Dynamics of a single bubble in a liquid in the presence of chemical reactions and interphase heat and mass exchange

Abstract

As is known [1, 2], detonation of bubble media can be related to heat-and mass-transfer processes, whose rate increase markedly with development of instability of the bubble surface, which leads to formation of microdrops in them [3]. Evaporation of microdrops has a significant effect on the gas-phase chemical reaction in the bubble. Moreover, in a system where the fuel and oxidizer are in different phases [1], formation of a detonation wave is impossible without interphase heat and mass exchange, which leads to formation of a chemically reactive mixture." The detonation regime of the reactions in bubbles was studied in [4].In the present work, as the first stage in the development of an adequate model for bubble detonation in such media, we consider the influence of inert and chemically reactive additives in the active gas mixture of a bubble on bubble dynamics and explosive process, and reaction propagation during formation of the mixture.The dependences of the parameters of a single bubble on the time of injection tinj, the initial dimensions of microdrops Do, and the mass of evaporated liquid Mr~ are analyzed in the case of instantaneous evaporation of microdrops and with allowance for evaporation dynamics.Bubble dynamics is described by the Rayleigh equation under the assumption that the bubble retains its spherical shape, and the gas is ideal: 3 i ~fl" + 5 ~ = P -P~o.Here ~ = R/Ro is the dimensionless radius of the bubble, fl~ and/~" are the derivatives of fl with respect to dimensionless time r = (~L/Ro)t (PL is the liquid density and t is time), R and R0 are the current the and initial radii of the bubble, P~o is the external pressure referred to the initial pressure/9o, and P is given by the following relation, which takes into account losses in acoustic radiation of the bubble: