Magnetic Gradient Force Research Articles

INSTABILITY OF NON-UNIFORM TOROIDAL MAGNETIC FIELDS IN ACCRETION DISKS

ABSTRACT We present a new type of instability that is expected to drive magnetohydrodynamic (MHD) turbulence from a purely toroidal magnetic field in an accretion disk. It is already known that in a differentially rotating system, the uniform toroidal magnetic field is unstable due to magnetorotational instability (MRI) under a non-axisymmetric and vertical perturbation, while it is stable under a purely vertical perturbation. Contrary to the previous study, this paper proposes an unstable mode completely confined to the equatorial plane, driven by the expansive nature of the magnetic pressure gradient force under a non-uniform toroidal field. The basic nature of this growing eigenmode, which we name “magneto-gradient driven instability,” is studied using linear analysis, and the corresponding nonlinear evolution is then investigated using two-dimensional ideal MHD simulations. Although a single localized magnetic field channel alone cannot provide sufficient Maxwell stress to contribute significantly to the angular momentum transport, we find that the mode coupling between neighboring toroidal fields under multiple localized magnetic field channels drastically generates a highly turbulent state and leads to the enhanced transport of angular momentum, which is comparable to the efficiency seen in previous studies on MRIs. This horizontally confined mode may play an important role in the saturation of an MRI through complementray growth with the toroidal MRIs and coupling with magnetic reconnection.

Potentiodynamic Polarization and Potentiostatic Polarization Behaviors for Iron in Sulfuric Acid Solution with or without a Magnetic Field

The behavior of iron during the corrosion process has been already studied in great detail due to its importance as a main constituent of many metallic construction materials. Magnetic field generated by electromagnetic facilities such as power generators, motors and solenoid valves and electric transmission lines can affect the corrosion of these facilities and their surrounding materials. Effects of imposed magnetic fields on the anodic behavior of iron has been investigated and discussed with respect to the modulation of the mass transport due to the Lorentz-force-driven magnetohydrodynamic (MHD) effect and magnetic field gradient force (MFGF) effect. Hydrogen evolution reaction (HER) on different metals/alloys in acidic or alkaline media is one of the most investigated cathodic reactions in the field of corrosion electrochemistry. Meanwhile, hydrogen is a potential energy source for fuel cells and other applications and the HER supplies the highly pure hydrogen. Its reaction kinetics of HER has been generalized. The effect of magnetic field on the kinetics and mechanism of HER needs investigation in details. In the present study, the effect of a magnetic field on the cathodic reaction of iron in a sulfuric acid solution was studied. Potentiodynamic polarization curves with or without a 0.4 T magnetic field and potentiostatic polarizations under the intermittent imposing or withdrawing of the magnetic field were used to determine the magnetic field effect on hydrogen evolution reaction. An electromagnet with a direct current source was used. The magnetic field was horizontal and oriented parallel to the electrode surface. Results of potentiostatic polarization curves show that the cathode current density at high acthodic over-poentials increased due to the presence of a 0.4T magnetic field while the shape of the polarization curve was not significantly changed by magnetic field, as shown in Fig. 1. The phenomenon has been described in previous studies that the magnetic field generates a new overpotential which leads to accelerating the hydrogen reaction. Figure 2 shows the impact of an applied magnetic field on the current vs. time curves under potentiostatic polarization for iron in sulphuric acid solution. The effect of magnetic field on cathodic current was related to the polarization sequence and the sequence of applying magnetic field. When the iron electrode has been polarized after many cycles of imposing or withdrawing the magnetic field, the magnetic field could cause a sudden decrease of the current density and then the current density maintained at a relatively low value, and withdrawing the magnet caused a sudden increase of the current density and then the current density maintained at a relatively high value. It has been found that if the magnetic field was applied at the start of polarization, withdrawing the magnetic field for the first time caused to a sudden but not big decrease of the current density and then the current density maintained at a relatively low value. The results the applied magnetic field effect on cathodic hydrogen evolution could be different depending on the cathodic polarization mode and the test sequence. One possible reason is that iron electrode would be subject to hydrogen charging that will change the properties of the iron electrode itself thus making the magnetic field effect different. Another possible reason can be the memory effect of magnetic field on solution properties or cathodic reaction. Systematic measurements are required for clarifying these issues. Figure 1

