Inertial settling of a sphere through an interface. Part 1. From sphere flotation to wake fragmentation

Abstract

Experiments are performed to better understand the characteristics of the flow induced by the gravity-driven settling of a rigid sphere through a two-layer arrangement of immiscible Newtonian fluids, mostly in inertia-controlled regimes. High-speed video imaging is employed to follow the sphere motion and the deformation of the interface separating the two fluids. The viscosity ratio between the lower and upper fluids is varied by four orders of magnitude, making it possible to observe highly contrasting interface patterns. Depending on the properties of the sphere and the fluids, the sphere may either float steadily at the interface or cross it by pulling a column of the upper fluid into the lower one. This column, which may be axisymmetric or three-dimensional depending on the relative magnitude of inertia effects in the upper fluid, generally pinches off at some position located either close to the initial interface or, more frequently, close to the sphere. Its lower part then recedes towards the sphere, forming a drop which remains attached to its top half. However, when inertia effects in the lower fluid are large enough and the upper fluid is not ‘too’ viscous, the tail quickly undergoes a complete fragmentation, giving birth to a large quantity of filaments and droplets. These various interface configurations are qualitatively analysed using the five independent dimensionless parameters characterizing the system, and regime maps based on the most relevant of them are provided. The influence of several of these parameters on four specific features observed in the course of the experiments, namely the pinch-off position, the floating/sinking transition, the volume of the attached drops and the average size of the droplets formed during the fragmentation process, is examined in detail. A simple model providing qualitative or quantitative predictions is established in each case, and its validity and limitations are assessed against experimental observations.