P. J. King

Magnetic levitation: Floating gold in cryogenic oxygen

In magnetic levitation, a strong and spatially varying magnetic field exerts an upward force on a body that is sufficient to counteract its weight due to gravity. Here we show that this effect can be enhanced by immersing the body in cold oxygen gas, which provides a further strong and adjustable buoyancy force that allows a wide range of materials to be levitated in an open, unpressurized vessel. The buoyancy of magnetized liquid oxygen is sufficient to float even gold and platinum, suggesting that this technique could find application in mineral separation. An interesting periodic pattern is created on the surface of this pure elemental paramagnetic fluid.

Cryogenically enhanced magneto-Archimedes levitation

The application of both a strong magnetic field and magnetic field gradient to a diamagnetic body can produce a vertical force which is sufficient to counteract its weight due to gravity. By immersing the body in a paramagnetic fluid, an additional adjustable magneto-buoyancy force is generated which enhances the levitation effect. Here we show that cryogenic oxygen and oxygen–nitrogen mixtures in both gaseous and liquid form provide sufficient buoyancy to permit the levitation and flotation of a wide range of materials. These fluids may provide an alternative to synthetic ferrofluids for the separation of minerals. We also report the dynamics of corrugation instabilities on the surface of magnetized liquid oxygen.

The water-enhanced Brazil nut effect

It is well known that a large dense intruder may rise to the surface of a vibrated granular bed, the Brazil nut effect. In this paper we describe a water-enhanced Brazil nut effect which occurs when the vibrated granular bed is fully immersed in a liquid. We use a bed of glass beads immersed in water and monitor the behaviour of a large steel intruder as the system is vibrated vertically. To aid our understanding, we have developed numerical simulations to model this system and provide detailed information on the fluid and grain motion. The mechanism responsible for the rapid rise of the intruder is shown to be fluid-enhanced ratcheting rather than simple differential drag.

The horizontal stability of a ball bouncing upon a vertically vibrated concave surface

In experiments a ball will not bounce repeatedly in the same place upon a vertically vibrating horizontal surface due to imperfections in the ball and the surface. Consequently, a concave surface is often used to restrain the horizontal movement of the ball while measurements are made of its vertical motion. Here we use two numerical-simulation models to study the horizontal motion of an inelastic sphere bouncing chaotically under gravity upon a vertically vibrated parabolic surface. Both models predict the same generic features. For almost flat surfaces the ball makes wandering horizontal excursions and as the surface curvature is increased the horizontal motion of the ball becomes more and more constrained. However, the horizontal motion may exhibit intermittent, abrupt and erratic bursts of very large amplitude. These bursts occur with a probability which increases extremely rapidly with surface curvature such that there is an effective threshold curvature for their observation within a finite sequence of bounces. We study the behaviour of this intermittency as a function of the vibration amplitude, of the surface curvature and of the normal coefficient of restitution.

Geometric contact resistances in anisotropic conductors

For any real arrangement of contacts on an electronic device, the resistance obtained from a two-terminal measurement includes effects due to the curvature of current paths near to the contacts as well as the intrinsic bulk effects which are of primary interest and the resistance due to the interface between the contact material and the device material. Provided that the contacts are sufficiently well separated that the geometric curvature effect associated with one contact is negligible at the other then separate contact resistances can be defined for the two contacts. In this case the measured resistance can be interpreted as a series combination of two contact resistances (each including both interface and geometric effects) and a bulk resistance. The object of this paper is to show analytically that the contact resistance associated with a single contact can be obtained from an appropriate three-terminal measurement using a remote voltage probe well away from the current contacts. The limits of validity of this result are examined and are found to be relatively undemanding.

The Dynamics of Spheres in Oscillatory Fluid Flows

We describe a range of phenomena which occur when a collection of dense rigid spheres on a surface is subjected to horizontal oscillatory fluid flows. Pairs of equal‐sized spheres are found to align perpendicular to the direction of oscillation with a well‐defined gap between them. Similarly, multiple particles form chains aligned across the direction of vibration. Two unequal sized spheres are found to migrate at a constant velocity, also across the direction of vibration. These systems have been investigated both in experiment and simulation. The mechanisms responsible for these effects can be traced to the streaming flows induced by the motion of the solid spheres relative to the fluid.

Influence of vibrational wave form on intruder clustering

It has recently been shown that, within a two-dimensional granular bed subjected to sinusoidal, vertical vibration, neutrally buoyant intruders attract each other over a distance of up to five intruder diameters. The interaction between these intruders is the net result of attractive and repulsive forces which occur at different parts of the vibration cycle. Here we show that these forces may be manipulated by altering the vibration wave form to vary the strength of the overall attraction, or even to produce a weak repulsion. This ability is important for controlling the mixing of larger grains held within a granular bed.