Computational investigation of unusual behavior in certain capillary tubes

We investigate computationally two recent mathematical findings involving unusual behavior of solutions of the Young-Laplace capillary, equation in cylindrical tubes of particular sections. The first concerns a configuration for which smoothing of the boundary curve at a sharp corner leads from existence to non-existence of a solution over the container section in zero gravity. The second describes a discontinuous behavior of relative rise height in nesting tubes placed vertically in an infinite reservoir The numerical results support and quantify the mathematical predictions.