Effect of startup conditions on drop breakup under shear with inertia

A spherical drop is suspended in another liquid and sheared between parallel walls. Numerical simulations for drop deformation under simple shear typically begin with the drop placed in an established flow. For Stokes flow, the drop evolves in a mono-tone manner to a stationary state or to breakup. Experimental and numerical studies of this result in a critical curve which delineates the capillary number for breakup at each viscosity ratio. With inertia, however, the history depends on the initial condition. Direct numerical simulations are performed to examine the effect of in-ertia through the influence of initial data on critical conditions. An abrupt startup induces drop oscillations which are sufficiently large to lead to breakup, while a gentle startup can allow the drop to reach a stationary state. An oscillator model is developed for the manner in which momentum is transferred to the drop and how it is distributed into surface deformation and dissipation as a function of the Reynolds number and capillary number