Effect of self-sustained oscillations on critical fluctuations

Abstract

As is known [1, 2], the space of the parameters of an exothermic flow reactor includes a bistability region, where either a low- or high-temperature stationary regime is realized, depending on the initial conditions. The boundary of this region has a cusp, where the difference between regimes disappears. The properties of the cusp are similar to those of a critical point on the phase diagram of a substance with the first-order phase transition between the phases with the same symmetry [3]. In particular, it is the endpoint of the equilibrium line between a liquid and vapor (boiling curve) on the pressure‐temperature plane, where the bistability domain is bounded by a spinodal. Fluctuations of the reaction rate must be large near the cusp [4] the same as density fluctuations increase near the critical point. At the same time, this similarity is not universal: the stationary regimes of a reactor lose stability for certain parameter values and become periodic [5‐7]. In [4], an increase in fluctuations was calculated in the linear approximation and disregarding the oscillation mode. In this work, critical fluctuations are analyzed by numerical simulation for the conditions when they cannot be treated as small, as well as upon the transition from the stationary regime to the periodic one at the cusp. 1. The reactor state is determined by three parameters [8] such as the Damkohler number D , which is the ratio of the substance residence time in the reactor to the characteristic reaction time τ R ; the Semenov number, which is the ratio of the heat-exchange time of the reactor with the environment to τ R ; and the Zel’dovich number