Transition between an exothermic chemical wave front and a generic flame

Fragility of reaction-diffusion models with respect to competing advective processes

We study the coupling of a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation to a separate, advection-only transport process. We find that an infinitesimal coupling can cause a finite change in the speed and shape of the reaction front, indicating the fragility of the FKPP model with respect to such a perturbation. The front dynamics can be mapped to an effective FKPP equation only at sufficiently fast diffusion or large coupling strength. We also discover conditions when the front width diverges and when its speed is insensitive to the coupling. At zero diffusion in our mean-field description, the downwind front speed goes to a finite value as the coupling goes to zero.

Front propagation in a bistable system: how the energy is released

In this Rapid Communication we consider a front of transition between metastable and stable states in a conservative system. Due to the difference of energies between initial and finite states, such transition front can propagate only while radiating energy. A simulation of such a process in a one-dimensional nonlinear lattice shows an essential imbalance between the energy released in each act of transition, and the density of energy of oscillations behind the front. It means that the stationary front propagation must be accompanied by an essentially nonstationary radiative process. We reveal the origin of this phenomenon and show that the characteristics of the front propagation critically depend on boundary conditions. In the framework of a simple model of a bistable system we propose analytic evaluation of all important features of the transition process, such as front velocity, radiation frequency, and oscillation amplitude. All calculated values are in good agreement with numerical simulation data.

Steady dynamics of exothermic chemical wave fronts in van der Waals fluids

We study the steady dynamics of an exothermic Fisher-Kolmogorov-Petrovsky-Piskunov chemical wave front traveling in a one-dimensional van der Waals fluid. The propagating wave is initiated by a nonuniformity in reactant concentration contrary to usual combustion ignition processes. The heat release and activation energy of the reaction play the role of control parameters. We recently proved that the propagation of an exothermic chemical wave front in a perfect gas displays a forbidden interval of stationary wave front speeds [G. Dumazer, M. Leda, B. Nowakowski, and A. Lemarchand, Phys. Rev. E 78, 016309 (2008)]. We examine how this result is modified for nonideal fluids and determine the effect of the van der Waals parameters and fluid density on the bifurcation between diffusion flames and Chapman-Jouguet detonation waves as heat release increases. Analytical predictions are confirmed by the numerical solution of the hydrodynamic equations including reaction kinetics.