Buoyancy-driven instability of bubbly layers: analogy with thermal convection

Abstract

An analogy has been established between the buoyancy-driven instability of thermal layers (Rayleigh–Benard instability) and bubbly layers (homogeneous–heterogeneous regime transition). On the physical level, the analogy is a simple scaling theory based on a suitable definition of the Rayleigh, Prandtl, and Nusselt numbers for bubbly layers. The analogy yields a stability criterion in terms of the critical voidage. The criterion predicts the destabilizing effect of layer dimensions, both the height and width, and the stabilizing effect of the liquid viscosity and hydrodynamic bubble diffusivity. The predictions are in agreement with available experimental data from water–air bubbly layers. On the formal level, the analogy is based on similarities between the governing equations of thermal and bubbly layers. It is shown, how the equations of bubbly layers can be converted into those of thermal layers, provided that the bubble inertia and slip speed are negligible. The suggested analogy applies generally to dispersed two-phase systems controlled by buoyancy, viscosity, and hydrodynamic diffusion (e.g. sedimentation and fluidization).