Characteristics of jet droplet produced by bubble bursting on the free liquid surface

Abstract

Droplet formation that follows gas bubblebursting at a freeliquidsurface, being known as “entrainment”, is a common phenomenon in many fields. Though there were a couple of investigations focusing on entrainment, specific characteristics of jet drops produced by bubblebursting on freesurface are still unknown in the current stage. Efforts were performed to try to determine the expression of critical bubble size, above which the bubble does not produce any drops by bursting on liquidsurface. Dimensionless analyses show that in air–liquid systems, ReFr−0.5, ReWe−0.5 and WeFr−0.5Re−1 can be readily correlated to Mo. Error analysis demonstrated the following expression: Dcr=100.1914σL0.5517ρL−0.4830g−0.5170μL−0.0688 can give the most accurate prediction of Dcr as a universal expression. Further, for correlating the number of droplets to bubble diameter in air–water and air–iron system, Dcr was used as the length scale to normalize the bubblediameter. Through curve fitting, a universal expression has been obtained to predict the number of dropletsproduced by bubblebursting on freeliquidsurfacein any air–liquid system: Ndr=7.9 exp(−DB/(0.338Dcr))−0.41. Comparison shows that this expression is able to give more accurate prediction than the previous empirical expressions. The most significant innovation is that it is a universal model that can be used in various gas–liquid systems.