Scaling laws of top jet drop size and speed from bubble bursting including gravity and inviscid limit

Jet droplets from bubble bursting are determined by a limited parametrical space: the liquid properties (surface tension σ, viscosity μ, and density ρ), mother bubble size R_o and acceleration of gravity g (i.e. 5 dimensional parameters). A detailed physical description of the ejection process to model both the ejected droplet radius R and its initial launch speed V is provided, leading to a scaling law including both resulting parameters from dimensional analysis: the Ohnesorge and Bond numbers (Oh and Bo). Two limits are identified for Oh: one (Oh₁=0.038) is the critical value above which no droplet ejection takes place, and the other (Oh₂=0.0045) is a new critical value which signals when viscous effects vanish. Gravity effects are consistently introduced from energy conservation principles. The proposed scaling law produces an extraordinary collapse of all published experimental measurements collected for both the ejected droplet radius and ejection speed.