On the impulsive generation of drops at the interface of two inviscid fluids

The numerical simulation of the deformation of an inviscid fluid–fluid interface subjected to an axisymmetric impulse in pressure is considered. Using a boundary integral formulation, the interface is evolved for a range of upper-fluid and lower-fluid density ratios under the influence of inertial, interfacial and gravitational forces. The interface is seen to evolve into axisymmetric waves or droplets depending upon the density ratio, level of surface tension and gravity. Moreover, the droplets may be spherical, tear shaped or elongated. These conclusions are expressed in a phase diagram of inverse Weber number We−1 versus Atwood number At at zero gravity, i.e. with the Froude number Fr−1→0, and complement the earlier findings of Tjan & Phillips, who present a phase diagram of We−1 versus Fr−1 for the case in which the upper fluid has zero density. They too report tear-shaped droplets; however, while, in their paper, they form as a result of gravity, those reported here form as a result of surface tension. It is also found that the pinch-off process which effects drops remains of the power-law type with exponent 2/3 irrespective of the presence of gravity and an upper fluid. However, the constant K that relates the necking radius to the time from pinch off, which is universal in the absence of gravity and an upper fluid, is affected by the presence gravity, an upper fluid and the class of drops which form.