Transitions of deformation to bag breakup and bag to bag-stamen breakup for droplets subjected to a continuous gas flow

The transitions of deformation/squeezing breakup to bag breakup and bag to bag-stamen breakup modes for liquid droplets are studied numerically and theoretically. The multiphase flow model is based on the solution of the Navier-Stocks equations and a coupled volume-of-fluid and level-set method. By employing the adaptive mesh refinement technique, the computational cost is significantly reduced. The simulation is validated against published experimental results for the bag breakup and the bag-stamen breakup, which proves that the present model is adequate for capturing qualitatively the breakup processes. The transitions of different modes are investigated at a wide range of Ohnesorge (Oh) numbers (0.001-2). Results indicate that the breakup modes in the bag-type regimes are determined by the ratio of the cross-stream diameter of the flattened droplet to the wavelength of the most unstable Rayleigh-Taylor (RT) wave. The increase of Oh numbers leads to an increasing insensitiveness of the transition behaviors to the Weber (We) number. Furthermore, according to the RT instability, a new theoretical model for predicting transition We numbers is derived in a more reasonable approach. Results further indicate that the present theoretical model could predict the transition behaviors more accurately by comparing with the present numerical results and the experimental data of earlier studies.