The influence of the form of autocatalysis on the speed of chemical waves

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Abstract
When a travelling wave of chemical reaction is supported by isothermal autocatalysis, the speed of the wave depends on the way in which reaction rate depends on concentration as well as on the maximum rate attainable, For systems with quadratic and cubic autocatalytic processes mixed in the ratio ν : (1 - ν ), the wave speed c is given by c = 1 / [ 2 ( 1 − υ ) ] 1 2 , for 0 ⩽ υ ⩽ 1 2 , c = ( 2 υ ) 1 2 , for 1 2 ⩽ υ ⩽ 1 , with a smooth change between these solutions at ν = 1 2 , c = 1. Thus, there is a factor of 2 in the wave speed in going from pure cubic ( ν = 0) to pure quadratic ( ν = 1). The selection of the permanent form travelling wave is discussed in terms of the phase plane.