Comparison of the potential energy for different equilibrium configurations of symmetric and asymmetric floating drops

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 R2 and R3. 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 R2. Non-uniqueness of solutions to the corresponding Euler–Lagrange equations is displayed, and strong evidence of non-uniqueness of energy minimizers is given.