Hopf bifurcation and solution multiplicity in a model for destabilized Bridgman crystal growth

Flow instabilities are analyzed within a destabilized vertical Bridgman crystal growth system, first studied experimentally by Kim et al. (J. Electrochem. Soc. 119(1972) 1218), using a distributed-parameter model consisting of balance equations for energy and momentum transport. Numerical solution of the governing equations via a Galerkin finite element method reveals multiple operating states and dynamic phenomena. Bifurcation analysis shows that the onset of time-periodic flows occurs in the model system via a supercritical Hopf bifurcation, consistent with prior experimental observations on the dynamics of flow in similar systems.