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

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

doi:10.1016/j.ces.2004.10.006

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

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

Chemical Engineering and Materials Science

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	1323-1336
Number of pages	14
Journal	Chemical Engineering Science
Volume	60
Issue number	5
DOIs	https://doi.org/10.1016/j.ces.2004.10.006
State	Published - 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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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.",

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AU - Sonda, Paul

AU - Yeckel, Andrew

AU - Daoutidis, Prodromos

AU - Derby, Jeffrey J.

N1 - 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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N2 - 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.

AB - 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.

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

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