Circuit sensor contours created by using the technology of printed circuit boards and placed between spheres of radius R that are in contact allow measuring magnetic (micro-)fluxes Φ c over the cores of different radii r c in a magnetized chain of spheres, which are basic elements of a granular medium. The main goal is to obtain information about the magnetic properties of the “pipe-layers” of a magnetized chain of spheres as a quasi-continuous magnet by virtue of the fact that such step-by-step data Φ c can also be used to directly judge the step-by-step changes in magnetic fluxes along the “pipe-layers” (limited by adjacent circuit sensors). According to the data Φ c, measured using eight sensors (from r c/ R = 0.2 to r c/ R = 0.9 at steps of 0.1), magnetic fluxes Φ p were obtained along seven thin “pipe-layers” of different relative radii r p/ R (from 0.25 to 0.85). The Φ p data were obtained using chains in which the number of spheres (from 2 to 12) and the intensity of the magnetizing field varied (from 10 to 55 kA/m). The induction values in each of the “pipe-layers” were found and characterized. The values of their magnetic permeability were also found, which reflect the magnitude of the excess field intensity between the granules in comparison with the intensity of the magnetization field, which is of fundamental importance, for example, in matters of fine magnetic separation.
The basic structural elements of the magnetized granular medium (effectively used, in particular, in apparatus of thin magnetic separation) are granule chains (according to channel-by-channel model), in connection with which there is a need to detail the features of their magnetization. The purpose of the work is to develop and implement an approach to measuring magnetic (micro)flows along the cores of different radius r in the chain of granules using a specially developed (by printed circuit board technology) sensor, with high radius R (15 and 20 mm) spheres available for such measurements.From the data of measuring magnetic (micro)flows data of average induction in each of the quasi-continuous cores of the spheres chain are obtained, as well as data of magnetic permeability and susceptibility of these cores, their magnetization for different values of the intensity of the magnetizing field. It is shown that dependences of mentioned magnetic parameters from number n spheres in a chain are generalized on r /R for different R.These relationships, increasing as n increases due to a decrease in the demagnetizing factor N of any of the cores and the chain as a whole, demonstrate the achievement of individually limiting values of magnetic parameters and corresponding auto-model regions where N→0. At the same time, the transition to each of these regions, manifesting almost independently of r /R and intensity, falls on the value of n = 10–12 = [n]. Thus, in fact, such a criterion value [n] distinguishes chains by sufficiently “long” – when n ≥ [n] and “short” – when 2 ≤ n ˂ [n]. Data of demagnetizing factor for different cores of “short” chains of spheres are obtained and phenomenologically described.
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