A mathematical approach for oxygenation using micro bubbles: Application to the micro-oxygenation of wine

This work is the logical following of our previous work [Devatine, A., Chiciuc, I., Poupot, C., Mietton-Peuchot, M., 2007. Micro-oxygenation of wine in presence of dissolved carbon dioxide. Chemical Engineering Science 62, 4579–4588] about micro-oxygenation of wine, where, when dissolved carbon dioxide was present in the liquid phase, a surprising decrease in the value of the apparent kLa was pointed out. Only qualitative explanation was given, and no modelling was proposed. Here, we attempted to fill this gap, using very simple equations. Especially, the rising bubble velocity was assumed to follow the Stokes law, and no interaction between rising bubbles was considered. By making the necessary simplifications, analytical solutions to the set of equations are proposed and simple-to-use expressions for the oxygen transfer yield are established. From them, importance of the ratio “column height” to “diffuser pore diameter” is clearly seen. Comparison with our previous experimental results is also done and validates the prominent role of the “dilution effect” inside the bubble in respect to the observed decrease in the apparent kLa.