Modelling flow-distributed oscillations in the CDIMA reaction

The development of spatial patterns (‘flow distributed oscillations’) in a model representing the chlorine dioxide–iodine–malonic acid (CDIMA) reaction is investigated analytically and numerically. Flow distributed oscillations arise in a plug-flow reactor (PFR) for which the inflow concentrations of the various reacting species are maintained at appropriate constant values. Unlike other situations, the patterning here does not require any difference in diffusion coefficients for the different species. The patterns are, however, closely related to operating conditions for which the same chemical system would show temporal oscillations in a well-stirred batch reactor. As the flow rate through the PFR is varied, the system undergoes a sequence of transitions from absolute to convective instability and subsequently to stationary patterns. The onset of stationary patterns is found to be subcritical, so there is a range of operating conditions for which there is bistability between a stationary pattern and an essentially uniform state. The results indicate that these patterns occur for conditions that should be realisable experimentally and that typical wavelengths of the patterns would be of the order of 0.1 mm.