Pose control of the chain composed of magnetic particles using external uniform and gradient magnetic fields

Magnetic particles (MPs) are known to respond to a magnetic field and can be moved by magnetic force, which make them good carriers in bioengineering and pharmaceutical engineering. In this paper, a pose control method for the straight chain composed of MPs is proposed, and the chain with one pose can be moved to another position with another pose using alternately employed uniform and gradient magnetic fields. Based on computer simulations, it is revealed that in the uniform magnetic field, the MPs form a straight chain with the same separation space along the field lines, and once the uniform magnetic field rotates, the chain also rotates with the field. In the gradient magnetic field, the MPs move toward the higher field so that the translation of the chain can be realized. The simulation results indicate that while the uniform magnetic field is rotating, there exists certain hysteresis between the chain and the field, and the chain is not straight anymore. So the uniform magnetic field should rest at the target angle for a period to make the chain fully relax to be straight. For nanoMP, its magnetic moment directly determines the gradient magnetic force which is much smaller than the dipole–dipole force among MPs. Therefore, the translation of the chain is much more time-consuming than rotation. To enlarge the translational velocity, it is suggested to increase the size of MPs or the magnetic field gradient.

Magnetic Field simulation and experimental tests of Special Cross-section Shape Matrices for High Gradient Magnetic Separation

The cross-sectional shape has great influence on the magnetic field characteristics of magnetic matrices in high gradient magnetic separation (HGMS). Suitable cross-sectional matrices can improve the recovery of fine weakly magnetic minerals and reduce mineral processing energy consumption. The performance of four types of cross-sectional shape matrices in the axial configuration of HGMS was studied through numerical simulation combined with experimental tests. The magnetic field generated by the matrices was simulated with ANSYS software, and the magnetic field strength, gradient, and magnetic force were analyzed and compared. The simulation results showed that diamond shaped, elliptical, square, and circular steel matrices reach magnetization saturation successively with increasing the magnetic induction, and the required magnetic induction is approximately 0.7, 0.8, 1, and 1.1 T, respectively. The magnetic field gradient increases with increasing the magnetic induction and then keeps constant when the matrices reach magnetization saturation. Within a wide range of the magnetic induction, the elliptical and square matrices present good magnetic field characteristics. The magnetic force near the surface of the square matrices is the largest but decreases rapidly and consequently has a small effect depth. The magnetic force near the surface of the elliptical matrices is relatively lower but decreases slowly and has a larger effect depth. The diamond-shaped matrices are easy to reach magnetization saturation, and the magnetic force decreases most rapidly. Magnetic matrices were manufactured, and magnetic separation experiments were conducted to verify the simulation results. The experimental results show that the elliptical and square matrices can obtain higher recovery in a wide range of magnetic induction, and the recovery of the elliptical matrices is the highest. The experimental results correspond well with the numerical simulation results, and the results indicate that the magnetic force effect depth is a very important factor influencing the performance of the matrices.

In situ analysis of copper electrodeposition reaction using unilateral NMR sensor

The uses of high-resolution NMR spectroscopy and imaging (MRI) to study electrochemical reactions in situ have greatly increased in the last decade. However, most of these applications are limited to specialized NMR laboratories and not feasible for routine analysis. Recently we have shown that a bench top, time domain NMR spectrometer can be used to monitor in situ copper electrodeposition reaction and the effect of Lorentz force in the reaction rate. However these spectrometers limit the cell size to the magnet gap and cannot be used with standard electrochemical cells. In this paper we are demonstrating that unilateral NMR sensor (UNMR), which does not limit sample size/volume, can be used to monitor electrodeposition of paramagnetic ions in situ. The copper electrodeposition reaction was monitored remotely and in situ, placing the electrochemical cell on top of the UNMR sensor. The Cu2+ concentration was measured during three hours of the electrodeposition reactions, by using the transverse relaxation rate (R2) determined with the Carr–Purcell–Meiboom–Gill pulse sequence. The reaction rate increased fourfold when the reaction was performed in the presence of a magnetic field (in situ), in comparison to the reactions in the absence of the magnetic field (ex situ). The increase of reaction rate, in the presence of the UNMR magnet, was related to the magneto hydrodynamic force (FB) and magnetic field gradient force (F∇B). F∇B was calculated to be one order of magnitude stronger than FB. The UNMR sensor has several advantages for in situ measurements when compared to standard NMR spectrometers. It is a low cost, portable, open system, which does not limit sample size/volume and can be easily be adapted to standard electrochemical cells or large industrial reactors.

