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METHOD FOR MEASURING DENSITIES BASED ON CIRCULAR MAGNETIC LEVITATION

20210215589 ยท 2021-07-15

    Inventors

    Cpc classification

    International classification

    Abstract

    A sample to be measured is placed in a medium solution between two circular magnets to ensure that the sample to be measured is levitated in a set circular area between the two circular magnets, and a levitation position of the sample to be measured in the magnetic field is measured. The density of the sample is calculated according to formula (I):

    [00001] s = m + m - s g 0 ( B r B z r + B z B z z ) .

    Compared to the prior art, the method of the present disclosure provides a novel method for measuring a density of a substance, in which the involved device is easy to operate and has low cost, and the measurement results are easy to observe and have high accuracy.

    Claims

    1. A method for measuring a density based on circular magnetic levitation, comprising: placing a sample to be measured in a medium solution located between two circular magnets to ensure that the sample to be measured is levitated in a set circular area between the two circular magnets; measuring a levitation position of the sample to be measured in a magnetic field; and calculating the density of the sample to be measured according to formula (I): s = m + m - s g 0 ( B r B z r + B z B z z ) ; wherein .sub.s is the density of the sample to be measured, g/cm.sup.3; .sub.m is a density of the medium solution, g/cm.sup.3; .sub.s is a magnetic susceptibility of the sample to be measured, dimensionless; .sub.m is a magnetic susceptibility of the medium solution, dimensionless; g is a gravitational acceleration, m/s.sup.2; .sub.0 is a vacuum permeability, N/A.sup.2; B.sub.r, B.sub.z are respectively a radial magnetic field intensity and an axial magnetic field intensity at the levitation position; r,z are respectively a levitation radius (a distance from a center line of the two circular magnets to the sample to be measured) and a levitation height (a distance from an upper surface of a lower magnet to the sample to be measured) of the sample to be measured in the medium solution, mm.

    2. The method of claim 1, wherein the two circular magnets have the same specification and are arranged coaxially up and down; and like poles of the two circular magnets face each other; and the medium solution is arranged between the two circular magnets.

    3. The method of claim 1, wherein a distance between the two circular magnets satisfies: (1) a curve expressed by a formula B r B z r + B z B r z = 0 does not completely coincide with a center line of the two circular magnets; and (2) a gradient of the curve expressed by an expression B r B z r + B z B r z in r direction is greater than 0.

    4. The method of claim 1, wherein an outer radius of each of the two circular magnets is 20-40 mm; an inner radius of each of the two circular magnets is 10-30 mm; a height of each of the two circular magnets is 10-30 mm; a magnetic induction intensity of each of the two circular magnets is 0.08-0.2 T; and a distance between the two circular magnets is 30-50 mm.

    5. The method of claim 2, wherein an outer radius of each of the two circular magnets is 20-40 mm; an inner radius of each of the two circular magnets is 10-30 mm; a height of each of the two circular magnets is 10-30 mm; a magnetic induction intensity of each of the two circular magnets is 0.08-0.2 T; and a distance between the two circular magnets is 30-50 mm.

    6. The method of claim 3, wherein an outer radius of each of the two circular magnets is 20-40 mm; an inner radius of each of the two circular magnets is 10-30 mm; a height of each of the two circular magnets is 10-30 mm; a magnetic induction intensity of each of the two circular magnets is 0.08-0.2 T; and a distance between the two circular magnets is 30-50 mm.

    7. The method of claim 1, wherein before preparing the medium solution, the density and the magnetic susceptibility of the medium solution are calibrated to obtain a relationship between the density and the magnetic susceptibility of the medium solution.

    8. The method of claim 1, wherein the sample to be measured is a spherical sample, an ellipsoidal sample, an oblate sample, a disc-shaped sample, a cylindrical sample, a biconical sample, a cube-shaped sample, or a rectangular parallelepiped sample with a square cross section.

    9. The method of claim 1, wherein the medium solution is a solution of manganese salt, iron salt, or gadolinium salt.

    10. The method of claim 9, wherein the medium solution is an alcoholic solution or an aqueous solution of manganese salt, iron salt, or gadolinium salt with a concentration of 0.5-5 mol/L.

