Theory of high-gradient magnetic filter performance

Abbasov, Teymuraz; Köksal, M.; Herdem, Saadetdin

doi:10.1109/20.774182

Cited by 19 publications

(23 citation statements)

References 9 publications

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“…The mechanical recovery fraction was considered as (16) Therefore, the equation below could be written for the total fractional recovery of paramagnetic particles (17) In fact, because of the very irregular packing of the steel wool fibers in the filter, there is a significant fraction of the particles to be mechanically trapped. According to these results as well as to the work done by Uchima [20], in the case of a random packed wool matrix, not only magnetic particles but also nonmagnetic particles will be mechanically trapped at the portion perpendicular to the slurry flow, which is unfavorable not only for the separation of magnetic particles from nonmagnetic ones but also for the flushing of the filter.…”

Section: Review Of the Mathematical Modeling Of The Process A Cmentioning

confidence: 99%

“…Moreover, a viscous drag force acts on the particle moving under a magnetic field in the opposite direction, which is given by the Stokes equation (8) where is the liquid viscosity, is the relative velocity of the moving particle, and is the particle radius. By assuming that the liquid flow is laminar with a uniform velocity of containing a low particle concentration, and the gradient of the magnetic flux density in the vicinity of the magnetically saturated ferromagnetic wires in the matrix of the magnetic filter is , the ratio of to can, therefore, be written by (9) The characteristic velocity, so-called magnetic velocity, can be obtained as follows from the balance of the magnetization and drag forces acting on the particle, i.e., : The magnetic filter performance can be calculated by taking account of the ratio of the number of escaping particles to the number of particles entering into the filter , that is (11) Then, the ratio of escaping particles to particles entering into the magnetic filter may be obtained by the following equation [10], [14]- [16]: (12) where is the normalized filter length defined by (13) Based on the characterization of the applied flow and the type of the matrix of the magnetic filter, the most important given formula for the filter efficiency were classified in Table I. Following Watson, Clarkson and Kelland developed a model based on the balance equation between magnetic, hydrodynamic, gravitational, and inertial forces over each increment in a piecewise linear path, as shown in Fig. 5.…”

Section: Review Of the Mathematical Modeling Of The Process A Cmentioning

confidence: 99%

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Superconducting Magnetic Filter: Performance, Recovery, and Design

Eskandarpour

Iwai

Asai

2009

IEEE Trans. Appl. Supercond.

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Due to the development of superconducting magnets, the magnetic filtration process is now undergoing its biggest evolution since its conception. In Japan, the first industrial superconducting magnetic filter has been successfully applied for factory wastewater treatment. Much effort in both theory and practice is needed to further contribute to the new developments of this high gradient magnetic filtration process. In this substantial review, we have collected the most important theoretical and practical data about magnetic filtration, its recovery and design to establish a good framework for further development of this amazing technology.Index Terms-Electromagnetic processing of materials, high gradient magnetic field, superconducting filter, wastewater treatment.

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Section: Review Of the Mathematical Modeling Of The Process A Cmentioning

confidence: 99%

Section: Review Of the Mathematical Modeling Of The Process A Cmentioning

confidence: 99%

Superconducting Magnetic Filter: Performance, Recovery, and Design

Eskandarpour

Iwai

Asai

2009

IEEE Trans. Appl. Supercond.

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“…Bütün bu çalışmalarda gradyantlı manyetik alan esasen dış homojen manyetik alan kutuplarının arasına farklı geometriye sahip olan ferromanyetik malzemelerin (küre, çubuk, ince tel, metal yünü, talaşlar, şekillendirilmiş profiller vb.) yerleştirilmesi ile elde edilmiştir [1][2][3][4] [31]. Bu nedenle HGMS'lerde manyetik parçacıkların tutulması teorisinde de esasen "trajektory model" yaklaşımında iki boyutlu hareket denklemi incelenmektedir [3,4,7,13,14].…”

Section: Gi̇ri̇ş (Introduction)unclassified

Mıknatıslanmış Granül Dolgulu Yataklarda Submikron Parçacıklarının Yakalanması

Karadağ

2020

Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım Ve Teknoloji

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The diffusion separation of micron and submicron sized particles was examined theoretically in the gradient magnetic field formed by tangent ferromagnetic spheres magnetized in external homogeneous magnetic field. In the gradient field around the tangent points of the magnetized spheres, the analytical solution of the diffusion equation for steady states is obtained by using the expression of the magnetic force acting on the submicron-sized particle. The concentration distribution of the particles in these regions was calculated.. a) Fe3O4 particles b) Mn 2 P 2 O 7 , CuO particles Figure A. Changes of the critical dimensions of the sunmicron particles held around the tangent points of the magnetized ferromagnetic spheres according to the magnetic field strength Purpose: In this article, the retention of micron and submicron particles in the gradient magnetic field formed by ferromagnetic spheres magnetized by the external homogeneous magnetic field was investigated by the diffusion approach. The analytical solutions of the diffusion equation for steady states were obtained, and the distribution profile of the concentration of the particles was determined in the gradient magnetic field. The critical dimensions of the particles were evaluated to hold the ferromagnetic spheres around their tangent points. Theory and Methods: The basic principle of high gradient magnetic separation (HGMS) and filtration (HGMF) processes is to retain these particles by applying effective magnetic force () to micron-sized, magnetic properties particles in the high gradient magnetic field, or separate the external homogeneous magnetic field from high gradient magnetic fields in HGMS systems. They are formed around ferromagnetic materials (sphere, wire, rod, metal shavings, metal wool, etc.) magnetized by the effect of (H). Results: In Figure A, the changes in the critical dimensions of the particles held in the magnetic field with the gradient formed by the magnetized spheres are shown according to the magnetic field intensity. This relationship is calculated according to equations. The critical size of the particles trapped decreases with increasing outer magnetic field intensity. But in this case, it is important that the particles are single-domain or multi-domain. Conclusion: The diffusion equation of the micron and submicron particles in matrix elements formed from magnetized ferromagnetic spheres has been investigated. Analytical solutions for steady states of the diffusion equation in the high gradient magnetic field formed around the tangent points of the magnetized spheres were obtained.

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“…By assuming that the liquid flow is laminar with a uniform velocity of V m and low particle concentration, and the gradient of the magnetic flux density ٌB in the vicinity of the magnetically saturated ferromagnetic wires in the matrix of the magnetic filter is M s m 0 /a, the ratio of Considering f as the packing fraction of ferromagnetic wires located in a matrix, the ratio of escaping particles to particles entering in a magnetic filter may be obtained by the following equation. 18,25) ..................... (9) where L a is the normalized filter length defined as below. (10) where L is the length of a filter.…”

Section: Magnetic Filter Performancementioning

confidence: 99%

“…16) In a magnetic filter with randomly packed-ferromagnetic wires, magnetization and drag forces are assumed as the main forces acting on a paramagnetic particle passing through the filter, but the effect of the gravity and Archimedes forces are neglected due to fine size particles. [17][18][19][20][21][22][23][24][25][26][27] The main force in the magnetic separation is the magnetization force which is expressed as;…”

Section: Magnetic Filter Performancementioning

confidence: 99%