A Floating Cylinder on An Unbounded Bath

TL;DR

This paper analyzes the equilibrium and stability of a floating cylinder on an unbounded fluid surface, extending previous models by establishing energy-force relations and addressing interface intersection issues.

Contribution

It introduces a modified approach to relate energy and force, studies equilibrium configurations, and clarifies stability conditions for floating cylinders.

Findings

Maximum two equilibrium points for any contact angle.

Stable equilibrium corresponds to smaller wetting angle.

Unstable equilibrium may involve intersecting fluid interfaces.

Abstract

In this paper, we reconsider a circular cylinder horizontally floating on an unbounded reservoir in a gravitational field directed downwards, which was studied by Bhatnargar and Finn in 2006. We follow their approach but with some modifications. We establish the relation between the total energy relative to the undisturbed state and the total force. There is a monotone relation between the height of the centre and the wetting angle. We study the number of equilibria, the floating configurations and their stability for all parameter values. We find that the system admits at most two equilibrium points for arbitrary contact angle, the one with smaller wetting angle is stable and the one with larger wetting angle is unstable. The initial model has a limitation that the fluid interfaces may intersect. We show that the stable equilibrium point never lies in the intersection region, while the unstable equilibrium point may lie in the intersection region.