    11. The method of claim 1, wherein the density of the sample to be measured is 0.8-1.5 g/cm.

    12. The method of claim 1, wherein the medium solution is a 2-2.5 mol/L aqueous solution of MnCl.sub.2 or a 0.8-1.5 mol/L alcohol solution of MnCl.sub.2.

    Description

    BRIEF DESCRIPTION OF THE DRAWINGS

    [0053] FIG. 1 is a schematic diagram of a magnetic levitation device according to an embodiment of the present disclosure, in which a sample is placed in a medium solution to measure the density of the sample.

    [0054] FIG. 2 is a graph showing measurement results of balls with different standard densities using a method for measuring a density based on circular magnetic levitation according to an embodiment of the present disclosure.

    [0055] FIG. 3 shows a measurement curve of the method of the present disclosure versus a measurement curve of an existing density measurement method.

    [0056] FIG. 4 is a structural diagram of the magnetic levitation device according to an embodiment of the present disclosure.

    DETAILED DESCRIPTION OF EMBODIMENTS

    [0057] The present disclosure will be further described in detail in conjunction with specific embodiments and the accompanying drawings, from which the present disclosure will be more clearly understood.

    [0058] FIG. 1 is a schematic diagram of a magnetic levitation device of the present disclosure; and FIG. 4 is a structural diagram of the magnetic levitation device of the present disclosure. Illustrated is a magnetic levitation device, including a lower magnet 1, an upper magnet 5, a medium solution 2, a sample to be measured 3 and a container 4 (transparent container). The container is required to be transparent to measure a height of the sample therein easily. A levitation position of the sample to be measured 3 is (r,z). The container 4 is arranged between the lower magnet 1 and the upper magnet 5, and the container 4, the lower magnet 1 and the upper magnet are arranged inside a mounting base.

    [0059] The lower magnet 1 and the upper magnet 5 are both a circular magnet with an outer radius of 30 mm, an inner radius of 20 mm, a height (h) of 20 mm, and a central magnetic induction intensity of 0.125 T. A curve of

    [00012] B r B z r + B z B r z = 0

    (i.e., a curve of levitation position) can be obtained by calculation, which is plotted with a dotted line (the circular area corresponding to the magnets) in FIG. 1. A distance d between the upper magnet and the lower magnet is 40 mm. The lower magnet 1 and the upper magnet 5 are arranged horizontally and coaxially up and down, and a negative pole of the lower magnet 1 and a negative pole of the upper magnet 5 face each other.

    [0060] A density measurement is carried out based on the circular magnets with the outer radius of 30 mm, the inner radius of 20 mm, the height (h) of 20 mm, and the central magnetic induction intensity of 0.125 T. The medium solution is 2 mol/L aqueous solution of MnCl.sub.2, and the samples to be measured are standard glass balls with a size of 4 mm, where the densities of these standard glass balls are respectively 1.2000, 1.2300, 1.2600 and 1.2900 g/cm.sup.3. Positions where the samples can be stably levitated is shown by the dotted line between the lower magnet 1 and the upper magnet 5. Due to the symmetry of the circular magnets, the sample to be measured can stably levitate at all positions around the center axis at the corresponding height of the curve, so that a circular levitation area is formed, facilitating the density measurement. Therefore, the density of the sample to be measured can be calculated according to its levitation height to facilitate measurement, as shown in FIG. 2. In FIG. 2, the solid squares are the results of the positions of the samples with known densities placed in the above-mentioned magnetic field system, and the curve shows the results calculated by the above-mentioned formula. It can be seen from FIG. 2 that the measurement result of the method of the present disclosure is extremely consistent with the actual result.

    [0061] The measurement accuracy of the method of the present disclosure is much higher than that of the centerline magnetic levitation method (using the device disclosed in the embodiment of Chinese Patent Publication No. 108872007 A) under the same conditions. As shown in FIG. 3, in the same condition (each of the two circular magnets has an outer radius of 30 mm, an inner radius of 20 mm, a height (h) of 20 mm, and a central magnetic induction intensity of 0.125 T, and the medium solution is a 1.0 mol/L aqueous solution of MnCl.sub.2), by comparing the measurement curves of this method (d=40 mm, circular levitation) and the existing centerline magnetic levitation measurement method (d=20 mm, central levitation), it can be seen that at the center, a slope of the curve of this method (plotted with a dashed curve) is closer to 0 than a slope of the curve of the centerline magnetic levitation measurement method (plotted with a solid curve). The slope of the curve of this method is at least 0.00003 g/cm/mm; and the slope of the curve of the centerline magnetic levitation measurement method is at least 0.00099 g/cm.sup.3/mm, which indicates that this method can distinguish a smaller density difference than the existing centerline magnetic levitation measurement method in the case of the same height difference, that is, the resolution and the measurement accuracy of this method are higher than that of the existing centerline magnetic levitation measurement method.

