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

Paul Sonda, Andrew Yeckel, Prodromos Daoutidis, Jeffrey J. Derby

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10 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1323-1336
Number of pages14
JournalChemical Engineering Science
Volume60
Issue number5
DOIs
StatePublished - Mar 2005

Bibliographical note

Funding Information:
This material is based upon work supported by the National Science Foundation under Grant No. 0201486. This work was also supported in part by the United States National Aeronautics and Space Administration and the Minnesota Supercomputing Institute. PS also expresses thanks to the University of Minnesota Graduate School for a Doctoral Dissertation Fellowship.

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