Simulation of Helical Patterns in Free Boundary Dynamics of Frontal Polymerization
Narahari S. Pujari and Satish R. Inamdar
We will investigate the dynamics of a frontal polymerization reaction carried out in a cylindrical tube, which is a batch reactor. The micrograph shows that spatial patterns form confirming a helical motion near the core of the helix, which is around 1/0 singularity at the center of the tube. We will show in the text that self-organization occurs on a winding staircase coordinate. Hence we consider a first-order harmonic term where we add an asymptotic phase of the helix and analyze the spatial pattern formation via a linear stability analysis. The result of Greenberg for spirals in reaction-diffusion system is extended to derive a fundamental relation. The resulting complex differential equation gives the necessary analytical results to find dispersion and winding staircase coordinate expressions. The detailed computational analysis of the complex self-organization is presented as a simulation exercise.
Keywords: Helical motion; winding staircase coordinate; motion of helix; Stefan condition; frontal polymerization