TITLE:
Examples of Non-Uniqueness of the Equilibrium States for a Floating Ball
AUTHORS:
Ray Treinen
KEYWORDS:
Floating Ball, Capillarity
JOURNAL NAME:
Advances in Materials Physics and Chemistry,
Vol.6 No.7,
July
5,
2016
ABSTRACT: We provide a numerical algorithm for numerically approximating a centrally located floating ball. We give examples of equilibria, and we present non-unique cases for the same physical parameters when the density of the ball is either greater than the supporting liquid (heavy) or lighter than the density of the vapor above (light). We classify the non-uniqueness by analyzing a function related to the force balance. We derive the potential energy of these states, and make comparisons of the non-unique cases. In the cases of both the light and heavy floating balls, the evidence presented supports the conjecture that when there are two equilibria, the one with lower energy corresponds to the location of triple junction (between the ball, the vapor and the liquid) that is closer to the equator of the ball.