Spinning wave motion in frontal polymerization

Abstract

We present a mathematical model describing dynamics of spinning waves which propagate during frontal polymerization reaction taking place in a cylindrical reactor tube. The self-organization of spatio-temporal solution of wave equations due to interplay between thermal diffusion and kinetics gives rise to pattern formation. We begin with a fundamental equation of motion of radial coordinate after defining an asymptotic phase for spinmode. The motion is analyzed near a critical (Hopf) point and a perturbation solution is used to obtain patterns for a case of preparation of poly(2-hydroxyethyl methacrylate) (PHEMA) via frontal polymerization reaction. The model uses the distance as seen in photograph taken using scanning electron microscope (SEM) from which motion begins around core of spiral and calculates pitch of spiral which matches closely with experimental observation in micrograph. Also the model predicts qualitatively the ramp wave and spiral wave motion as observed under SEM. Both these results are reported in open literature for the first time to our best knowledge.