Relation between bulk and interface descriptions of alloy solidification.

From a simple bulk model for the one-dimensional steady-state solidification of a dilute binary alloy we derive the corresponding interface description. Our derivation leads to exact expressions for the fluxes and forces at the interface and for the set of Onsager coefficients. The constitutive equations, connecting the crystallization and diffusion fluxes and forces, decouple in the low-velocity limit and there generate an occasionally negative, but nevertheless thermodynamically consistent friction coefficient. We, moreover, discover a continuous symmetry, which is independent of our model and allows to decouple the constitutive equations for the two components of the alloy for arbitrary growth velocities.

Domain of oscillatory growth in directional solidification of dilute binary alloys.

The oscillatory growth of a dilute binary alloy has recently been described by a nonlinear oscillator equation that applies to small temperature gradients and large growth velocities in the setup of directional solidification. Based on a one-dimensional stability analysis of stationary solutions of this equation, we explore in the present paper the complete region where the solidification front propagates in an oscillatory way. The boundary of this region is calculated exactly, and the nature of the oscillations is evaluated numerically in several segments of the region.

Capillary-wave description of rapid directional solidification.

A recently introduced capillary-wave description of binary-alloy solidification is generalized to include the procedure of directional solidification. For a class of model systems a universal dispersion relation of the unstable eigenmodes of a planar steady-state solidification front is derived, which readjusts previously known stability considerations. We moreover establish a differential equation for oscillatory motions of a planar interface that offers a limit-cycle scenario for the formation of solute bands and, taking into account the Mullins-Sekerka instability, of banded structures.

Diffusion-induced oscillations of extended defects.

From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is negative, we find limit-cycle solutions, describing an oscillatory propagation of the interface. In the case of a growing solidification front this offers a transparent scenario for the formation of solute bands in binary alloys and, taking into account the Mullins-Sekerka instability, of banded structures.

Capillary-wave model for the solidification of dilute binary alloys.

Starting from a phase-field description of the isothermal solidification of a dilute binary alloy, we establish a model where capillary waves of the solidification front interact with the diffusive concentration field of the solute. The model does not rely on the sharp-interface assumption and includes nonequilibrium effects, relevant in the rapid-growth regime. In many applications it can be evaluated analytically, culminating in the appearance of an instability that, interfering with the Mullins-Sekerka instability, is similar to that found by Cahn in grain-boundary motion.

Segregation instabilities of moving interfaces.

The segregation of solute particles on a moving interface leads to the appearance of two types of instabilities near competing velocity thresholds. This behavior is shown to occur in a variety of exactly solvable models where the interface motion is coupled to a diffusion process of the solute particles. These models directly apply to the propagation of internal domain walls, but can also be generalized to surfaces of growing crystals in the kinetics-limited regime.

Kinetic complete wetting of a planar defect close to a bulk tricritical point.

The nucleation of a new phase at a moving planar defect is considered in the high-symmetry phase of a bulk tricritical point. In the first-order regime a kinetic complete-wetting transition is found where the thickness of the nucleation layer diverges, inducing a change of the drag coefficient of the defect. When the tricritical point is approached, the complete-wetting transition disappears, and, in the adjacent second-order regime, the layer thickness is finite in the full nucleation region.

Kinetic wetting of a moving planar defect by a new phase.

Close to a bulk phase transition, a moving planar defect can be covered by a layer of the ordered phase. This, in fact, happens above the transition point in some finite region of the temperature-velocity diagram. In the case of a first-order transition this region is furnished with a net of nonequilibrium phase-transition lines. The topology of this net resembles that of the phase diagram of a first-order wetting transition in thermal equilibrium. In particular, there appears a kinetic complete-wetting line where a significant change of the drag coefficient of the defect is predicted.

Stability of soap films: hysteresis and nucleation of black films.

We study the stability of soap films of a nonionic surfactant under different applied capillary pressures on the film. Depending on the pressure, either a thick common black film (CBF), or a micro-scopically thin Newton black film (NBF) is formed as a (metastable) equilibrium state, with a first-order (discontinuous) transition between the two. Studying the dynamics of the CBF-NBF transition, it is found that under certain conditions a hysteresis for the transition is observed: for a given range of pressures, either of the two states may be observed. We quantify the nucleation process that is at the basis of these observations both experimentally and theoretically.