Study of flow fractionation characteristics of magnetic chromatography utilizing high-temperature superconducting bulk magnet

Abstract

We present numerical simulation of separating magnetic particles with different magnetic susceptibilities by magnetic chromatography using a high-temperature superconducting bulk magnet. The transient transport is numerically simulated for two kinds of particles having different magnetic susceptibilities. The time evolutions were calculated for the particle concentration in the narrow channel of the spiral arrangement placed in the magnetic field. The field is produced by the highly magnetized high-temperature superconducting bulk magnet. The numerical results show the flow velocity difference of the particle transport corresponding to the difference in the magnetic susceptibility, as well as the possible separation of paramagnetic particles of 20 nm diameter.     

Study of flow fractionation characteristics of magnetic chromatography utilizing high-temperature superconducting bulk magnet

We present numerical simulation of separating magnetic particles with different magnetic susceptibilities by magnetic chromatography using a high-temperature superconducting bulk magnet. The transient transport is numerically simulated for two kinds of particles having different magnetic susceptibilities. The time evolutions were calculated for the particle concentration in the narrow channel of the spiral arrangement placed in the magnetic field. The field is produced by the highly magnetized high-temperature superconducting bulk magnet. The numerical results show the flow velocity difference of the particle transport corresponding to the difference in the magnetic susceptibility, as well as the possible separation of paramagnetic particles of 20 nm diameter.     

Evolution of Phononic Band Gaps in One-Dimensional Phononic Crystals that Incorporate High-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> Superconductor and Magnetostrictive Materials

In this work, we calculate the reflectance of one-dimensional phononic crystals (1D PnCs) using the transfer matrix method. We present numerical results for two different PnC structures, the first one, PnCs1, contains high- T _c superconducting compound (Bi-2223) and the second, PnCs2, contains a giant magnetostrictive material (Terfenol-D). Magnetostriction is a property of ferromagnetic materials that causes them to change their shape/dimensions when subjected to external magnetic field. PnC studies that dealt with such materials are few. In this study, we focus on discussing the effects of the temperature and the magnetic field on the phononic gaps of these PnCs. For PnCs1, numerical results show that local resonant modes of elastic waves with brilliant sharpness can be realized. In addition, increasing the temperature leads to a decrease in the gap width which can be controlled by the magnetic field due to the effect of the magnetic field on the velocity of waves in the high- T _c superconducting compound, the magnetic field effectively can widen the gap. For PnCs2, numerical results show that the gap width increases by increasing the magnetic field because the magnetostrictive material directly expanded in the presence of the magnetic field.     

Numerical simulation of chainlike cluster movement of feeble magnetic particles by induced magnetic dipole moment under high magnetic fields

Abstract

In this paper, the motion of a chainlike cluster of feeble magnetic particles induced by high magnetic field is discussed on the basis of the results of numerical simulations. The simulations were performed on glass particles with a diameter of 0.8 mm; and the viscosity, applied magnetic field and magnetic properties of the surrounding medium were changed. In addition to the magnetic field and the difference in magnetic susceptibility between the particles and the surrounding medium, the obtained results indicate that the viscosity is an essential factor for the formation of the chainlike alignment of feeble magnetic particles. We also carried out simulations using glass particles with a smaller diameter of 0.1 mm. Chainlike clusters were produced similar to those of ferromagnetic particles formed in a ferromagnetic fluid.     

Magnetic Field Analysis of an Ironless Brushless DC Machine

This paper presents an analytical solution for the magnetic field inside an unconventional ironless brushless (ILBL) dc motor design. We discuss the unique characteristics of the design, which adopts an “inside-out” construction with an internal ironless stator. With the intention of obtaining an analytical solution for the magnetic field, we propose a model based on a magnetic pole concept for representing the magnetic circuit. The magnetic field inside the motor, which has no iron for guiding magnetic flux paths, is obtained by solving Laplace's equation for magnetic scalar potential. We present both analytical and numerical solutions for the magnetic field and compare them with measured results of a 20-pole prototype IL design to show the validity of the model. The IL design is simple, easy to manufacture and, as indicated by the results, has an optimum number of magnets, for which its performance becomes maximum.     

