Bifurcation of Pulsating and Spinning Reaction Fronts in Condensed Two-Phase Combustion

Linear stability analysis of reaction fronts in liquids

“…Such propagation modes were first found experimentally [30], [44] and studied theoretically [19], [27], [28], [51], [52] in combustion, and then for polymerization processes [7], [50], [55]. The theoretical analysis of the problem usually involves the investigation of the thermal instability; however, if the reactants are in a liquid phase, the hydrodynamical perturbations can also influence the stability of the front.…”

Historical perspective and contribution of US researchers into the field of self-propagating high-temperature synthesis (SHS)/combustion synthesis (CS): Personal reflections

“…Theoretical research describing combustion front stability and bifurcation analysis was done by Matkowsky from Northwestern University, and Margolis, Armstrong and Koszykowski from Lawrence Livermore National Laboratory. Professor Matkowsky has published numerous theoretical papers on the subject of gasless and gas-solid reactions [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. His pioneering work with Margolis, Kaper, and Leaf on bifurcation on pulsating and spinning reactions in condensed twophase combustion belongs to very fundamental classics of combustion synthesis [39].…”

“…Professor Matkowsky has published numerous theoretical papers on the subject of gasless and gas-solid reactions [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. His pioneering work with Margolis, Kaper, and Leaf on bifurcation on pulsating and spinning reactions in condensed twophase combustion belongs to very fundamental classics of combustion synthesis [39]. His further analysis with Bayliss of two routes to chaos in condensed phase combustion as well as a series of theoretical papers on filtration combustion with Booty and scientists from Chernogolovka, Russia made very significant contribution to better understanding of complex nonlinear phenomena in combustion synthesis.…”

Weakly Nonlinear and Numerical Analysis of Auto-Oscillatory Dynamics in a Solid Propellant Combustion Model

“…These studies have predicted a wide variety of nonsteady burning regimes where the temporal form of the oscillations is usually dependent on physical parameters, while their spatial form depends on the model geometry. Rectangular geometries have been found to produce sinusoidal variations in front temperature, location, and velocity [4][5][6], while cylindrical geometries have been found to produce more complex spatial patterns including "multiple point" and "spinning" combustion where spots or bands of relatively higher or lower temperature appear and disappear or rotate around the combustion zone, respectively [7][8][9]. In either geometry, a planar, pulsating mode is usually possible as are oscillations containing multiple spatial modes.…”