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.
Highlights
Consider a ball of density ρ B floating at the surface of a fluid that has density ρ
The energy analysis is used to determine which of the two equilibria has the lower energy, and at least amongst centrally located floating balls, this process finds the energy minimizing configuration
We have developed a robust numerical solver for finding the equilibria of a centrally located floating ball in both bounded and unbounded problems in 2
Summary
Consider a ball of density ρ B floating at the surface of a fluid that has density ρ. Amples of non-uniqueness of the equilibrium states for these configurations. We will provide a framework for the classification of these states, including an energy analysis. The energy analysis is used to determine which of the two equilibria has the lower energy, and at least amongst centrally located floating balls, this process finds the energy minimizing configuration. Under these conditions, this is the configuration that our model predicts which will be found in experiments. We begin with a precise formulation of our model
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