From an obliquely falling rod in a viscous fluid to the motion of suspended magnetic bead chains that are driven by a gradient magnetic field and that make an arbitrary angle with the magnetic force vector: A Stokes flow study.

In view of the growing role of magnetic particles under magnetic field influence in medical and other applications, and perforce the bead chaining, it is important to understand more generally the chain dynamics. As is well known, in the presence of a magnetic field, magnetic beads tend to form chains that are aligned with the magnetic field vector. In addition, if there is a magnetic field gradient, there will be a magnetic force acting on this chain. The main goal of the present research is to study the motion of a magnetic bead chain that makes an arbitrary angle with the magnetic force vector in the Stokes flow limit, that is, in the limit of zero Reynolds number. We used the public-domain computer program HYDRO++ to calculate the mobility matrix, which relates the magnetic force acting on the chain to the velocity of the chain, for a chain of N beads making an arbitrary angle with the magnetic force vector. Because of the presence of off-diagonal elements of the mobility matrix, as the chain is drawn in the direction of the magnetic force, it is also deflected to the side. We derived analytic solutions for this motion. Also, for bead chains moving in directions both parallel and perpendicular to their lengths, we fit three-parameter functions to solutions from HYDRO++. We found the fits to be excellent. Combining these results with the analytic solutions, we obtained expressions for the velocity components for the bead chains that provide excellent fits to HYDRO++ solutions for arbitrary angles. Finally, we apply the methodology used for the bead chain studies to the study of an obliquely falling rod in a viscous fluid and derive analytic solutions for the velocity components of the obliquely falling rod.

An ON-OFF Magneto-Optical Probe of Anisotropic Biofluid Crystals: A ß-Hematin Case Study.

We have designed, developed and evaluated an innovative portable magneto-optical detector (MOD) in which a light beam with variable polarization passes through a fluid sample immersed in a variable magnetic field. The light intensity is measured downstream along the forward scattering direction. The field is turned on and off through the in-and-out motion of nearby permanent magnets. As a result, for sufficiently magnetically and optically anisotropic samples, the optical absorption is sensitive to changes in the light polarization. Both detection and characterization applications are therefore available. For instance, both the degree of malaria infection can be measured and hemozoin crystalline properties can be studied. We present experimental results for synthetic hemozoin, and describe them in terms of the basic physics and chemistry underlying the correlations of the directions of the external magnetic field and the light beam polarization. We connect this work to a commercialized product for malaria detection and compare it to other magneto-optical instruments and methods. We conduct tests of absorption parameters, the electric polarizability tensor, and we discuss the connection to magnetic and electric dipole moments.

Growth of Plasmodium falciparum in response to a rotating magnetic field.

BACKGROUND: Plasmodium falciparum is the deadliest strain of malaria and the mortality rate is increasing because of pathogen drug resistance. Increasing knowledge of the parasite life cycle and mechanism of infection may provide new models for improved treatment paradigms. This study sought to investigate the paramagnetic nature of the parasite's haemozoin to inhibit parasite viability. RESULTS: Paramagnetic haemozoin crystals, a byproduct of the parasite's haemoglobin digestion, interact with a rotating magnetic field, which prevents their complete formation, causing the accumulation of free haem, which is lethal to the parasites. Plasmodium falciparum cultures of different stages of intraerythrocytic growth (rings, trophozoites, and schizonts) were exposed to a magnetic field of 0.46 T at frequencies of 0 Hz (static), 1, 5, and 10 Hz for 48 h. The numbers of parasites were counted over the course of one intraerythrocytic life cycle via flow cytometry. At 10 Hz the schizont life stage was most affected by the rotating magnetic fields (p = 0.0075) as compared to a static magnetic field of the same strength. Parasite growth in the presence of a static magnetic field appears to aid parasite growth. CONCLUSIONS: Sequestration of the toxic haem resulting from haemoglobin digestion is key for the parasites' survival and the focus of almost all existing anti-malarial drugs. Understanding how the parasites create the haemozoin molecule and the disruption of its creation aids in the development of drugs to combat this disease.

Conceptual designs of conduction cooled MgB2 magnets for 1.5 and 3.0T full body MRI systems.

