A Floating Cylinder on an Unbounded Bath

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 Bhatnagar and Finn (Phys Fluids 18(4):047103, 2006). We follow their approach but with some modifications. We establish the relation between the total energy $E_T$ relative to the undisturbed state and the total force $F_T$, that is, $F_T = -\frac{dE_T}{dh}$, where h is the height of the center of the cylinder relative to the undisturbed fluid level. There is a monotone relation between h and the wetting angle $\phi _0$. 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 $\gamma$, the one with smaller $\phi _0$ is stable and the one with larger $\phi _0$ is unstable. Since the one-sided solution can be translated horizontally, 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.