controlled vertical movement upward in a column of liquid under the action of gravity, Archimedes, Stokes forces and a magnetic force created by a non-uniform magnetic field with coordinate characteristics, according to the coordinates of the particle’s movement, on the particle such magnetic field parameters as strength H and/or induction B, gradient gradH and/or gradB, and the pole pieces of the electromagnetic system used to obtain this field, which provides the ability to change the magnetic parameters of its current load for subsequent experiments with spherical tips, are placed on both sides of the liquid column, when between the tips used there are two vertically symmetrical zones of magnetic influence on the particle, located respectively above and below the axial line of the tips, and the lower zone, in which the gravity force is directed downwards and the magnetic force is directed upwards, is used as the working zone , being mutually competitive, counteract each other, causing the possibility of a slow upward movement of the particle being studied, and the magnetic susceptibility χ of the particle is determined based on the equation of the forces acting on it, characterized in that with magnetic control of the upward movement of the particle being studied, the current load of the electromagnetic system is varied directly at carrying out the experiment, causing inhibition in the movement of the particle until it hangs, thereby eliminating the Stokes force in the compiled equation of the forces acting on it, while using from the established coordinate characteristics of the parameters H and/or B the values of these parameters at the point where the particle hangs and, in addition In addition, using the values of these parameters at the same point from the coordinate characteristics of the parameters gradH and/or gradB obtained on the basis of the mentioned characteristics, the magnetic susceptibility χ of the particle under study is determined based on the narrowed equation of the forces acting on it using any of two expressions: $$\chi =\frac{g(\rho -{\rho }_{\eta })}{{\mu }_0\cdot HgradH}$$ or $$\chi =\frac{g(\rho -{\rho }_{\eta })}{\mathrm{IN}grad\mathrm{IN}}{\mu }_0$$ , depending on which of the parameters is selected by the operator to obtain the coordinate characteristics of the magnetic field between the pole pieces, namely intensity H or induction B = μ ₀ H, where g is the acceleration of gravity, μ ₀ = 4π·10 ^-7 H/m – magnetic constant, ρ and ρ _η – density of the particle and liquid being studied. 2. The method according to claim 1, characterized in that the value of the field induction parameter B at the hovering point of the particle under study is determined from a pre-established coordinate characteristic of parameter B through step-by-step measurements with a Teslameter with a Hall sensor, in particular, mounted on a coordinate table, while accessible a simple calculation is the coordinate characteristic of the field strength H = B/μ ₀ and its value at a specified point. 3. The method according to claims 1, 2, characterized in that the value of the parameter gradB and/or gradH at the hovering point of the particle is determined from the coordinate characteristic of the parameter gradB and/or gradH, obtained after approximating the coordinate characteristic of the parameter B and/or H, for example, using the Excel program with a polynomial of at least the fourth degree, and subsequent differentiation of this characteristic, which is the dependence of the parameter B and/or H on the coordinate of the magnetically controlled movement of the particle being studied.