Fingering Instability in Combustion

A thin solid (e.g., paper), burning against an oxidizing wind, develops a fingering instability with two decoupled length scales. The spacing between fingers is determined by the P\'eclet number (ratio between advection and diffusion). The finger width is determined by the degree two dimensionality. Dense fingers develop by recurrent tip splitting. The effect is observed when vertical mass transport (due to gravity) is suppressed. The experimental results quantitatively verify a model based on diffusion limited transport

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.Comment: 6 pages, 5 figure

Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.Comment: Standard LaTeX, no figures, 29 pages; (to appear in J. Stat. Phys. vol.81, 1995). Complete file available at http://www.physics.helsinki.fi/tft/tft.html or anonymous ftp at ftp://rock.helsinki.fi/pub/preprints/tft

Toward the Control of the Smoldering Front in the Reaction-Trailing Mode in Oil Shale Semicoke Porous Media

Results of an experimental investigation on the feasibility of propagating a smoldering front in reaction-trailing mode throughout an oil shale semicoke porous medium are reported. For oil recovery applications, this mode is particularly interesting to avoid low-temperature oxidation reactions, which appear simultaneously with organic matter devolatilization in the reaction-leading mode and are responsible for oxidation of part of the heavy oil. The particularity of this mode is that, contrary to the reaction-leading mode largely studied in the literature, the heat-transfer layer precedes the combustion layer. This leads to two separated high-temperature zones: (i) a devolatilization zone (free of oxygen), where the organic matter is thermally decomposed to incondensable gases, heavy oil, andfixed carbon, also called coke in the literature, without any oxidation, followed by (ii) an oxidation zone, where thefixed carbon left by devolatilization is oxidized. The transition from reaction-leading to reaction-trailing mode was obtained using low oxygen contents in the fed air. It is shown that two distinct layers, the heat-transfer layer and the combustion layer, propagate in a stable and repeatable way. The decrease of the oxygen fraction leads to a decrease of the smoldering temperature and to strongly limit the decarbonation of the mineral matrix. The CO2 emissions are limited. Regardless of the front temperature, all of the fed oxygen is consumed and all of thefixed carbon is oxidized at the passage of the smoldering front