Modeling the cycles of growth and detachment of bubbles in carbonated beverages.

In this paper, a model for the formation of bubbles in carbonated beverages is presented. It has previously been shown that bubbles form from cellulose fibers within such beverages and the passage of such bubbles from the fibers to the liquid surface has been modeled. A model is thus presented here that considers the process of formation, which is governed by diffusion through the fiber and bubble surfaces. The model comprises two stages, growth and detachment, and it is shown here that both play an important role. The latter process is found to occur over a much shorter time scale than the former, enabling the models to be partially decoupled. The total number of bubbles released from individual fibers over time is found to be approximated well by an exponential relationship, and the parameters in this relationship are presented for a range of different detachment angles and fiber sizes. It is found that bubble formation is promoted in narrow, long tubes, but that the time constant is solely determined by the rate of diffusion across the liquid surface. The surface tension is found to have minimal influence on the number of bubbles produced.