The present study addresses the role of molecular non-equilibrium effects in thermal ignition problems. We consider a single binary reaction of the form A+B -> C+C. Molecular dynamics calculations were performed for activation energies ranging between RT and 7.5RT and heat release of 2.5RT and 10RT. The evolution of up to 10,000 particles was calculated as the system undergoes a thermal ignition at constant volume. Ensemble averages of 100 calculations for each parameter set permitted to determine the ignition delay, along with a measure of the stochasticity of the process. A well behaved convergence to large system sizes is also demonstrated. The ignition delay calculations were compared with those obtained at the continuum level using rates derived from kinetic theory: the standard rate assuming that the distribution of the speed of the particles is the Maxwell-Boltzmann distribution, and the perturbed rates by Prigogine and Xhrouet [1] for an isothermal system, and Prigogine and Mahieu [2] for an energy releasing reaction, obtained by the Chapman-Enskog perturbation procedure. The molecular results were found in very good agreement with the latter at low temperatures, confirming that non-equilibrium effects promote the formation of energetic particles, that serve as seeds for subsequent reaction events: i.e., hot spots. This effect was found to lower the ignition delay by up to 30%. At high temperatures, the ignition delay obtained from the standard equilibrium rate was found to be up to 60% longer than the molecular calculations. This effect is due to the rapidity of the reactive collisions that do not allow the system to equilibrate. For this regime, none of the perturbation solutions obtained by the Chapman-Enskog procedure were valid. This study thus shows the importance of non-equilibrium effects in thermal ignition problems, for most temperatures of practical interest.
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