Effect of small-amplitude periodic parameter variation in thermokinetic systems

Abstract

The stability of a non-oscillatory, purely thermal explosive system to small periodic fluctuations in the ambient temperature has been investigated by analytical methods. It is shown that when the frequency of the imposed oscillations is high compared with the intrinsic relaxation rate of the system, the external fluctuations do not become magnified. The converse is true for low-frequency fluctuations. Next, the stability of a thermokinetic self-oscillator exercising stable limit cycles in the vicinity of a region of marginal stability is investigated by computational means. At frequencies of external perturbations far removed from the natural frequencies of the self-oscillator, the results are analogous to the non-oscillatory case. However, in the intermediate range of frequencies of the imposed oscillations, resonance phenomena occur and the system jumps to a different steady state in an apparently unpredictable manner, although the amplitude of the external oscillations is quite small (0.5 K). The experimentally observed interspersion of repeated ignitions with cool flames in the oxidation of acetaldehyde in a flow reactor is discussed in the light of the present theoretical results. It is suggested that deliberate variation of the frequencies of fluctuations of external parameters in self-oscillating chemical systems may be a profitable way of investigating the origin of complex oscillatory patterns and the so-called ‘chaotic’ behaviour.