Peter Guba

Nonlinear oscillatory convection in mushy layers

We study the problem of nonlinear development of oscillatory convective instability in a two-dimensional mushy layer during solidification of a binary mixture. We adopt the near-eutectic limit, making the problem analytically tractable using standard perturbation techniques. We consider also a distinguished limit of large Stefan number, which allows a destabilization of the system to an oscillatory mode of convection. We find that either travelling waves or standing waves can be supercritically stable, depending strongly on the sensitivity of permeability of the mushy layer to variations in the local solid fraction: mushy-layer systems with relatively weak sensitivity are more likely to select travelling waves rather than standing waves in the nonlinear regime. Furthermore, the decrease in permeability is found to promote the subcritical, and hence more unstable, primary oscillatory states. In addition to mapping out the location of different stable oscillatory patterns in the available parameter space, we give the detailed spatio-temporal structure of the corresponding thermal, flow and solid-fraction fields within the mushy layer, as well as the local bulk composition in the resulting eutectic solid.

On the finite-amplitude steady convection in rotating mushy layers

This study concentrates on a relatively simple model of a mushy layer originally proposed by Amberg & Homsy and later studied in further detail by Anderson & Worster. We extend this model to the case in which the system is in a state of uniform rotation about the vertical, of particular interest is to determine how the rotation of the system controls the bifurcating convection with both the oblique-roll planform and the planform of hexagonal symmetry

Interactions between steady and oscillatory convection in mushy layers

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

Electric Discharges in the Protoplanetary Nebula as a Source of Impulse Magnetic Fields to Promote Dust Aggregation

Lightning discharge generated in the protoplanetary nebula is viewed as a temporally isolated surge in the flow of electrically charged particles, similar to that of terrestrial lightning. If the current is intense enough, a powerful circular impulse magnetic field is generated around the instantaneous virtual electric conductor. Such magnetic field is capable of magnetizing dust grains containing ferromagnetic components present in its vicinity to their saturation levels. As a result, dust grains attract one another, forming the aggregates. This magnetically driven attraction suggests an important process possibly operational at an early stage of the planetary accretion. Based on both a classical model for electric conductor, and the theory of Lienard–Wiechert electromagnetic potentials, our calculations show that the magnetic impulse due to a discharge channel of a few cm in diameter transferring a charge of about 104 electrons reaches as high as 10 T. At these magnetic fields, the ferromagnetic dust grains, and possibly the already-formed larger aggregates as well, are easily magnetized to the saturation levels, producing compact clusters exhibiting permanent magnetic moments.

Free convection in laterally solidifying mushy regions

An analysis is presented of the lateral solidification of a semi-infinite mushy region influenced by vertical, buoyancy-driven convection of the residual, interstitial melt. We consider a parameter regime in which the flow is steady on the time scale of the transient evolution of the mushy region. Our idealized model predicts patterns of macrosegregation consistent with earlier experimental studies and sheds light on the mechanisms involved.

The Effect of Uniform Rotation on Convective Instability of a Mushy Layer During Binary Alloys Solidification

The linear stability analysis of interstitial liquid within the mushy layer relative to a steady basic state is performed in order to incorporate the effect of uniform rotation on the onset of convective instability whose existence was found by Anderson and Worster (1996). The full set of non–dimensional governing equations for the temperature field, the local solid fraction and the fluid velocity are reduced asymptotically. In particular, the limit of small dimensionless mushy layer thickness, the limit of small differences between the initial and eutectic compositions of the liquid and the limit of large Stefan number are considered. The square root of Taylor number is assumed to be of the order unity. These simplifying assumptions involved in our analysis lead to a much simplified model which can essentially be solved analytically.

Screw dislocation-induced enhancement of the c-axis critical current in anisotropic superconductors

Abstract Supercurrent in the weakly conducting c -axis direction of layered superconductors is studied. It is shown that in the presence of screw dislocations with Burgers vectors parallel to the c -axis, the critical current of small samples is enhanced with respect to the perfect crystal, each dislocation being able to carry a supercurrent I 0 .