Conceptual designs of 1.5 and 3.0 T full-body magnetic resonance imaging (MRI) magnets using conduction cooled MgB2 superconductor are presented. The sizes, locations, and number of turns in the eight coil bundles are determined using optimization methods that minimize the amount of superconducting wire and produce magnetic fields with an inhomogeneity of less than 10 ppm over a 45 cm diameter spherical volume. MgB2 superconducting wire is assessed in terms of the transport, thermal, and mechanical properties for these magnet designs. Careful calculations of the normal zone propagation velocity and minimum quench energies provide support for the necessity of active quench protection instead of passive protection for medium temperature superconductors such as MgB2. A new 'active' protection scheme for medium Tc based MRI magnets is presented and simulations demonstrate that the magnet can be protected. Recent progress on persistent joints for multifilamentary MgB2 wire is presented. Finite difference calculations of the quench propagation and temperature rise during a quench conclude that active intervention is needed to reduce the temperature rise in the coil bundles and prevent damage to the superconductor. Comprehensive multiphysics and multiscale analytical and finite element analysis of the mechanical stress and strain in the MgB2 wire and epoxy for these designs are presented for the first time. From mechanical and thermal analysis of our designs we conclude there would be no damage to such a magnet during the manufacturing or operating stages, and that the magnet would survive various quench scenarios. This comprehensive set of magnet design considerations and analyses demonstrate the overall viability of 1.5 and 3.0 T MgB2 magnet designs.

Dependence of Brownian and Néel relaxation times on magnetic field strength.

PURPOSE: In magnetic particle imaging (MPI) and magnetic particle spectroscopy (MPS) the relaxation time of the magnetization in response to externally applied magnetic fields is determined by the Brownian and Néel relaxation mechanisms. Here the authors investigate the dependence of the relaxation times on the magnetic field strength and the implications for MPI and MPS. METHODS: The Fokker-Planck equation with Brownian relaxation and the Fokker-Planck equation with Néel relaxation are solved numerically for a time-varying externally applied magnetic field, including a step-function, a sinusoidally varying, and a linearly ramped magnetic field. For magnetic fields that are applied as a step function, an eigenvalue approach is used to directly calculate both the Brownian and Néel relaxation times for a range of magnetic field strengths. For Néel relaxation, the eigenvalue calculations are compared to Brown's high-barrier approximation formula. RESULTS: The relaxation times due to the Brownian or Néel mechanisms depend on the magnitude of the applied magnetic field. In particular, the Néel relaxation time is sensitive to the magnetic field strength, and varies by many orders of magnitude for nanoparticle properties and magnetic field strengths relevant for MPI and MPS. Therefore, the well-known zero-field relaxation times underestimate the actual relaxation times and, in particular, can underestimate the Néel relaxation time by many orders of magnitude. When only Néel relaxation is present--if the particles are embedded in a solid for instance--the authors found that there can be a strong magnetization response to a sinusoidal driving field, even if the period is much less than the zero-field relaxation time. For a ferrofluid in which both Brownian and Néel relaxation are present, only one relaxation mechanism may dominate depending on the magnetic field strength, the driving frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field. CONCLUSIONS: A simple treatment of Néel relaxation using the common zero-field relaxation time overestimates the relaxation time of the magnetization in situations relevant for MPI and MPS. For sinusoidally driven (or ramped) systems, whether or not a particular relaxation mechanism dominates or is even relevant depends on the magnetic field strength, the frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field.

Modeling the Brownian relaxation of nanoparticle ferrofluids: comparison with experiment.

PURPOSE: The authors investigate the ability of current models for magnetic nanoparticles immersed in dilute ferrofluids and external sinusoidal magnetic fields to explain recent experiments in which the relaxation effects are dominated by viscous damping. METHODS: The Fokker-Planck (FP) equation appropriate for the nanoparticle magnetic moment distribution corresponding to the underlying stochastic Langevin model is numerically studied and solutions compared to experimental results. The FP equation is solved using an expansion in Legendre polynomials. The polydisperse properties of the ferrofluids are incorporated into the analysis. RESULTS: By using a FP approach that includes polydispersion, the authors obtain good agreement with recent experimental results using ferrofluids containing nanoparticles with average hydrodynamic diameters in the 40-120 nm range. CONCLUSIONS: For nanoparticles used in recent magnetic spectroscopy experiments, the FP approach can be used to accurately model experimental data in the situation where Brownian relaxation effects are dominant and the ferrofluids are dilute.

Dipole in a magnetic field, work, and quantum spin.

The behavior of an atom in a nonuniform magnetic field is analyzed, as well as the motion of a classical magnetic dipole (a spinning charged ball) and a rotating charged ring. For the atom it is shown that, while the magnetic field does no work on the electron-orbital contribution to the magnetic moment (the source of translational kinetic energy being the internal energy of the atom), whether or not it does work on the electron-spin contribution to the magnetic moment depends on whether the electron has an intrinsic rotational kinetic energy associated with its spin. A rotational kinetic energy for the electron is shown to be consistent with the Dirac equation. If the electron does have a rotational kinetic energy, the acceleration of a silver atom in a Stern-Gerlach experiment or the emission of a photon from an electron spin flip can be explained without requiring the magnetic field to do work. For a constant magnetic field gradient along the z axis, it is found that the classical objects oscillate in simple harmonic motion along the z axis, the total kinetic energy -- translational plus rotational -- being a constant of the motion. For the charged ball, the change in rotational kinetic energy is associated only with a change in the precession frequency, the rotation rate about the figure axis remaining constant.