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

TL;DR

This paper develops scaling laws for the size and speed of jet droplets from bubble bursting, incorporating gravity and viscous effects, and validates them against experimental data.

Contribution

It introduces a comprehensive physical model with new critical Ohnesorge numbers and includes gravity effects, unifying previous observations into a predictive framework.

Findings

Scaling laws accurately collapse experimental data

Identification of two critical Ohnesorge numbers

Gravity effects incorporated via energy conservation

Abstract

Jet droplets from bubble bursting are determined by a limited parametrical space: the liquid properties (surface tension, viscosity, and density), mother bubble size and acceleration of gravity. Thus, the two resulting parameters from dimensional analysis (usually, the Ohnesorge and Bond numbers, Oh and Bo) completely define this phenomenon when both the trapped gas in the bubble and the environment gas have negligible density. A detailed physical description of the ejection process to model both the ejected droplet radius and its initial launch speed is provided, leading to a scaling law including both Oh and Bo. Two critical values of Oh determine two limiting situations: one (Oh$_1$=0.038) is the critical value for which the ejected droplet size is minimum and the ejection speed maximum, and the other (Oh$_2$=0.0045) is a new critical value which signals when viscous effects vanish. Gravity effects (Bo) are consistently introduced from energy conservation principles. The proposed scaling laws produce a remarkable collapse of published experimental measurements collected for both the ejected droplet radius and ejection speed.