Axial segregation in a cylindrical centrifuge

We propose a theory for axial segregation of suspensions of non-neutrally buoyant particles in a rotating cylinder. The cylinder is oriented in the horizontal plane, so that any axial forces must arise from interparticle interactions. We show that the hydrodynamic interaction between pairs of particles produces a relative motion in the axial direction, independent of the gravitational force. If the particles are denser than the suspending fluid, differential centrifuging between particles at different radial positions leads to an at-tractive interaction, inducing a rapid growth of axial density perturbations. We suggest that this mecha-nism can explain the origin of band formation in rotating suspensions of non-neutrally buoyant particles.     

Particle-like and fluid-like settling of a stratified suspension

The gravitational settling of inhomogeneously suspended particles in a fluid has been investigated. Of particular interest is whether collective or individual motion of particles is dominant during their settlings, i.e., whether the particles settle as a continuous suspension or they settle individually relative to the surrounding fluid. We observed the settling of a stratified suspension which has the lower and upper concentration interfaces in a quasi-two-dimensional vessel. In some cases, the suspension behaves perfectly as a continuous fluid and the motion of the constituent particle is subject to bulk flow caused by the interfacial instability. In other cases, the particle behaves individually relative to the surrounding fluid. The existence of a concentration interface plays a significant role in these extreme behaviors of suspension. The transition from the collective to individual behaviors can be predicted quantitatively by a parameter which expresses the border resolution of the concentration interface.     

Nonlinear waves in a rotating plasma cylinder

Previous work on exact cylindrical surface waves in a nonneutral cold-electron plasma bounded by a dielectric is extended to include plasma rotation. A set of nonlinear rate equations describing the temporal behavior of the system is derived by first determining an appropriate spatial wave structure. Physically relevant periodic solutions are obtained     

Realistic rotating convection in a DNA suspension

In this work we report theoretical and numerical results on convection in a viscoelastic binary mixture under rotation for realistic rigid-rigid boundary conditions. We focus our analysis in the DNA aqueous suspensions. Instability thresholds for oscillatory convection are calculated. Finally, we analyze the stabilizing effect for the onset of convection.     

Oscillatory patterns in a rotating aqueous suspension

Suspensions of granular material in glycerin-water mixtures agitated in horizontally aligned rotating tubes show a whole variety of patterns. The stationary pattern of a homogeneous distribution and a chain of rings have been investigated before. Here we report on two types of oscillatory states in the same system. For a certain range of the rotation frequency and sufficiently high viscosity traveling waves propagate with constant velocity back and forth along the tube in an almost homogeneous distribution of sedimenting particles. The transition from a stationary to the traveling-wave state is found to be an imperfect supercritical bifurcation. The dependence of the wave length and speed on the tube's rotation frequency and the dynamic viscosity of the fluid are determined. Experiments with low viscosities show no traveling waves but low-frequency oscillations, when the previously known chain of rings undergoes a secondary instability.     

Axial segregation of granular materials

When mixtures of granular materials are rotated, it is often found that they segregate into bands, along the axis of rotation, which are rich in the various components. This effect is discussed experimentally and theoretically, with emphasis on a mechanism based on surface flow. The complimentary phenomenon of radial segregation is reviewed, and a mechanism is proposed. Finally, we consider the long-time behavior of rotating mixtures, particularly their anomolous coarsening. (c) 1999 American Institute of Physics.     

Axial discharge stabilization using a rotating magnetic field

A new axial gas discharge stabilization technique is described. Thermal instabilities and discharge constrictions are suppressed through the use of a transverse rotating magnetic field. The enhanced plasma stability observed is a result of a transverse Lorentz force that deflects the plasma column off-axis. As the magnetic field rotates, the plasma sweeps across the tube cross-section at the angular velocity of the impressed field. A 25% increase in power loading has been achieved using the stabilization technique.     

Energy dissipation characteristics of particle sloshing in a rotating cylinder

A study on the energy dissipation characteristics of granular materials flowing/sloshing in a rotating container is presented here. The objective is to develop a configuration for control of excessive structural oscillations, similar to those of tuned vibration absorbers and tuned sloshing absorbers. The effectiveness of energy dissipation through granular flow is primarily determined experimentally. A computational model is developed to understand the flow behavior and energy dissipation in this system. A promising kinematic match of the particle behavior is demonstrated between the numerical predictions and the experimental observations. The use of the granular flow in a rotating drum for vibration control is being investigated for the first time.     

