Thermodynamic theory of diffusion−controlled bubble growth or dissolution and experimental examination of the predictions

Abstract

Although the evolution of a bubble in a liquid containing a single dissolved gas has been treated frequently in the past, a prediction of the time−dependent radius of a bubble in a liquid solution containing several dissolved gases, all diffusing simultaneously, has not been given previously. For this multiple solute case, the set of assumptions corresponding to those used in the single−component case leads to a set of undetermined equations so that these assumptions are insufficient to specify the bubble radius as a function of time. Here the assumption of near−equilibrium evolution is extended to include an assumption concerning the local rate of entropy production: it is assumed that the solute concentrations at the boundary of the bubble must be such as to minimize this local rate at each instant of the bubble evolution. This is shown to be sufficient to close the set of governing equations and thereby allow the prediction of the time−dependent bubble radius for the multiple−solute case. This general set of equations is then applied to predict the radius of a bubble dissolving in a water−oxygen−nitrogen solution. The predictions are compared with the results of a set of measurements and it is found that they agree well, thus giving confidence in the validity of the assumptions used in making the theoretical predictions.