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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.

KEYWORDS

Floating Ball, Capillarity

Cite this paper

Treinen, R. 2016 Examples of Non-Uniqueness of the Equilibrium States for a Floating Ball. Advances in Materials Physics and Chemistry, 6, 177-194. doi: 10.4236-ampc.2016.67019.





Autor: Ray Treinen

Fuente: http://www.scirp.org/



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