Comparison of the potential energy for different equilibrium configurations of symmetric and asymmetric floating drops
This work provides a computational tool for studying floating drop equilibria, but it is an incremental contribution to the field of free boundary problems.
The paper presents a numerical method for computing equilibrium states of floating drops, exploring a nine-dimensional parameter space and demonstrating non-uniqueness of solutions and energy minimizers.
We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value problems, and at each iterative step a Chebyshev spectral collocation method is employed. The problems considered here are those that can be described by using generating curves, and include problems in $\mathbb{R}^2$ and $\mathbb{R}^3$. The resulting nine-dimensional space of physical parameters is explored, and examples are given that highlight the potential energy of centrally located drops, wall-bound drops, and asymmetrical configurations in $\mathbb{R}^2$. Non-uniqueness of solutions to the corresponding Euler-Lagrange equations is displayed, and also strong evidence of non-uniqueness of energy minimizers is given.