Correlations and Asymptotic Behaviors of the Shape Parameters of Floating Bubbles Using an Improved Numerical Procedure

Abstract

An improved numerical procedure is used to present the correlations between the shape parameters and Bond numbers of floating bubbles for a wider range of Bond numbers (5×10−5<Bo<5000) than the previously reported range of Bond numbers (0.003<Bo<241), and their asymptotic relations as Bo → 0 and Bo → ∞. The proposed method is proven to be more precise and robust than the conventional methods in comparison with previous numerical and experimental results. In addition, the profile of floating bubbles and the related parameters are presented for a wide range of bubble sizes. The shape parameters are divided into three distinct Bond number regions, and are fitted with a fifth-order polynomial as a function of Bond number on a log-log scale for each region. The parameters show two asymptotes, which can be expressed in a simple power law. In addition, the dimensionless maximum depth of the floating bubble is obtained as H=0.7291015 when Bo=4.755563. These correlations and asymptotic relations are expected to assist in the development of scale models of dynamic bubble-related phenomena such as bubble bursting.