Instability of aerosol boundary accelerated in a direction perpendicular to its plane

Abstract

Theory of Rayleigh–Taylor instability (RTI) is extended for the case of a dilute aerosol system. Equations of interpenetrating continua are investigated on stability to small perturbations by the method of normal modes. In contrast with homogeneous, equations of two-phase, two-velocity medium possess three types of disturbances: an entropy-vorticity one along with two acoustic ones. The difference in the amplitude constant signs of these types is able to affect the disturbance shape and phase convection inside mixing layer. The acoustic branch of solution is responsible for mechanism of instability, while the entropy-vorticity one determines damping mechanism. Instability of a plane accelerating surface, which separates aerosol and homogeneous incompressible fluid, is then investigated. Dispersion relation of the boundary-value problem for perturbations has two aperiodic unstable roots; one of them coincides with the classic R–T root in the particle absence limit, another is able to compete with only at huge accelerations. Instability is governed by modified Shields and Atwood numbers. As applications, systems with different aerosol densities are considered: atmospheric dust, mist around atomizing drop and explosively dispersed powder. Conclusion is done that a suspension somewhat destabilizes the system at small particle volume concentrations, while at a denser content it has essential damping influence on RTI.