Levitation forces of a bulk YBCO superconductor in gradient varying magnetic fields

The levitation forces of a bulk YBCO superconductor in gradient varying high and low magnetic fields generated from a superconducting magnet were investigated. The magnetic field intensity of the superconducting magnet was measured when the exciting current was 90 A. The magnetic field gradient and magnetic force field were both calculated. The YBCO bulk was cooled by liquid nitrogen in field-cooling (FC) and zero-field-cooling (ZFC) condition. The results showed that the levitation forces increased with increasing the magnetic field intensity. Moreover, the levitation forces were more dependent on magnetic field gradient and magnetic force field than magnetic field intensity.

Magnetic control: Switchable ultrahigh magnetic gradients at Fe3O4 nanoparticles to enhance solution-phase mass transport

Enhancing mass transport to electrodes is desired in almost all types of electrochemical sensing, electrocatalysis, and energy storage or conversion. Here, a method of doing so by means of the magnetic gradient force generated at magnetic-nanoparticle-modified electrodes is presented. It is shown using Fe3O4-nanoparticle-modified electrodes that the ultrahigh magnetic gradients (>10 8 T·m –1 ) established at the magnetized Fe3O4 nanoparticles speed up the transport of reactants and products at the electrode surface. Using the Fe(III)/ Fe(II)-hexacyanoferrate redox couple, it is demonstrated that this mass transport enhancement can conveniently and repeatedly be switched on and off by applying and removing an external magnetic field, owing to the superparamagnetic properties of magnetite nanoparticles. Thus, it is shown for the first time that magnetic nanoparticles can be used to control mass transport in electrochemical systems. Importantly, this approach does not require any means of mechanical agitation and is therefore particularly interesting for application in micro- and nanofluidic systems and devices.

Magnetophoretic potential at the movement of cluster products of electrochemical reactions in an inhomogeneous magnetic field

An electric field arises from the influence of a nonuniform static magnetic field on charged colloid particles with magnetic susceptibility different from that of the surrounding liquid. It arises, for example, under the influence of a nonuniform static magnetic field in clusters of electrochemical reaction products created during metal etching, deposition, and corrosion processes without an external electric current passing through an electrolyte near a magnetized electrode surface. The corresponding potential consists of a Nernst potential of inhomogeneous distribution of concentration of colloid particles and a magnetophoretic potential (MPP). This potential has been calculated using a thermodynamic approach based on the equations of thermodynamics of nonequilibrium systems and the Onsager relations for a mass flow of correlated magnetic clusters under a gradient magnetic force in the electrolyte. The conditions under which the MPP contribution to the total electric potential may be significant are discussed with a reference to the example of a corroding spherical ferromagnetic steel electrode.

Modification of Electrodeposited Co-Pd Alloy Catalysts By Superimposed High Magnetic Field

Palladium and its alloys have been a subject of interest in many research centers all over the world. Due to the price and accessibility of Pd, intensive tests are conducted aiming to invent alloys with catalytic properties similar to those of platinum, but much cheaper than palladium itself. Alloys of Co-Pd, Pd-Fe, Pd-Ni and Pd-Cr exhibit high catalytic activity for the four electron oxygen reduction reaction.The properties of Co-Pd alloys for the hydrogen evolution reaction are close to the properties of pure platinum. This makes it possible to use them, for example, in fuel cells. Tests performed so far have demonstrated that the Pd-Co alloys are characterized by much better electrocatalytic properties for HER than pure palladium. Application of an external magnetic field during the deposition of an alloy causes an additional convection at the electrode surface through the magnetohydrodynamic effect (MHD), paramagnetic force and magnetic field gradient force. This additional convection results in changes of the alloy composition, structure and morphology, and these, in turn, affect the further properties as magnetic as catalytical of the produced alloys. Magnetic field applied parallel to the surface of the electrode generates convection (magnetohydrodynamic effect MHD) of the electrolyte; it results in a laminar flow on the surface of the electrode which reduces the diffusion layer and increases the concentrations gradients. This results in change of the size of the grains and thus can also influence the texture and formation of various phases of the deposits. These various effects can be caused at the same time by the above mentioned convection but also by the magnetic properties, when the field is superimposed the growth in the direction of easier magnetization appears. Optimal conditions of electrolytic deposition of cobalt matrix nanoalloys will be sought through selection of proper composition of electrolyte, changes of electrolysis parameters and by application of external electromagnetic field with intensity up to 12 Tesla. Initial experiments, when the magnetic field was limited up to 1 T, show the improvement of catalytical properties together with increase of magnetic field orientated parallel to the surface of electrode. The influence of magnetic field with higher strength on electrodeposition of alloys with catalytical properties is needed to be clarified. Acknowledgement This work was supported by Polish National Science Center under grants 011/01/N/ST5/05509 and 2013/09/B/ST8/00211. This work was also supported by Polish Ministry of Science and Higher Education under grant IP2012/001072.

THE PULSATING PULSAR MAGNETOSPHERE

Following the basic principles of a charge separated pulsar magnetosphere \citep{goldreich1969}, we consider the magnetosphere be stationary in space, instead of corotating, and the electric field be uploaded from the potential distribution on the pulsar surface, set up by the unipolar induction. Consequently, the plasma of the magnetosphere undergoes guiding center drifts of the gyro motion due to the transverse forces to the magnetic field. These forces are the electric force, magnetic gradient force, and field line curvature force. Since these plasma velocities are of drift nature, there is no need to introduce an emf along the field lines, which would contradict the $E_{\parallel}=\vec E\cdot\vec B=0$ plasma condition. Furthermore, there is also no need to introduce the critical field line separating the electron and ion open field lines. We present a self-consistent description where the magnetosphere is described in terms of electric and magnetic fields and also in terms of plasma velocities. The fields and velocities are then connected through the space charge densities self-consistently. We solve the pulsar equation analytically for the fields and construct the standard steady state pulsar magnetosphere. By considering the unipolar induction inside the pulsar and the magnetosphere outside the pulsar as one coupled system, and under the condition that the unipolar pumping rate exceeds the Poynting flux in the open field lines, plasma pressure can build up in the magnetosphere, in particular in the closed region. This could cause a periodic openning up of the closed region, leading to a pulsating magnetosphere, which could be an alternative for pulsar beacons. The closed region can also be openned periodically by the build-up of toroidal magnetic field through a positive feedback cycle.

Enhanced paramagnetic Cu2+ ions removal by coupling a weak magnetic field with zero valent iron

A weak magnetic field (WMF) was proposed to enhance paramagnetic Cu2+ ions removal by zero valent iron (ZVI). The rate constants of Cu2+ removal by ZVI with WMF at pH 3.0–6.0 were −10.8 to −383.7 fold greater than those without WMF. XRD and XPS analyses revealed that applying a WMF enhanced both the Cu2+ adsorption to the ZVI surface and the transformation of Cu2+ to Cu0 by ZVI. The enhanced Cu2+ sequestration by ZVI with WMF was accompanied with expedited ZVI corrosion and solution ORP drop. The uneven distribution of paramagnetic Cu2+ along an iron wire in an inhomogeneous MF verified that the magnetic field gradient force would accelerate the paramagnetic Cu2+ transportation toward the ZVI surface due to the WMF-induced sharp decay of magnetic flux intensity from ZVI surface to bulk Cu2+ solution. The paramagnetic Fe2+ ions generated by ZVI corrosion would also accumulate at the position with the highest magnetic flux intensity on the ZVI surface, causing uneven distribution of Fe2+, and facilitate the local galvanic corrosion of ZVI, and thus, Cu2+ reduction by ZVI. The electrochemical analysis verified that the accelerated ZVI corrosion in the presence of WMF partly arose from the Lorentz force-enhanced mass transfer.

