Stabilizing/destabilizing effects of axial accelerations in Bridgman growth

The stabilizing/destabilizing effects of axial accelerations are analyzed for Bridgman growth systems that are subjected to small transverse accelerations. The core flows and transport for thermally stabilized dilute systems are modeled by solving the linearized one-dimensional momentum equation simultaneously with the heat transport equation. The resulting velocity function is then used with the mass transport equation to obtain the concentration field. Compositionally stabilized, non-dilute systems were modeled by solving the momentum equation with the mass transport equation and using the result to obtain the thermal field. The axial acceleration is characterized by the Rayleigh number, Ra-x = Gr(x)Pr for dilute systems, and Pa-x = Gr(x)Sc for non-dilute systems (Gr(x) being the Grashof number corresponding to the axial component of gravity). Microgravity experiments, in which the Ra-x is small, are shown to be easily disturbed by very small (< 1 mu g)transverse accelerations. The application of an axial acceleration O(1 mu g) can provide a modest stabilization for non-dilute growth systems with Sc much greater than 1, but does not significantly affect dilute systems with Pr much less than 1. Similarly, for vertical Bridgman growth in normal gravity, it is shown that compositionally stabilized non-dilute systems are much more tolerant to a small misalignment relative to the local vertical than thermally stabilized dilute systems.