Secondary breakup of axisymmetric liquid drops. II. Impulsive acceleration

Abstract

The secondary breakup of impulsively accelerated liquid drops is examined for small density differences between the drops and the ambient fluid. Two cases are examined in detail: a density ratio close to unity and a density ratio of 10. A finite difference/front tracking numerical technique is used to solve the unsteady axisymmetric Navier–Stokes equations for both the drops and the ambient fluid. The breakup is governed by the Weber number, the Reynolds number, the viscosity ratio, and the density ratio. The results show that Weber number effects are dominant. In the higher density ratio case, ρd/ρo=10, different breakup modes—oscillatory deformation, backward-facing bag mode, and forward-facing bag mode—are seen as the Weber number increases. The forward-facing bag mode observed at high Weber numbers is an essentially inviscid phenomenon, as confirmed by comparisons with inviscid flow simulations. At the lower density ratio, ρd/ρo=1.15, the backward-facing bag mode is absent. The deformation rate also becomes larger as the Weber number increases. The Reynolds number has a secondary effect, changing the critical Weber numbers for the transitions between breakup modes. The increase of the drop viscosity reduces the drop deformation. The results are summarized by “breakup maps” where the different breakup modes are shown in the We–Re plane for different values of the density ratios.