Magnetic Separation of Paramagnetic Ions From Initially Homogeneous Solutions

The concentration change in an initially homogeneous paramagnetic solution is studied interferometrically upon applying sufficiently strong inhomogeneous magnetic fields. For this purpose, five different magnetic field configurations are analyzed. Clear evidence is provided that an enrichment of paramagnetic ions occurs in the field gradient. In particular, we show that the shape of this enrichment layer maps the spatial distribution of the magnetic field gradient force.

Determination of nanoparticle force balance in an electrical magnetic separation system.

Analytical expressions for magnetic force gradient computation are given. FEM simulation of the matrix core in the working gap of a magnetic system is conducted. The magnetic force distribution is presented as a relative ratio. A force balance equation taking into account the magnetic force pattern is derived.

Modulation of monocytic leukemia cell function and survival by high gradient magnetic fields and mathematical modeling studies

The influence of spatially modulated high gradient magnetic fields on cellular functions of human THP-1 leukemia cells is studied. We demonstrate that arrays of high-gradient micrometer-sized magnets induce i) cell swelling, ii) prolonged increased ROS production, and iii) inhibit cell proliferation, and iv) elicit apoptosis of THP-1 monocytic leukemia cells in the absence of chemical or biological agents. Mathematical modeling indicates that mechanical stress exerted on the cells by high magnetic gradient forces is responsible for triggering cell swelling and formation of reactive oxygen species followed by apoptosis. We discuss physical aspects of controlling cell functions by focused magnetic gradient forces, i.e. by a noninvasive and nondestructive physical approach.

Effects of the Lorentz force and the gradient magnetic force on the anodic dissolution of nickel in HNO3 + NaCl solution

In this paper, the magnetic field perturbation method is used to study the effects of the Lorentz force and the gradient magnetic force on the anodic dissolution of Ni in 0.50mol dm-3 HNO3+5.0mmol dm-3 NaCl solution. During the anodic dissolution process, magnetic fields are applied in two directions: parallel (B//) and perpendicular (B⊥) to the surface of the electrode. Thus, the effects of different magnetic forces on the anodic dissolution can be analyzed. After the application of B//, the current may increase, decrease or remain stable under different potentials, while the peak potential, the oscillatory region and the passive potential shift positively. These are always caused by the Lorentz force, which enhances the mass-transport processes. However, after the application of B⊥, the peak potential, the oscillatory region and the passive potential shift negatively. The currents always tend to decrease under the different potentials, which can be explained as follows: the gradient magnetic force suppresses convection to increase the concentration of corrosion products, such as the paramagnetic Ni(II) species, in local positions at the electrode|electrolyte interface. However, neither B// nor B⊥ affects the anodic dissolution in the passive region for the oxide film on the electrode surface inhibits the MF effects. If Ni dissolves in 0.50mol dm-3 HNO3 with different chloride ions containing solution at the same potential, the effects caused by B// are different for it is in different regions and the rate-determining steps are different, however, the currents still tend to decrease with application of B⊥.

Weak magnetic field significantly enhances selenite removal kinetics by zero valent iron

The effect of weak magnetic field (WMF) on Se(IV) removal by zero valent iron (ZVI) was investigated as functions of pH and initial Se(IV) concentrations. The presence of WMF significantly accelerated Se(IV) removal and extended the working pH range of ZVI from 4.0–6.0 to 4.0–7.2. The WMF induced greater enhancement in Se(IV) removal by ZVI at lower initial Se(IV) concentrations. The influence of WMF on Se(IV) removal by ZVI was associated with a more dramatic drop in ORP and a more rapid release of Fe2+ compared to the case without WMF. SEM and XRD analysis revealed that WMF accelerated the corrosion of ZVI and the transformation of amorphous iron (hdyr)oxides to lepidocrocite. XANES analyses showed that WMF expedited the reduction of Se(IV) to Se(0) by ZVI at pH 6.0 when its initial concentration was ≤20.0 mg L−1. Se(IV) dosed at 40.0 mg L−1 was removed by ZVI via adsorption followed by reduction to Se(0) at pH 7.0 but via adsorption at 7.2 in the presence of WMF. Regardless of WMF, Se(IV) applied at 40.0 mg L−1 was removed by reduction at pH 4.0–6.0. The WMF-induced improvement in Se(IV) removal by ZVI may be mainly attributable to the Lorentz force and magnetic field gradient force. Employing WMF to enhance Se(IV) removal by ZVI is a promising and environmental-friendly method since it does not need extra energy and costly reagents.

