Zero Dimensional Model for the Growth of Heterogeneous Gas Bubbles Available to Purchase

A zero dimensional energy based model for heterogeneous gas bubble growth from conical surface pits is presented. The spherical cap bubble growth is divided into 3 stages. In the first stage, the bubble is within the surface pit. In the second stage, the bubble is anchored to the circular opening of the surface cavity and the apparent bubble contact angle decreases while the bubble's contact radius remains the same. The third growth stage starts when the apparent contact angle becomes the same as the contact angle under the ambient conditions. In the third growth stage, the contact radius increases while the contact angle remains constant. The predicted bubble radius versus time since the detachment of the previous bubble was found to be in good agreement with published experimental data for CO₂ bubbles growing in water. The long wait time observed in the experiments before a measurable bubble appears after the detachment of the previous bubble was also calculated.