Bubble bursting jets are driven by the purely inertial collapse of gas cavities

Abstract

The analysis of numerical simulations describing the collapse of capillary cavities reveals that the jets originated from the bursting of bubbles are driven by the condition that the dimensionless liquid flow rate per unit length directed towards the axis of symmetry, $q_\infty$, remains nearly constant in time. This observation, which is justified in physical terms because liquid inertia prevents appreciable changes in $q_\infty$ during the short time scale characterizing the jet ejection process, together with the fact that bubble bursting jets are produced from the bottom of a conical cavity, justify the purely inertial scalings for the jet width and velocity found here, $r_{jet}\propto\sqrt{q_\infty\tau}$ and $v_{jet}\propto \sqrt{q_\infty/\tau}$, with $\tau$ indicating the dimensionless time after the jet is ejected, a result which notably differs from the common belief that the jet width and velocity follow the inertio-capillary scaling $r_{jet}\propto \tau^{2/3}$ and $v_{jet}\propto \tau^{-1/3}$. Our description reproduces the time evolution of the jet width and velocity for over three decades in time, obtaining good agreement with numerical simulations from the instant of jet inception until the jet width is comparable to that of the initial bubble.