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 oscilla...

We describe a model for non-convecting diffusion-controlled solidification of a ternary (three-component) alloy cooled from below at a planar boundary. The modelling extends previous theory for binary alloy solidification by including a conservation equation for the additional solute component and coupling the conservation equations for heat and species to equilibrium relations from the ternary...

The influence of an external shear flow on the evolution of a solidifying array of dendritic crystals, termed a mushy layer, is investigated through controlled cooling of an aqueous ammonium chloride solution in a laboratory flume. The controlled cooling produces a mushy layer that grows at a constant rate from the base of the flume over which a laminar shear flow is applied. We find a critical...

We consider the solidi cation of a binary alloy in a mushy layer and analyse the system near the onset of buoyancy-driven convection in the layer. We employ a near-eutectic approximation and consider the limit of large fareld temperature. These asymptotic limits allow us to examine the rich dynamics of the mushy layer in the form of small deviations from the classical case of convection in a ho...

We introduce a notion of viscosity solutions for the two-phase Stefan problem, which incorporates possible existence of a mushy region generated by the initial data. We show that a comparison principle holds between viscosity solutions, and investigate the coincidence of the viscosity solutions and the weak solutions defined via integration by parts. In particular, in the absence of initial mus...

Two important factors affecting hot tearing – semi-solid constitutive behaviour and grain percolation – have been simulated through the use of microstructure models based on granular structures. The semi-solid model geometry is based on a modified Voronoi tessellation, and includes rounded corners to approximate an equiaxed-globular grain structure with liquid surrounding the grains. The percol...

[1] A recent prospective on the Yellowstone Caldera discounts its explosive potential based on inferences from tomographic studies which suggests a high degree of crystallization of the underlying magma body. In this study, we show that many of the first teleseismic P-wave arrivals observed at seismic stations on the edge of the caldera did not travel through the magma body but have taken longe...

In many scientific and engineering problems the solidification of an alloy leads to a highly convoluted crystalline matrix modeled as a thermodynamically controlled reactive porous medium called a mushy layer. We analyze the interaction of an external shear flow with a solidifying mushy layer through a corrugated mush–liquid interface. We find that the external flow can drive forced convective ...