Bifurcation Analysis of Polymerization Fronts

Nonlinear Dynamics of Frontal Polymerization with Autoacceleration

“…According to the initiator used in the reaction, supercritical standing waves became the stable mode along the front for very specific initiator concentrations. Upon setting α = 0, we recovered the results of Comissiong, Gross and Volpert [6] for a two-dimensional system without the autoacceleration effect. The quantities β 1r and β 2r were found to be always negative (for all parameter values investigated).…”

“…With α = 0, for the most part β 2r < β 1r < 0, but for a very small range of initiator concentration j 0 we find that β 1r < β 2r < 0 (see Table 1 and Figure 4). Supercritical traveling and standing waves are both detected, and for the most part the traveling waves are stable while the standing waves are unstable, except for a very small range where supercritical standing waves become the stable mode of propagation [6]. Upon repeating the investigation for α = 0, it was found that upon increasing the autoacceleration effect (to α = 0·05), we find that β 2r < β 1r < 0 always.…”

“…A detailed account of the linear stability analysis can be found in [3,5,6]. We use the following non-dimensional parameters in the analysis Instability occurs when a pair of complex conjugate eigenvalues crosses the imaginary axis as the parameters vary.…”

“…Comissiong, Gross and Volpert [6] found that both traveling and standing waves result from a supercritical bifurcation for certain initiators. The supercritical traveling wave solution was found to be the stable mode in most parameter regimes, as also observed by experiment [2].…”

“…A complete linear stability analysis was first presented by Schult and Volpert [3] and Spade and Volpert [4]. Weakly nonlinear analyses for the simplest model were performed in [5,6]. The focus of this paper is a weakly nonlinear analysis of a more complex model that allows for autoacceleration of the polymerization reactions by the reaction product.…”