Thermal ignition revisited with two-dimensional molecular dynamics: Role of fluctuations in activated collisions

Abstract

The problem of thermal ignition in a homogeneous gas is revisited from a molecular dynamics perspective. A two-dimensional model is adopted, which assumes reactive disks of type A and B in a fixed domain that react to form type C products if an activation threshold for impact is surpassed. Such a reaction liberates kinetic energy to the product particles, representative of the heat release. The results for the ignition delay are compared with those obtained from the continuum description with the reaction rate evaluated from kinetic theory assuming local thermodynamic equilibrium and Maxwell-Boltzmann statistics, in order to assess the role played by molecular fluctuations. Ignition times obtained using molecular dynamics are ensemble averaged over 100 simulations to address the statistics of the ignition event. Results show two regimes of non-equilibrium ignition whereby ignition occurs at different times as compared to that for homogeneous ignition assuming local equilibrium. The first regime is at low activation energies, where the ignition time is found to be higher than that expected from theory for all values of heat release. The lower reaction rate is shown to occur due to a departure from local equilibrium for the different species, in agreement with predictions from Prigogine and Xhrouet. In this low activation energy regime, the ignition times from molecular dynamics are also found to be independent of domain size and there is little variance between different realizations under similar conditions, which suggests that the ignition is spa-Email addresses: nsirmas@uottawa.ca (N. Sirmas), matei@uottawa.ca (M. I. Radulescu)

Non-equilibrium effects on thermal ignition using hard sphere molecular dynamics

“…These do not have enough time to equilibrate with the rest of the system, thus giving rise to what we would like to call molecular hotspots. This result is also in accordance with the previous numerical results by Sirmas and Radulescu in the two-dimensional system [22]. In this regime of ignition, where non-equilibrium effects significantly promote ignition, we also observe a much higher stochasticity of ignition, as shown in Fig.…”

“…In our previous study, we compared the results only with reaction rate assuming homogenous ignition [22]. Whereas, in the present work along with the equilibrium reaction rate, we compared our results with the existing kinetic theory models which takes into account the effect of heat of reaction while calculating the reaction rate.…”

“…Recently, more relevant to the present study, Sirmas et al have investigated the role of nonequilibrium effects in the problem of thermal ignition in a model system characterized by a single binary reaction by molecular dynamics in two-dimensions [22]. They have identified large departures from the equilibrium prediction at both low and high activation energies.…”

“…However, the simplifications used unambiguously identify various mechanisms for departures from the predictions using the macroscopic models based on local equilibrium. Figure 1: Schematic of interactions between particles A and B before impact (left), during impact (center) and after impact (right) along the line of action [22]…”

Acceleration of laminar hydrogen/oxygen flames in a tube and the possible onset of detonation

“…(19). This value is determined less by In a detonation, reaction might decouple from the shock and it has been found that the coherence and stability of a detonation are enhanced by low values of [67][68][69]. To this product can be added [2], the dimensionless gradient at a hot spot, and it follows that:…”