Turbulent plumes with heterogeneous chemical reaction on the surface of small buoyant droplets

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Abstract
A model is developed for a turbulent plume with heterogeneous chemical reaction rising in an unbounded environment. The chemical reaction, which may generate or deplete buoyancy in the plume, occurs at the interface between two phases, a continuous phase and a dispersed one. We study the case in which a buoyant reactant is released at the source and forms the dispersed phase, consisting of very small bubbles, droplets or particles. Once in contact with the ambient fluid, a first-order irreversible reaction takes place at the surface of the, for example, droplets. The behaviour of this plume in a uniform and stratified environment is examined. We show that the dynamics of a pure plume with such heterogeneous reaction is completely determined by the ratio of the environmental buoyancy frequency N and a frequency parameter associated with the chemical reaction, G. The group G is a measure of the ability of the reaction to generate buoyancy in the plume. In a uniform environment, the sign of parameter G fully determines the plume motion. When the reaction generates buoyancy (positive G) the motion is unbounded, whilst when reaction depletes buoyancy (negative G) the plume reaches a level of neutral buoyancy. A relation for this neutral buoyancy level as a function of the initial buoyancy flux of the plume and G is calculated. Our theoretical predictions compared well with experimental results using a plume of calcium carbonate particles descending in an acidic aqueous solution. In a stratified environment, the motion of the plume is always bounded, irrespective of the magnitude of G, and we determine the level of maximum buoyancy flux, as well as those of zero buoyancy and zero momentum as a function of N/G. Finally, our model is applied to study the dynamics of a localized release of carbon dioxide in the ocean.