Residual bubble volume formed behind a sphere plunging into liquid bath (meniscus breakdown with finite velocity of sphere penetration)

Abstract

The residual bubble formed from spherical particles plunging into a liquid bath has an important effect on the performance of CaO particles used for the desulfurization of melted iron. Previous work has theoretically estimated the residual bubble volume resulting from quasi-static sphere immersion by applying the energy minimization principle to the gas–liquid interface meniscus at its rupture [Katoh et al., “Residual bubble formed behind a sphere plunging into liquid bath (in Japanese),” Jpn. J. Multiphase Flow 28, 547–553 (2015)]. Here, we propose a method to theoretically estimate the residual bubble volume for sphere penetration with a finite velocity from 0.05 to 30 mm/s into a liquid bath. To do so, the meniscus rupture at the sphere’s critical depth was calculated via a dynamic equation in which the energy gradient along the sphere surface was considered as the driving force to move the triple-phase contact line. The bubble volume was then estimated by calculating the system energy at the meniscus breakpoint and by using the principle of minimum energy. The model results were verified experimentally for a variety of liquids, showing that the proposed model can be used for estimation of the residual bubble volume.