Oscillations in a combustible gas bubble

The dynamical behaviour of an isolated combustible gas bubble surrounded by unlimited inviscid liquid is analysed in the case of large activation energy and using spatially uniform assumptions. The pressure effect is crucial in this problem because of the limited gas volume. The mathematical model used is a system of three nonlinear ordinary differential equations including the energy equation, the concentration equation and the Rayleigh equation. The thermal behaviour is classified into slow and explosive regimes, and the thermal explosion criterion is obtained analytically, along the lines of the classical Semenov theory. The system is shown to reveal temperature and volumetric oscillations, the amplitude and frequency of which depend strongly on the intensity of the thermal process. In particular, the amplitude of slow and explosive regimes differs by at least an order of magnitude.