Towards a theory of bubble reactor combustion (displacement reactor)

We examine the thermal regime of a displacement reactor in which a monodisperse bubble medium is reacting. We propose a model of the thermal processes taking place in the reactor which differs significantly from the known models of homogeneous single-temperature reactors. Classification of the operating regimes of a reactor is based on the dynamic balance method, which consists of comparing the local values of the combustion wave velocity $u(x)$ computed along the channel length in a quasisteady approximation, with characteristic velocity $u_0$. We determine the regions of steady solutions in the parameter plane and classify the stable and unstable states on the basis of the solution to a system of equations. This system connects the values of the combustion wave propagation velocity, the position of the front in the reactor channel, the initial and final temperatures of the phases, and a measure of the completeness of combustion.