Robert J. Deissler

Stokes flow studies are fundamental to advancing medical and industrial technologies, particularly in areas such as drug targeting, cell studies, the optimization of drug carrier vehicles, high viscosity flows, and magnetic particle imaging. While previous research has focused on the motion of obliquely falling cylindrical rods and magnetic particle chains, a broader analytical framework is required to understand more complex particle-fluid migrations. In this paper, we first generalize the two-dimensional motion of an obliquely falling rod in a gravitational field to the three-dimensional motion of an object possessing three mutually perpendicular planes of symmetry falling through a viscous fluid in the Stokes limit. We derive a general formula for the three components of velocity—including both downward and sideways components—for objects of arbitrary orientation and uniform density. These analytical solutions are defined in terms of the object’s orientation, specified via Euler angles, and the velocity of the object falling along each of its three principal axes, or the drag coefficient along each of those axes. We give a variety of examples of objects that satisfy this general formula. In addition, we apply the formula to a cuboid for which those velocity components along each of its principal axes have been measured experimentally by other researchers, thus giving both the downward and sideways components for arbitrary orientation. We then analyze the motion in a gradient magnetic field of elongated magnetic particles, such as nanorods and nanoellipsoids, for which the induced magnetic moment is along the long axis of the particle. We discuss the similarities and differences with the gravitational case. By providing a unified framework for predicting the trajectories of these symmetric bodies, this work enhances the understanding of the motion of inertial and magnetic particles under the influence of gravitational and gradient magnetic fields, respectively.

We study the orientation in a uniform magnetic field of rod-like anisotropic biofluid crystals with an easy plane that makes an oblique angle with the crystal’s c-axis. For a sufficiently strong field, these crystalline rods orient themselves such that the crystal’s easy plane is parallel to the magnetic field, the rod’s direction being defined as the direction of the crystal’s c-axis. As the rod rotates about the crystal’s hard axis there will therefore be a range of angles that the rod makes with the magnetic field. We detail this behavior by first providing illustrations of hemozoin crystals at various orientations. These illustrations clearly demonstrate that the orientation angle that the crystalline rod makes with respect to the magnetic field varies from about 30° to 150°. We also derive an analytical expression for the probability density function for the orientation angle. We find that the orientation angles are not uniformly distributed between the limits of 30° and 150°, but rather tend to cluster near these limits. This suggests experimental tests and addresses confusion about the rod orientation found in past literature. The relevance to other anisotropic biofluid crystals, such as those produced by gout, is also discussed.

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.

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.

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.

The effect of magnetoresistance, magnetothermal conductivity (MTC), and RRR value on the active quench protection of a persistent-mode conduction-cooled 1.5 T MgB ₂ superconducting magnet is studied using numerical simulation. It is found that inclusion of magnetoresistance in the simulation can significantly decrease the calculated maximum temperature reached in this magnet during a quench, e.g., by 9 K for RRR = 100. The inclusion of both magnetoresistance and MTC similarly decreases the peak temperature, but by a smaller amount, e.g., by 7 K for RRR = 100. Using copper with a lower RRR value can also significantly decrease the peak temperature reached in this magnet, e.g., by 16 K for RRR = 50 as compared to RRR = 200. However, decreasing the RRR value to much less than 50 results in a significantly higher voltage, e.g., decreasing the RRR value from 50 to 10 results in a 1000 V increase. A RRR value between 50 and 100 may provide a good balance.

The active quench protection of a 1.5 T MgB ₂ conduction-cooled MRI magnet operating in persistent current mode is considered. An active quench protection system relies on the detection of the resistive voltage developed in the magnet, which is used to trigger the external energizing of quench heaters located on the surfaces of all ten coil bundles. A numerical integration of the heat equation is used to determine the development of the temperature profile and the maximum temperature in the coil at the origin, or ‘hot spot’, of the quench. Both n -value of the superconductor and magnetoresistance of the wire are included in the simulations. An MgB ₂ wire manufactured by Hyper Tech Research, Inc. was used as the basis to model the wire for the simulations. With the proposed active quench protection system, the maximum temperature was limited to 200 K or less, which is considered low enough to prevent damage to the magnet. By substituting Glidcop for the Monel in the wire sheath or by increasing the thermal conductivity of the insulation, the margin for safe operation was further increased, the maximum temperature decreasing by more than 40 K. The strain on the MgB ₂ filaments is calculated using ANSYS, verifying that the stress and strain limits in the MgB ₂ superconductor and epoxy insulation are not exceeded.

We investigate how the criteria for two prototype instabilities in one-dimensional pattern-forming systems, namely for the Eckhaus instability and for the Benjamin-Feir instability, change as one goes from a continuous bifurcation to a spatially periodic or spatially and/or time-periodic state to the corresponding weakly inverted, i.e., hysteretic, cases. We also give the generalization to two-dimensional patterns in systems with anisotropy as they arise, for example, for hydrodynamic instabilities in nematic liquid crystals.