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

Droplet formation that follows gas bubble bursting at a free liquid surface, 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 bubble bursting on free surface 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 liquid surface. Dimensionless analyses show that in air-liquid systems, ReFr(-0.5), ReWe(-0.5) and WeFr(-0.5)Re(-1) can be readily correlated to Mo. Error analysis demonstrated the following expression: D(cr)=10(0.1914) sigma(0.5517)(L)rho(L)-(0.4830-)g(-0.5170)mu(-0.0688)(L) can give the most accurate prediction of D, as a universal expression. Further, for correlating the number of droplets to bubble diameter in air-water and air-iron system, D was used as the length scale to normalize the bubble diameter. Through curve fitting, a universal expression has been obtained to predict the number of droplets produced by bubble bursting on free liquid surface in any air-liquid system: N(dr) = 7.9 exp( -D(B)/(0.338D(cr))) - 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. (C) 2011 Elsevier Ltd. All rights reserved.