Isothermal Autocatalysis in Open Systems (CSTR): Simple Models and Complex Behaviour

Abstract

Autocatalysis lies at the heart of all isothermal oscillatory systems. When the catalyst is not completely stable but undergoes decay [1–5], particularly varied behaviour is possible even in the simplest of open systems — the cstr operating isothermally. The kinetics may be represented by the scheme

$$ quadratic\quad A + B \to 2B\quad rate = {k_1}ab $$

(1a)

$$ cubic\quad \quad A + 2B \to 3B\quad rate = {k_1}a{b^2} $$

(1b)

$$ B \to C\quad rate = {k_2}b $$

(2)

Cubic autocatalysis with catalyst decay can give rise to strange patterns of stationary states and to sustained oscillations. (This is also true of enlarged schemes [6J incorporating the reverse steps and the uncatalyzed reaction although the algebra is heavier.) Today we are mainly concerned with the birth, growth and extinction of stable oscillations and to the response of the system to continuous changes in residence time.