Isothermal flame balls.
The existence of steady, spherically symmetric wave fronts ("isothermal flame balls") in chemical reaction systems exhibiting autocatalysis is demonstrated. Such solutions require relatively high kinetic orders p with respect to the autocatalytic species, with p>5, but occur even with equal diffusion coefficients. The flame balls are unstable, but have relevance as they indicate the minimum size for a perturbation to initiate a propagating front. A flame ball radius R(b) is identified and the dependence of this quantity on the autocatalytic order is determined. This shows R(b) tending to infinity as p-->5(+) and as p--> infinity, with a minimum for p approximately 6.71. Numerical computations are confirmed by asymptotic analysis appropriate for p-->5(+) and for systems with p large.
Jakab
Eva
E
Department of Physical Chemistry, University of Szeged, P.O. Box 105, Szeged H-6701, Hungary.
Horváth
Dezso
D
Merkin
John H
JH
Scott
Stephen K
SK
Simon
Péter L
PL
Tóth
Agota
A