67 research outputs found
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
Self-similarity in Laplacian Growth
We consider Laplacian Growth of self-similar domains in different geometries.
Self-similarity determines the analytic structure of the Schwarz function of
the moving boundary. The knowledge of this analytic structure allows us to
derive the integral equation for the conformal map. It is shown that solutions
to the integral equation obey also a second order differential equation which
is the one dimensional Schroedinger equation with the sinh inverse square
potential. The solutions, which are expressed through the Gauss hypergeometric
function, characterize the geometry of self-similar patterns in a wedge. We
also find the potential for the Coulomb gas representation of the self-similar
Laplacian growth in a wedge and calculate the corresponding free energy.Comment: 16 pages, 9 figure
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
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