Nonequilibrium molecular velocity distribution in binary reactive gaseous mixture

Master equation for a bistable chemical system with perturbed particle velocity distribution function

We present a modified master equation for a homogeneous gaseous reactive system which includes nonequilibrium corrections due to the reaction-induced perturbation of the particle velocity distribution function. For the Schlögl model, the modified stochastic approach predicts nonequilibrium-induced transitions between different dynamical regimes, including the transformation of a monostable system into a bistable one, and vice versa. These predictions are confirmed by the comparison with microscopic simulations using the direct simulation Monte Carlo method. Compared to microscopic simulations of the particle dynamics, the modified master equation approach proves to be much more efficient.

Transition between an exothermic chemical wave front and a generic flame

We consider the two classes of exothermic chemical wave fronts, propagating toward a stable or an unstable steady state. The hydrodynamic equations for stream velocity, temperature, and concentrations are solved numerically for increasing values of the reaction heat. For a critical value of the heat release, we find a transition between a chemical front, whose speed depends on the chemical dynamics, and a generic flame, whose speed is entirely determined by heat release. We derive an analytical expression of the flame speed from the invariants of the hydrodynamic equations. This result substantiates macroscopic approaches widely used in combustion, in which the chemical models include only simplified reaction mechanisms.

Sensitivity of explosion to departure from partial equilibrium

We study a thermochemical gaseous system in the vicinity of the bifurcation related to the emergence of bistability. Corrections to the standard deterministic dynamics induced by the perturbation of the particle velocity distribution are obtained from the solution of the Boltzmann equation. Using these results, analytical expressions including the nonequilibrium effects are derived for the ignition time in the explosive regime and mean first passage time in the bistable regime. It is demonstrated that a departure from partial equilibrium can shift the bifurcation point. The system which was bistable according to the standard deterministic approach, can become monostable and explosive in the presence of nonequilibrium effects. Even when the system remains in the bistable regime, the mean first passage time can be changed by several orders of magnitude. In the monostable domain, the ignition time can be about ten times smaller than the unperturbed value. These analytical predictions agree well with the results of the microscopic simulations of the dilute gas system.

Macroscopic effects of the perturbation of the particle velocity distribution in a trigger wave

Departure from the equilibrium particle velocity distribution induced by a chemical reaction is studied in an inhomogeneous chemical bistable system in which a trigger wave can propagate. These nonequilibrium effects influence the speed and shape of the trigger wave propagating between the two stable stationary states. In contrast to the Fisher front, the discretization of the variables and the internal fluctuations do not sensitively modify the macroscopic properties of the trigger wave. Analytical results deduced from the Boltzmann equation agree well with microscopic simulations using Bird's method. Both approaches lead to large relative corrections to the front speed, in particular for parameter values close to that corresponding to a stationary interface between the two stable states.