2003
DOI: 10.1103/physreve.68.036210
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Isothermal flame balls: Effect of autocatalyst decay

Abstract: The steady, spherically symmetric solutions to the reaction-diffusion equations based on a simple autocatalytic reaction followed by the decay of the autocatalyst are considered. Three parameters-the orders with respect to the autocatalyst in the autocatalysis p and in the decay q and the rate of decay of the autocatalyst relative to its autocatalytic production K-determine the steady concentration profiles. Numerical integrations for a fixed value of the order of the autocatalyst show that the concentration p… Show more

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Cited by 7 publications
(6 citation statements)
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“…analogous to (16). Since, with k > 0, the wave speed is less than in the purely autocatalytic system (for which c 2 0 = 2D 2 [10,11]), we can expect T 1 to be negative.…”
Section: Q ∼ Pmentioning
confidence: 93%
See 1 more Smart Citation
“…analogous to (16). Since, with k > 0, the wave speed is less than in the purely autocatalytic system (for which c 2 0 = 2D 2 [10,11]), we can expect T 1 to be negative.…”
Section: Q ∼ Pmentioning
confidence: 93%
“…Asymptotics based on high powers of autocatalysis have been used with some success in understanding the structure of isothermal 'flame balls' (steady reaction-diffusion structures governed by autocatalytic reactions) [15,16] and in estimating the conditions where planar reaction fronts can become longitudinally unstable [11]. Finally, we note that the cases when p, q < 1 are qualitatively different to those referenced above and treated here.…”
Section: Introductionmentioning
confidence: 93%
“…In the absence of buoyancy-driven flow, spherical autocatalytic reaction fronts have previously been studied both theoretically and numerically. These studies have focused on the existence and stability of spherically symmetric solutions of the reactiondiffusion equations [30,31], and on the effect of autocatalyst decay [32]. Threshold conditions needed to form spherical autocatalytic reaction fronts have also been calculated for both quadratic and cubic autocatalytic reaction fronts [33].…”
Section: Autocatalytic Ballsmentioning
confidence: 99%
“…It has been suggested (see [17][18][19]33]) that the dynamics of (1.2) is bistable, with two stable non-negative steady-state solutions (one of them is the trivial solution (u 1 , u 2 ) = (0, 0)), and that there exists a threshold set in the phase space separating the basins of attraction of the two stable steady states. Our first result in this paper is to confirm the multiplicity of positive steady-state solutions.…”
Section: Introductionmentioning
confidence: 99%
“…Based on the autocatalytic reaction (1.1), Jakab et al . [17,18] considered the following reactiondiffusion model [18]:…”
Section: Introductionmentioning
confidence: 99%