Detachment Criterion for Static Axisymmetric Bubbles on Horizontal Flat Surfaces

The static Young-Laplace equation is solved with the geometry method to yield the bubble shape on a horizontal flat surface under various contact angles. Multi-solution modes are found. Among the many possible equilibrium shapes of the bubble, however, only the fundamental solution mode could occur naturally. The value of VAR (volume to contact area ratio) could be a good measure for stability of equilibrium bubbles. The bubble becomes less stable when VAR increases. The numerical result reveals that in the course of bubble growth (i.e. volume increases) the VAR of the bubble increases linearly until the maximum contact area is reached. After that, VAR has a sharp increase due to a decreasing contact area. Beyond the maximum volume, equilibrium bubble does not seem possible. Based on the finding, it is postulated that bubble detachment occurs somewhere between the maximum contact area and the maximum volume according to perturbations from environment. However, the postulation seems to underestimate the stability of the bubble significantly for contact angles of larger than 160 degrees. A correction is proposed in the paper. Numerical result of bubble detachment criterion is fitted with polynomial functions of the contact angle.