Weakly nonlinear stability analysis of frontal polymerization

L. K. Gross*, V. A. Volpert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

A description of frontal polymerization is given via a free boundary model with nonlinear kinetic and kinematic conditions at the free boundary. We perform a weakly nonlinear analysis for the development of pulsating instabilities on the cylinder, building on the linear stability analysis of [1]. We take as a bifurcation parameter an experimentally measurable combination of material and kinetic parameters. The asymptotic analysis leads to the derivation of an ordinary differential equation of Landau-Stuart type for the slowly varying amplitude of a linearly unstable mode. We classify nonlinear dynamics of the polymerization front by doing a parameter sensitivity study of the amplitude equation.

Original languageEnglish (US)
Pages (from-to)351-375
Number of pages25
JournalStudies in Applied Mathematics
Volume110
Issue number4
DOIs
StatePublished - May 1 2003

ASJC Scopus subject areas

  • Applied Mathematics

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