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The dynamics of flame propagation in systems with infinite Lewis number andspatially discretized sources of heat release is examined, which is applicableto the combustion of suspensions of fuel particles in air. The system isanalyzed numerically using a one-dimensional heat equation with a source termfor the reaction progress variable, which is specified to have zerodiffusivity, and the model reveals a spectrum of flame-propagation regimes. Forthe case of a switch-type reaction rate and homogeneous media (continuousregime), the flame propagates steadily at a velocity in agreement withanalytical solutions. As the sources are spatially concentrated into{\delta}-function-like sources, propagation approaches the discrete regime witha fixed period between ignition of the sources, for which an analytic solutionis also available for validation. When the source term is governed by anArrhenius rate and the activation energy is increased beyond the stabilityboundary, the flame begins to exhibit a long-wavelength (4-5 times the thermalflame thickness) oscillation characteristic of the thermo-diffusiveinstability, in good agreement with prior stability analysis. When spatialdiscreteness is introduced, a competition is observed between the long-periodoscillations of the thermo-diffusive instability and the pulsations associatedwith the rapid heat release of the concentrated sources. Interestingly, thepresence of spatial discreteness is able to excite higher modes (perioddoubling and chaotic solutions) of the thermo-diffusive instability, suggestingthat the introduction of discreteness may have an influence qualitativelysimilar to that of increasing activation energy. Relevance of the modelparameters to experimental systems is then discussed.

The Influence of Spatial Discreteness on the Thermo-Diffusive Instability of Flame Propagation with Infinite Lewis Number