Bubble Bursting: Universal Cavity and Jet Profiles.

After a bubble bursts at a liquid surface, the collapse of the cavity generates capillary waves, which focus on the axis of symmetry to produce a jet. The cavity and jet dynamics are primarily controlled by a nondimensional number that compares capillary inertia and viscous forces, i.e., the Laplace number La=ργR_{0}/μ^{2}, where ρ, μ, γ, and R_{0} are the liquid density, viscosity, interfacial tension, and the initial bubble radius, respectively. In this Letter, we show that the time-dependent profiles of cavity collapse (t<t_{0}) and jet formation (t>t_{0}) both obey a |t-t_{0}|^{2/3} inviscid scaling, which results from a balance between surface tension and inertia forces. Moreover, we present a scaling law, valid above a critical Laplace number, which reconciles the time-dependent scaling with the recent scaling theory that links the Laplace number to the final jet velocity and ejected droplet size. This leads to a self-similar formula which describes the history of the jetting process, from cavity collapse to droplet formation.