Numerical simulation of chainlike cluster movement of feeble magnetic particles by induced magnetic dipole moment under high magnetic fields

In this paper, the motion of a chainlike cluster of feeble magnetic particles induced by high magnetic field is discussed on the basis of the results of numerical simulations. The simulations were performed on glass particles with a diameter of 0.8 mm; and the viscosity, applied magnetic field and magnetic properties of the surrounding medium were changed. In addition to the magnetic field and the difference in magnetic susceptibility between the particles and the surrounding medium, the obtained results indicate that the viscosity is an essential factor for the formation of the chainlike alignment of feeble magnetic particles. We also carried out simulations using glass particles with a smaller diameter of 0.1 mm. Chainlike clusters were produced similar to those of ferromagnetic particles formed in a ferromagnetic fluid.     

Electromagnetic control of convective heat transfer during electron beam evaporation: model experiments

The present paper aims to demonstrate that melt-flow during electron beam evaporation can be effectively controlled by using external magnetic fields to considerably reduce the convective heat transfer. We discuss the various effects of a static magnetic field, a static field combined with an applied electrical current, and a rotating magnetic field. We perform model experiments using GaInSn in eutectic composition as a test liquid. The liquid metal is heated locally at its free surface by an electric resistance heater. The results of the measurements are compared to prediction of numerical simulations.     

Dissipation in Mesoscopic Superconductors with Ac Magnetic Fields

The response of mesoscopic superconductors to an ac magnetic field is investigated both experimentally and with numerical simulations. We study small square samples with dimensions of the order of the penetration depth. We obtain the ac susceptibitity χ=χ′+iχ″ at microwave frequencies as a function of the dc magnetic field H _dc. We find that the dissipation, given by x″, has a non monotonous behavior in mesoscopic samples. In the numerical simulations we obtain that the dissipation increases before the penetration of vortices and then it decreases abruptly after vortices have entered, the sample. This is verified experimentally, where we find that χ″ has strong oscillations as a function of H _dc in small squares of Pb.     

The Stability of the Superfluid 3He AB Interface Pinned in an Aperture

We have been measuring the surface tension of the AB interface at zero pressure, in high magnetic fields and low temperatures below 0.2 T _c. We manipulate the phase boundary by controlling a magnetic field profile. We use the latent heat released/absorbed as the phase boundary moves to infer its position and velocity. We have observed that the motion of the interface through a small aperture is dependent on the magnetic field gradient. Here we extend numerical methods first used to calculate the shapes of liquid drops in a gravitational field to show that the gradient dependence can be accounted for by the deformation of the interface.     

Integral analysis of a magnetic field for an arbitrary geometry coil with rectangular cross section

The integral method can effectively analyze magnetic fields, but the traditional integral method can analyze only coils with regular geometries. Therefore, a new integral method was developed to calculate the three-dimensional (3-D) magnetic field created by an arbitrary geometry coil with a rectangular cross section using the local coordinate method and a 3-D coordinate transformation. However, when the field points are on the surface of the coil or the basic segment is the right angle trapezoidal prism, singularities occur that make the numerical analysis of the magnetic field more difficult. Thus, we present here some mathematical methods to eliminate the singularities to allow accurate numerical analysis of the magnetic field. We validate the integral method by comparing it with the analytical solutions for regular geometry coils.     

