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.
ASJC Scopus subject areas
- Applied Mathematics