Analysis of the Electrolyte Convection inside the Concentration Boundary Layer during Structured Electrodeposition of Copper in High Magnetic Gradient Fields

To experimentally reveal the correlation between electrodeposited structure and electrolyte convection induced inside the concentration boundary layer, a highly inhomogeneous magnetic field, generated by a magnetized Fe-wire, has been applied to an electrochemical system. The influence of Lorentz and magnetic field gradient force to the local transport phenomena of copper ions has been studied using a novel two-component laser Doppler velocity profile sensor. With this sensor, the electrolyte convection within 500 μm of a horizontally aligned cathode is presented. The electrode-normal two-component velocity profiles below the electrodeposited structure show that electrolyte convection is induced and directed toward the rim of the Fe-wire. The measured deposited structure directly correlates to the observed boundary layer flow. As the local concentration of Cu(2+) ions is enhanced due to the induced convection, maximum deposit thicknesses can be found at the rim of the Fe-wire. Furthermore, a complex boundary layer flow structure was determined, indicating that electrolyte convection of second order is induced. Moreover, the Lorentz force-driven convection rapidly vanishes, while the electrolyte convection induced by the magnetic field gradient force is preserved much longer. The progress for research is the first direct experimental proof of the electrolyte convection inside the concentration boundary layer that correlates to the deposited structure and reveals that the magnetic field gradient force is responsible for the observed structuring effect.

Optical velocity measurements of electrolytic boundary layer flows influenced by magnetic fields

Magnetic fields are applied to electrically conducting fluids in order to influence electrochemical processes through the magnetohydrodynamic effect. Various phenomena, e.g. on electrodeposited metal layers, which can be attributed to forced convections were observed. To provide information about acting forces, the laser Doppler velocity profile sensor was applied to measure the transition layer of a Lorentz force influenced flow over a backward-facing step and the velocity boundary layer during copper deposition. With this sensor, the electrolyte convection within < 500 μm of the front of an electrode is measured with a spatial resolution down to 15 μm. The interaction of buoyancy, Lorentz and magnetic field gradient forces is studied by measuring the velocities down to 10 μm in front of the cathode. Inside the concentration boundary layer, complex electrolyte convection is induced, which varies not only in time but also in its structure, depending on the forces present and their influence over time. In inhomogeneous magnetic field configurations, the magnetic field gradient force dominates the velocity boundary layer at steady state and transports electrolyte toward regions of high magnetic gradients, where maximum deposit thicknesses are found. In this way, the measurements confirm the predicted influence of the magnetic field gradient force on the structuring of copper deposits.

Enrichment of Paramagnetic Ions from Homogeneous Solutions in Inhomogeneous Magnetic Fields.

Applying interferometry to an aqueous solution of paramagnetic manganese ions, subjected to an inhomogeneous magnetic field, we observe an unexpected but highly reproducible change in the refractive index. This change occurs in the top layer of the solution, closest to the magnet. The shape of the layer is in accord with the spatial distribution of the largest component of the magnetic field gradient force. It turns out that this layer is heavier than the underlying solution because it undergoes a Rayleigh-Taylor instability upon removal of the magnet. The very good agreement between the magnitudes of buoyancy, associated with this layer, and the field gradient force at steady state provides conclusive evidence that the layer formation results from an enrichment of paramagnetic manganese ions in regions of high magnetic field gradient.

On the action of magnetic gradient forces in micro-structured copper deposition

On the action of magnetic gradient forces in micro-structured copper deposition