Application of asymptotic expansions to model two-dimensional induction heating systems. Part I: calculation of electromagnetic field distribution

We analyze the effect of a radio-frequency alternating magnetic field generated in the vicinity of solid or liquid electrically conducting components, such as used in induction heating processes. The field can penetrate only into a thin magnetic skin located beneath the conductor surface, where the generated heat and stresses are concentrated. This most often leads to major numerical difficulties, especially for very thin magnetic skins. Therefore, we have developed a mathematical model of the electromagnetic field distribution inside the conductors for planar and axisymmetric configurations by using a matched asymptotic expansion technique. Among other features, our method takes the curvature of the conductor surfaces into account. A practical numerical implementation of our model is detailed here, and numerical calculations are carried out in order to extend the model to limiting cases such as curvature discontinuities and corners. These calculations compare successfully with complete numerical computations.     

The effect of a uniform magnetic field on the onset of steady Bénard-Marangoni convection in a layer of conducting fluid

In this paper we use a combination of analytical and numerical techniques to analyse the effect of a uniform vertical magnetic field on the onset of steady Bénard-Marangoni convection in a horizontal layer of quiescent, electrically conducting fluid subject to a uniform vertical temperature gradient. The critical values of the Rayleigh and Marangoni numbers for the onset of steady convection are calculated and the latter is found to be critically dependent on the non-dimensional Crispation and Bond numbers. The stability of the layer to long wavelength disturbances is analysed and the two different asymptotic limits of strong surface tension (small Crispation number) and strong magnetic field (large Chandrasekhar number) are investigated. In the latter case analytical results for the critical Rayleigh and Marangoni numbers are obtained and are found to be in excellent agreement with the results of numerical calculations. We conclude that the presence of the magnetic field always has a stabilising effect on the layer. Treating the Marangoni number as the critical parameter we show that if the free surface is non-deformable then any particular disturbance can be stabilised with a sufficiently strong magnetic field, but if the free surface is deformable and gravity waves are excluded then the layer is always unstable to infinitely long wavelength disturbances with or without a magnetic field. Including gravity has a stabilising effect on the long wavelength modes, but not all disturbances can be stabilised no matter now strong the magnetic field is.     

Effects of Magnetic Quantum Dots on Magnetoconductance in Quantum Wires

We present a theoretical study of electronic transport in quantum wires (narrow two-dimensional electron gas) with array of magnetic quantum dots. Each magnetic quantum dot is defined by a small circular region where the strength of perpendicular magnetic field is modulated. By making use of a newly developed calculation method based on the gauge transformations, we calculated the conductance as a function of the external perpendicular magnetic field. Our numerical calculations show that the magnetoconductance is very sensitive to the number of magnetic quantum dots in the field region where the direction of the net magnetic field in dot regions is antiparallel to the external magnetic field.     

Current Accumulation for a Self Magnetic Field Calculation in a Finite-Element Gun Code

We describe a novel current accumulation algorithm for the three-dimensional self magnetic field calculation in a charged-particle beam optics code. The current source is a charged-particle beam represented by a collection of numerically-integrated current-carrying rays. We compute the magnetic vector potential using edge basis functions and the curl–curl formulation of the finite-element method. The current accumulation algorithm takes advantage of a novel particle tracker that happens to be ideal for this application. We show that our source vector is compatible with the singular finite-element matrix, even with modest numerical integration errors. Thus, a conjugate gradient matrix solver works well, with no need for additional gauge conditions. We confirmed this behavior in a series of numerical tests on a small problem with incomplete linear and quadratic basis functions on a variety of element shapes.     

Advanced model of laminated magnetic cores for two-dimensionalfield analysis

A numerical model for the analysis of laminated ferromagnetic cores of electromechanical devices is presented. The model is based on the finite-element solution of the two-dimensional (2-D) electromagnetic field problem in the lamination plane; a dynamical relation between local magnetic flux density and magnetic field strength is obtained by solving for the one-dimensional (1-D) eddy-current field developed in the lamination depth. The hysteresis of the magnetic material is accounted for by the Preisach approach. The model is first validated by comparison with an alternative held formulation available for axis-symmetric structures; finally, an application to a more complex 2-D laminated core is presented and the numerical results are confirmed by comparison with measured waveforms of electrical and magnetic quantities     

