We use a front-tracking method to simulate solidification with volume change of a droplet on a fixed cooling plate. The problem includes temporal evolution of three interfaces, i.e., solid–liquid, solid–air, and liquid–air, that are explicitly tracked under the assumption of axisymmetry. The solid–liquid interface is propagated with a normal velocity that is calculated from the normal temperature gradient across the front and the latent heat. The liquid–air front is advected by the velocity interpolated from nearest bulk fluid flow velocities. Accordingly, the evolution of the solid–air front is simply the temporal imprint of the triple point at which simple and straightforward conditions are imposed. The governing Navier–Stokes equations are solved for the whole domain, setting the velocities in the solid phase to zero and with the non-slip condition on the solid–liquid interface. Computational results are compared with exact solutions for two-dimensional Stefan problems and with corresponding experimental results, and show good agreement.

Hollow eutectic tin-lead solder spheres with diameters from 3.5 to 4.5 mm have been produced directly from the melt. Raw solder placed in a crucible was melted at a temperature of typically about 50 °C above its melting point. The molten solder was then extruded vertically downward into air at room temperature through the outer nozzle of a coaxial nozzle mounted at the crucible bottom. Capillary instability of the extruded hollow molten solder jet led to the formation of hollow solder spheres. This formation was assisted by a transverse nozzle placed close to the coaxial nozzle, which directed an inert gas past the hollow jet at position where sphere detached. The spheres were then quickly cooled and solidified by water mist prior to collection in a container filled with water. Most of these spheres were completely hermetic and had a relatively smooth surface. Hollow water spheres were also formed as a test of production of hollow solder spheres through the nozzle.