## Abstract

A RECENT communication on the generation of spatial waves by the Zhabotinskii reaction^{1}, although reporting interesting experimental results, unfortunately propagates a serious error originally perpetrated by Busse^{2}. This implies that periodic variations in space are possible for a simple linear autocatalytic reaction when diffusion of the autocatalytic species is taken into account. The steady state form of the equation in question is Dd^{2}c/dz^{2}+Kac=0 where c is the concentration of autocatalytic species C, and a is the concentration (assumed constant) of another reactant A. The general solution of this equation is c=C _{0}sin(2πz/λ+φ)where C_{0} and φ are arbitrary constants and λ=2π(D/Ka)^{1/2}In both refs. 1 and 2 boundary conditions are ignored; but it is obvious that a sink for C (non-zero gradient) must be postulated at the walls of the container if a steady solution is to be possible, in order to compensate for the autocatalytic production of C within the volume. Otherwise there would be an explosion. In fact equation (2) has long been known as representing the free radical concentration in a chain branching system with heterogeneous wall termination^{3}. Bursian and Sorokin^{3} did not, however, interpret the sinusoidal form of the solution as representing waves of any kind because they realized that the only physically acceptable solution is one which is positive throughout the container, if it is to represent a concentration. Thus equation (2) is a physically acceptable solution only when the container dimension is less than or equal to half a wavelength; otherwise negative concentrations intrude. The sinusoidal solution then simply represents a distributed concentration for the species C and has no connexion with chemical waves at all. The same criticism applies to Rastogi and Yadava^{1} except that they have transformed (incorrectly incidentally) into moving coordinates.

Original language | English |
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Pages (from-to) | 257 |

Number of pages | 1 |

Journal | Nature |

Volume | 242 |

Issue number | 5395 |

DOIs | |

Publication status | Published - 1973 |

Externally published | Yes |