Computer-aided development of a magnetron source with high target utilization

Target erosion in the straight section of a conventional and a novel rectangular magnetron cathode is simulated and tested. The simulation includes modeling the magnetic field, tracing electron trajectories with a fourth-order Runge-Kutta numerical method, predicting ionization distribution with a Monte-Carlo method etc. It is shown that the conventional and the novel magnetron cathodes yield a target utilization of ∼32% and 67% in the straight section, respectively. We demonstrate that the highly improved utilization is mainly due to a multi-zero-point feature of the magnetic field in the novel magnetron, i.e., the position of zero-point for the vertical component of the magnetic flux density shifts continuously from the inner side to outer side of the target with an increase in the distance from the target surface.     

The 1D Spin-1/2 XXZ Model in Transverse Uniform and Staggered Magnetic Fields

We have studied the ground state magnetic phase diagram of the one-dimensional anisotropic spin-1/2 XXZ model in the presence of transverse uniform and staggered magnetic fields. We have suggested that the presence study can be applied to a real magnet with the Dzyaloshinskii–Moriya interaction. In the absence of the staggered magnetic field, the phase diagram is divided into four regions. Using the numerical Lanczos method, we have done an accurate numerical experiment. We have presented a detailed numerical analysis of the low energy spectrum and the ground state magnetic phase diagram. Our numerical results show the staggered-field-induced effects depend on in which one of the four regions the system is. In one of the regions, we have identified two quantum phase transitions, which belong to the universality class of the commensurate-incommensurate phase transition.     

Numerical and analytical study of rotating flow in an enclosed cylinder under an axial magnetic field

Summary. A numerical and analytical study of the steady laminar flow driven by a rotating disk at the top of an enclosed cylinder, having an aspect ratio H/R equal to 1, filled with a liquid metal, and submitted to an axial magnetic field B, is presented. The governing equations in cylindrical coordinates are solved by a finite volume method. In the absence of a magnetic field, the numerical method is validated via a comparison with experimental data; the latter was found to be in good agreement with the predictions. In the presence of a magnetic field, the analytical velocity profiles under the rotating disk and on the bottom wall obtained for a high value of the magnetic interaction parameter N are in excellent agreement with those obtained by numerical simulations. The effect of the top, bottom and vertical walls' conductivity on the flow is studied and found to be an important parameter in the control of the flow.     

A Novel Method of Arraying Permanent Magnets Circumferentially to Generate a Rotation Magnetic Field

An outer magnetic field is extensively applied to drive the movement of a clinic micro-robot. However, how to produce a suitable magnetic field is a complicated problem. Commonly, the drive magnetic field is generated by a combination of power coils. This paper presents a novel method that circumferentially arrays identical permanent magnets to generate a rotational magnetic field in the center area of the array circle. First, we distribute permanent magnets uniformly in a circle, and adjust each of them at a corresponding initial angle. All of the magnets rotate in the same direction synchronously, generating a constant strength and reverse rotation magnetic field in the center area of the circle. The rotation speed of the generated magnetic field equals that of the permanent magnets. We used two models to analyze the magnetic field, and did some numerical analyses. We set up a test-bed and carried out some experiments to prove the feasibility of the novel method. The method seems to have wide applicability in designing magnets to drive micro-robots for diagnosis and treatment.      

Plane problem of magnetoelasticity for ferromagnetic media weakened by holes

We study a static problem of the intensity of stresses in a magnetically soft ferromagnetic medium with a hole in the presence of a strong magnetic field. The relevant boundary-value problem is reduced to a system of singular integral equations which is solved by the method of mechanical quadratures. We present the results of numerical calculations of the intensity of stresses near the elliptic hole as a function of the intensity of the source magnetic field and show that the influence of magnetization on the concentration of stresses near the hole may be significant.Sumy University, Sumy. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 6, pp. 38–45, November–December, 1995.