Bursting jet in two tandem bubbles at the free surface

Numerical simulations of the bubble-bursting phenomenon in two tandem bubbles at the free surface are conducted to explore the influence of a following bubble behind the bursting bubble on the jet ejection at fixed Bo = 0.05 and Oh = 0.022. The equivalent radius of the bursting bubble (R_B) is fixed, and the configuration of two tandem bubbles is varied systematically by changing the equivalent radius of the following bubble (R_F) and the gap distance between the two bubbles (L). An increase in the bubble–bubble interactive force (repulsive force) is observed with a decrease in L or an increase in R_F. As the repulsive force increases, the velocity of the primary capillary wave (PCW) increases due to the reduced wavelength of the PCW, thus increasing the bursting jet velocity. However, when the repulsive force is sufficiently large, the curvature of the PCW near the bottom of the bursting bubble is reversed, causing a new secondary capillary wave to be generated. An increase in the secondary capillary wavelength with an increase in the force disturbs the self-similar behavior of the interface of the bursting bubble, resulting in a decrease in the bursting jet velocity. In order to scale the bursting jet velocity using R_F and L in cases where PCWs are important to induce a bursting jet, a scaling law is formulated by defining the scaling variable φ in terms of R_F and L. The proposed scaling law is found to be capable of providing accurate predictions of capillary numbers as a function of φ.