Analysis of radial segregation of granular mixtures in a rotating drum

This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains differing only in size (slightly or widely) and only in surface properties are considered, and the predictions are in qualitative agreement with observations. The model yields results inconsistent with the assumptions for more general cases, and we speculate on how this may be corrected. Received 4 June 1999 and Received in final form 28 September 1999     

A relativistically rotating fluid cylinder

The field equations for stationary, axisymmetric, nonconvective perfect fluid are presented. A solution corresponding to a rigidly rotating cylinder with constant pressure is derived. Some properties of this solution are discussed.     

Radiation from a charge rotating around a perfectly conducting cylinder

The radiation from a charge uniformly rotating about a conducting cylinder immersed into a homogeneous medium was studied. Expressions for electric and magnetic fields, as well as for the surface charge and currents induced by the initial charge on the cylinder surface were obtained. A formula is derived for spectral-angular distribution of the radiation intensity. The results of a numerical analysis are presented.     

Energy absorption by a magnetic nanoparticle suspension in a rotating field

Heat generation by viscous dissipation in a dilute suspension of single-domain ferromagnetic particles in a rotating magnetic field is analyzed by assuming that the suspended particles have a high magnetic rigidity. The problem is solved by using a kinetic approach based on a rotational diffusion equation. Behavior of specific loss power (SLP) as a function of field strength H and frequency ω is examined at constant temperature. SLP increases as either of these parameters squared when the other is constant, eventually approaching a saturation value. The function SLP(H, ω) can be used to determine optimal and admissible ranges of magnetically induced heating.     

Transient settling of a dilute spherical suspension droplet at low Reynolds number

The transient settling in a viscous incompressible fluid of a spherical dilute cloud of particles starting from rest under the influence of a small constant applied force is studied in a continuum model on the basis of the linearized Navier-Stokes equations. Explicit expressions are derived for the motion of the cloud and for the flow velocity and pressure of the fluid. Equations of transient Stokesian dynamics are formulated that allow numerical study of the motion of a dilute cloud of particles of arbitrary initial configuration.     

Generalized radial oscillation modes of an acoustical medium rotating in a cylinder

Variants of closed wave equations for velocity perturbations in a rotating compressible medium (liquid or gas) are suggested. The effects of both the nonideal form of the equation of state of the medium and the character of its unperturbed state are taken into account in the equations. In the case of an ideal gas at an isothermal background state, these equations are solved exactly in analytic form, and the solutions describe the generalized radial oscillation modes. An inference is made about the existence of a shift of resonance frequencies of these modes because of the rotation of the medium. This shift is calculated as a function of the velocity of gas rotation and the radius of the cylinder.     

Axial time-averaged acoustic radiation force on a cylinder in a nonviscous fluid revisited

Objective

The present research examines the acoustic radiation force of axisymmetric waves incident upon a cylinder of circular surface immersed in a nonviscous fluid. The attempt here is to unify the various treatments of radiation force on a cylinder with arbitrary radius and provide a formulation suitable for any axisymmetric incident wave.

Method and results

Analytical equations are derived for the acoustic scattering field and the axial acoustic radiation force. A general formulation for the radiation force function, which is the radiation force per unit energy density per unit cross-sectional surface, is derived. Specialized forms of the radiation force function are provided for several types of incident waves including plane progressive, plane standing, plane quasi-standing, cylindrical progressive diverging, cylindrical progressive converging and cylindrical standing and quasi-standing diverging waves (with an extension to the case of spherical standing and quasi-standing diverging waves incident upon a sphere).

Significance and some potential applications

This study may be helpful essentially due to its inherent value as a canonical problem in physical acoustics. Potential applications include particle manipulation of cylindrical shaped structures in biomedicine, micro-gravity environments, fluid dynamics properties of cylindrical capillary bridges, and the micro-fabrication of new cylindrical crystals to better control light beams.