Reaction-Diffusion Fronts in Heterogeneous Combustion

Heterogeneous flames are modeled in a simplified system where the fuel particles are discrete heat sources embedded in an inert, heat conducting medium. Two asymptotic regimes of flame propagation are found and exhibit differences in both the propagation limits and the front speeds. When the flame thickness is much larger than the characteristic particle spacing, the media containing the sources can be approximated as homogeneous in the reaction zone. In this case, the propagation of the front is defined as being in the continuum regime. In contrast, when the front thickness is on the same scale as that of the heterogeneities, the front propagates in the discrete regime and a solution based on a continuum is no longer valid. Discrete effects arise from the localization of the reaction around the sources. The first contribution of this thesis investigates the effects of discreteness using numerical simulations. These effects result in a limit in the absence of heat losses, a strong dependence of the front speed on the dimensionality of the system and a weak dependence of the front speed on the reaction time of sources. In a system of regularly spaced particles, the limit can be found analytically in one-, two-, and three-dimensional systems and the front exhibits complex dynamics of bifurcations near this limit. Propagation beyond this limit is only possible through concentration fluctuations in a system with randomly distributed particles. Furthermore, the limit can only be defined as a probabilistic quantity reflecting different possible propagation outcomes depending on the presence, or absence, of propagation paths in discrete random systems.;Heterogeneous reaction-diffusion fronts were also studied experimentally in the context of laminar flames propagating in suspensions of iron particulates. Experiments were performed in a reduced-gravity environment on board a parabolic flight aircraft to minimize particle settling and buoyancy-induced convective flows that cause flame disruptions. The experiment consisted of producing a suspension of iron particulates inside a glass tube and initiating a propagating flame at the open-end of the tube. Quenching plate assemblies forming rectangular channels with variable widths were installed inside the tube. Pass and quench events across the channel were used to find the quenching distance. Flame propagation was recorded by a high-speed digital camera and spectral measurements were used to determine the temperature of the condensed-phase emitters in the flame. The objectives of these experiments were threefold. First, experimental measurements of the flame speed and the quenching distance were used to validate a previously developed one-dimensional dust flame model. Second, the particle combustion mode was investigated by varying the transport properties of the gas mixture by changing the balancing gas between helium and argon. It was found that the ratio between the flame speeds measured in helium and argon mixtures for 3 micron-sized particles was smaller compared to the ratios obtained for larger powders. The lower value of the ratio obtained for 3 micron-sized particles was attributed to a combustion controlled by kinetic rates. Flames propagating in mixtures containing particles larger than 7 microns exhibited a larger ratio of the flame speeds in helium and argon, which was associated to the diffusion mode of particle combustion. Lastly, evidence of a transition from a continuum to a discrete propagation regime was observed in experiments by changing the inert component of the gas mixtures from helium to xenon. The flame speeds measured in helium-balanced mixtures exhibited a stronger dependence on the oxygen concentration than flames propagating in xenon mixtures. A stronger dependence of the flame speed on the oxygen concentration is consistent with the continuum regime, whereas a weaker dependence on the oxygen concentration is evidence of the discrete propagation regime.