Deformation and Breakup of an Axisymmetric Falling Drop under Constant Body Force

Abstract

The secondary breakup of liquid drops, accelerated by a constant body force, is examined for small density differences between the drops and the surrounding fluid. a density ratio of ten has been studied. We used Volume of Fluid (VOF) method to simulate the breakup. The breakup is controlled by the Eotvos number (Eo), the Ohnesorge number (Oh), and the viscosity and density ratios. If viscous effects are small (small Oh), the Eotvos number is the main controlling parameter. At a density ratio of ten, as Eo increases the drops break up in a backward facing bag, transient breakup, and a shear breakup mode. Similar breakup modes have been seen experimentally for much larger density ratios. Although a backward facing bag is seen at low Oh, where viscous effects are small, comparisons with simulations of inviscid flows show that the bag breakup is a viscous phenomenon, due to boundary layer separation and the formation of a wake. At higher Oh, where viscous effects modify the evolution, the simulations show that the main effect of increasing Oh is to move the boundary between the different breakup modes to higher Eo. The results are summarized by “breakup maps” where the different breakup modes are shown in the Eo–Oh plane for different values of the viscosity and the density ratios.