Existence, stability, and nonlinear dynamics of detached Bridgman growth states under zero gravity

A thermocapillary model is used to study the existence, stability, and nonlinear dynamics of detached melt crystal growth in a vertical Bridgman system under zero gravity conditions. The model incorporates time-dependent heat, mass, and momentum transport, and accounts for temperature-dependent surface tension effects at the menisci bounding the melt. The positions of the menisci and phase-change boundary are computed to satisfy the conservation laws rigorously. A rich bifurcation structure in gap width versus pressure difference is uncovered, demarcating conditions under which growth with a stable gap is feasible. Thermal effects shift the bifurcation diagram to a slightly different pressure range, but do not alter its general structure. Necking and freeze-off are shown to be two different manifestations of the same instability mechanism. Supercooling of melt at the meniscus and low thermal gradients in the melt ahead of the crystal–melt–gas triple phase line, either of which may be destabilizing, are both observed under some conditions. The role of wetting and growth angles in dynamic shape stability is clarified.