On the physics of transient ejection from bubble bursting

Alfonso M Gañán-Calvo,José M López-Herrera

doi:10.1017/jfm.2021.791

Abstract

Using a dynamical scaling analysis of the flow variables and their evolution due to bubble bursting, here we predict the size and speed of ejected droplets for the whole range of experimental Ohnesorge and Bond numbers where ejection occurs. The transient ejection, which requires the backfire of a vortex ring inside the liquid to preserve physical symmetry, shows a delicate balance between inertia, surface tension and viscous forces around a critical Ohnesorge number, akin to an apparent singularity. Like in other natural phenomena, this balance makes the process extremely sensitive to initial conditions. Our model generalizes or displaces other recently proposed ones, impacting on, for instance, the statistical description of sea spray.

Highlights

Everyday experience teaches that radially convergent flows close to a liquid surface produce vigorous transient liquid ejections in the form of a jet perpendicular to the surface, as those seen after bubble bursting (Kientzler et al 1954), droplet impact on a liquid pool (Yarin 2006) or cavity collapse (Ismail et al 2018)
A set of relations among the radial and axial characteristic lengths and velocities was formulated in Gañán-Calvo (2017, 2018) on the basis that inertia, surface tension and viscous forces should be comparable very close to the instant of collapse of the free surface
The radial scale of that pilot spout, comparable to that of the front of the stream tube responsible for the ejection feed, should be μ, which is the natural spatial scale selected when inertial, viscous and surface tension forces dominate locally (Eggers 1993). All this is confirmed by our numerical simulations, where we use a spatial precision an order of magnitude smaller than μ to adequately resolve the finest details of the ejection

Summary

Introduction

Everyday experience teaches that radially convergent flows close to a liquid surface produce vigorous transient liquid ejections in the form of a jet perpendicular to the surface, as those seen after bubble bursting (Kientzler et al 1954), droplet impact on a liquid pool (Yarin 2006) or cavity collapse (Ismail et al 2018). Assuming that those time self-similarities exist, our focus is here to obtain closed relationships among those scales and to predict the size and speed of ejections reflected by the eventual values of R and V at the end of the process This approach, though, demands the identification of the key symmetries appearing in the problem that may lead to an effective problem closure (Gañán-Calvo, Rebollo-Muñoz & Montanero 2013). To this end, a set of relations among the radial and axial characteristic lengths and velocities was formulated in Gañán-Calvo (2017, 2018) on the basis that inertia, surface tension and viscous forces should be comparable very close to the instant of collapse of the free surface.

Energy balance

Final energy balance including viscous dissipation

Problem closure

Experimental verification

Findings

Concluding statements