    [0062] Specifically, the present disclosure provides a method for measuring a density based on circular levitation, including the following steps.

    [0063] (1) The density of the sample to be measured is estimated based on a material of the sample.

    [0064] Before the experiment, the density and the magnetic susceptibility of the medium solution is calibrated in advance. Specifically, during the calibration, the medium solution is prepared with a concentration of integral moles per liter, and then the density and the magnetic susceptibility are calibrated, as shown in Table 1.

    [0065] The medium solution is prepared according to the estimated density of the sample. Specifically, when preparing the medium solution, the density of the medium solution is slightly greater or slightly less than the density of the sample within an appropriate range to ensure excellent levitation of the sample to be measured.

    [0066] (2) The sample to be measured is placed into the medium solution.

    [0067] (3) The container containing the medium solution is placed in the magnetic levitation measurement device, i.e., the container is placed between the two circular magnets and coaxially arranged with the circular magnets.

    [0068] (4) The levitation height data (levitation height) and the radial position data (levitation radius) of the sample to be measured are measured.

    [0069] (5) The density of the sample to be measured is calculated according to the levitation height, the radial position data and the formula (I), where the formula (I) is as follows:

    [00013] s = m + m - s g 0 ( B r B z r + B z B z z ) ;

    [0070] wherein .sub.s is the density of the sample to be measured, g/cm.sup.3; .sub.m is the density of the medium solution, g/cm.sup.3; .sub.s is a magnetic susceptibility of the sample to be measured, dimensionless; .sub.m is a magnetic susceptibility of the medium solution, dimensionless; g is a gravitational acceleration, m/s.sup.2; .sub.0 is the vacuum permeability, N/A.sup.2; B.sub.r and B.sub.z are respectively a radial magnetic field intensity and an axial magnetic field intensity at the levitation position; r,z are respectively a levitation radius and a levitation height of the sample to be measured in the medium solution, mm.

    [0071] The densities and the magnetic susceptibilities of aqueous solutions of MnCl.sub.2 with different concentrations are shown in Table 1.

    TABLE-US-00001 TABLE 1 Densities and magnetic susceptibilities of aqueous solutions of MnCl.sub.2 with different concentrations Concentration(mol/L) Density(g/cm.sup.3) Magnetic susceptibility 1 1.099 1.774 10.sup.4 1.5 1.148 2.771 10.sup.4 2 1.196 3.630 10.sup.4 2.5 1.244 4.650 10.sup.4 3 1.292 5.438 10.sup.4

    [0072] Specifically, a density of a Polymethymethacrylate (PMMA) material (spherical particles with a diameter of 4 mm) was measured using the method of the present disclosure, in which a 2.0 mol/L aqueous solution of MnCl.sub.2 was selected as the medium solution, the samples were placed in the aqueous solution of MnCl.sub.2 after being cleaned with alcohol, and then placed in the measurement device. The measurement device was set aside for 3 minutes to allow the position of the samples to be stable, and the levitation position of the sample was measured with a millimeter ruler. The height is 20.4 mm, and the corresponding levitation radius is 11.3 mm.

    [0073] These data are substituted into the above formula (I) to obtain the density of the sample after calculation, where the obtained density is 1.19710.0008 g/cm.sup.3. The density measured by a density meter is 1.1960.005 g/cm.sup.3.

    [0074] This embodiment uses MnCl.sub.2 solution. However, other paramagnetic solutions such as a solution of MnC.sub.2, FeCl.sub.3, GdCl.sub.3 or Gd-DTPA can also be adopted as the medium solution of the present disclosure. Using the above method, these medium solutions can be calibrated, and the density can be measured.

    [0075] Described above is a preferred embodiment of the present disclosure, and is not intended to limit the scope of the present disclosure. Any changes, equivalent modifications and improvements based on the concept of the present disclosure and uses in all other related technical fields, shall fall within the protection scope of the present disclosure.