Turbulent two-phase plumes with bubble-size reduction owing to dissolution or chemical reaction

Abstract

Abstract Turbulent two-phase plumes consisting of a continuous phase of entrained fluid and a dispersed phase, in the form of buoyant droplets/bubbles, are investigated. Chemical reaction or dissolution causes both a decrease in the size of the droplets/bubbles and a change in the buoyancy of the plume. The behaviours of such a plume in environments with uniform and stratified density are considered. We show that the dynamics of the plume are determined by two dimensionless groups: $N/ T$ and $G/ T$ . Here, $N$ is the buoyancy frequency of the environment, $G$ measures the ability of the reaction to change buoyancy and $T$ reflects the effect of reaction on the size of the droplets/bubbles. We identify four regimes of behaviour of a plume in a stratified environment depending on whether the dominant effect on buoyancy arises from reaction or stratification, and on the occurrence of either multiple or single zero-buoyancy levels. For a uniform environment, perturbation solutions for the fluxes of volume, momentum, buoyancy and chemical species as a function of ascent distance are obtained. We apply our findings to understand the dynamics of both of the cases of a release of methane and a release of carbon dioxide in the ocean. For a methane release in the Gulf of Mexico, the motion of the plume is shown to be controlled by external density stratification for a bubble diameter of methane above ${\sim }1$ –2 mm. In the case of a carbon dioxide release in the Norwegian Sea, dissolution determines the motion of the plume when the bubble diameter is smaller than ${\sim }0. 5$ –3.5 cm. In both scenarios, the plume releases seawater enriched with the chemical at multiple levels.