Interactions of the interface of immiscible liquids with an impinging vortex ring

Abstract

The dynamic behaviors of an interface between two immiscible fluids, which are deformed by a vortex ring impinging normally onto the interface, are experimentally investigated. By varying the strength and size of the vortex ring generated by a piston-cylinder apparatus, several deformation modes of the immiscible interface are identified based on the deforming and rebounding processes and instability of the interface. At a given penetration depth, the profiles of the interfacial deformation shaped as ellipsoidal caps exhibit similarity even for different deformation modes. Geometric quantities that represent the interfacial deformation, such as the maximum penetration depth during the deforming phase and the maximum elevation during the rebounding phase, are closely related to the Froude number. However, the Froude-number range for each deformation mode and the interface profiles at a given Froude number differ by the Bond number because surface tension effects are not negligible in the scale of our model. An empirical dimensionless parameter, which combines the Froude and Bond numbers, is introduced to account for the effects of fluid inertia, gravitation, and surface tension together and is used to quantitatively characterize the interfacial deformation. Moreover, the boundaries between the deformation modes are clearly identified by the new parameter, while they are barely changed by the ratio of piston stroke length to cylinder diameter.