The onset of convection induced by buoyancy during gas diffusion in deep fluids

Abstract

The onset of convection induced by buoyancy caused by interfacial gas diffusion in deep fluids is analysed. It was found, as in heat transfer, that transient convection during mass diffusion is dependent on a Biot number. A transient diffusive Biot number ( Bi D ) was defined such that Bi D =0 and ∞ correspond to constant mass flux (CMF) and fixed surface concentration (FSC) boundaries, which have theoretical critical Rayleigh numbers of 669 and 1100, respectively. Transient Rayleigh numbers were derived for both boundary conditions. Experiments of soluble and sparingly soluble gases diffusing in water were found to agree very well with the theory advanced in this paper for the onset of convection in accordance with CMF and FSC models. The stable diffusion times were also predicted accurately for both gases. They also represent the theoretical time limits for the gas penetration theory, which relies on Fick’s law that assumes no convection. The horizontal dimension of the plunging plumes was also predicted with reasonable accuracy. Monolayer formed by surfactant was found to produce an FSC boundary for a soluble solute and to render the liquid surface rigid and prolonged the onset of convection.