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Propagation of frontal polymerization—crystallization waves

Published online by Cambridge University Press:  26 September 2008

Vit. Volpert  and
Vl. Volpert
Vit. Volpert
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Vl. Volpert
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
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Abstract

We consider polymerization–crystallization waves in a cylindrical reactor, in which monomer is converted to polymer in a planar front. The polymer is subsequently crystallized in a wider zone behind the front. Specifically, we study uniformly propagating polymerization–crystallization waves, and determine profiles of temperature, and concentrations of polymer and crystallized polymer, as well as the propagation velocity. A linear stability analysis of the travelling wave solutions indicates the possibility of Hopf bifurcation, which describes the transition to the experimentally observed spinning mode of propagation, in which a hot spot is observed to propagate along a helical path on the surface of the cylinder. Since conditions at the time of conversion determine the nature of the polymer produced, spiral hollows, which trace out a helical path, appear on the surface of the crystallized polymer product.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 5 , Issue 2 , June 1994 , pp. 201 - 215
Copyright
Copyright © Cambridge University Press 1994

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