A Ball Breaking Away from a Fluid

TL;DR

This study investigates the process and timing of fluid detachment from a ball withdrawn from a reservoir at various Reynolds numbers, revealing different pinch-off mechanisms and the influence of fluid coating and inertial effects.

Contribution

The paper introduces a scaling analysis linking fluid film drainage and coating mechanisms to pinch-off times during ball withdrawal at intermediate Reynolds numbers.

Findings

Pinch-off occurs near the surface at low Reynolds numbers and near the ball at higher Reynolds numbers.

Fluid coating mechanisms include surface tension wetting, quick visco-inertial coating, and inertial effects.

Pinch-off is viscosity-controlled, while coating is governed by inertial added mass.

Abstract

We consider the withdrawal of a ball from a fluid reservoir to understand the longevity of the connection between that ball and the fluid it breaks away from, at intermediate Reynolds numbers. Scaling arguments based on the processes observed as the ball interacts with the fluid surface were applied to the `pinch-off time', when the ball breaks its connection with the fluid from which it has been withdrawn, measured experimentally. At the lowest Reynolds numbers tested, pinch-off occurs in a `surface seal' close to the reservoir surface, where at larger Reynolds numbers pinch-off occurs in an `ejecta seal' close to the ball. Our scaling analysis shows that the connection between ball and fluid is controlled by the fluid film draining from the ball as it continues to be winched away from the fluid reservoir. The draining flow itself depends on the amount of fluid coating the ball on exit from the reservoir. We consider the possibilities that this coating was created through: a surface tension driven Landau Levitch Derjaguin wetting of the surface; a visco-inertial quick coating; or alternatively through the inertia of the fluid moving with the ball through the reservoir. We show that although the pinch-off mechanism is controlled by viscosity, the coating mechanism is governed by a different length and timescale, dictated by the inertial added mass of the ball when submersed.