Modelling of gas flux through bubbles at the air-water interface

Abstract

A theoretical approach to gas transfer by bubbles created by breaking waves at the air-waterinterface is undertaken. Based on a simple model, this study affords a basic understanding of thephysical mechanisms. The behaviour of a single bubble is examined. Similarities and differencesbetween the formulation of gas fluxes across a “flat” air-water interface and through bubbles areshown. The gas flux through bubbles is not strictly proportional to the solubility and to thedifference of concentrations between the bulk of the water and the surface. Nevertheless, fortrace gases, a linear relationship with this difference of concentrations, increasing with solubilityis predicted. Overpressure in the bubbles and dissolution favour invasion into the water andimply a water supersaturation at equilibrium. This supersaturation is more important when thegas solubility is low. The r61e of surfactants is studied and it is found that they can reduce the gasexchange by a factor of 5. The consequences of the model for the transfer velocity are brieflypresented. A better definition of the bubble lifetime, i.e., a better representation of waterdynamics under a breaking wave, is necessary to make more reliable model predictions, mostimportantly for gases with low solubility. Theoretical studies on the bubble source are necessaryin order to avoid, as far as possible, the use of the bubble distribution.