Surface deformations in dynamic thermocapillary convection under partial slip.

A prescribed, horizontal temperature gradient is imposed upon a horizontal liquid layer bounded from above by a deformable, liquid-gas interface and bounded from below by a partial-slip, rigid surface. A steady shear flow driven by thermocapillary motion emerges. This dynamic liquid layer is susceptible to the onset of oblique three-dimensional hydrothermal waves, purely two-dimensional hydrothermal waves, longitudinal traveling waves, and longitudinal rolls depending on the capillary number.

Strongly nonlinear theory of rapid solidification near absolute stability.

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise.

Instabilities in rapid directional solidification under weak flow.

We examine a rapidly solidifying binary alloy under directional solidification with nonequilibrium interfacial thermodynamics viz. the segregation coefficient and the liquidus slope are speed dependent and attachment-kinetic effects are present. Both of these effects alone give rise to (steady) cellular instabilities, mode S, and a pulsatile instability, mode P.