Autocatalytic continuous reactions in a stirred tank: I. Multiplicity of steady states

Abstract

The multiplicity of steady states in a stirred tank was considered, in which a continuum of autocatalytic reactions of the type A + 2 B → 3 B, B → C is taking place by letting A( x) be the “species” of a continuous mixture. The distribution of A( x) in the feed can be quite general (though it was found to be convenient to do calculations with gamma distributions) and a method is given for determining the region of parameter space coorresponding to qualitatively different behaviors in the case where the overall conversion curve has a single inflection point. As with the single component, there is a region in which there are three steady states, outside of which the steady state is unique. It was found that the size of the region of multiplicity only slightly as the variance of the feed distribution increases.