Ray Treinen

On Floating Equilibria in a Laterally Finite Container

The main contribution of this paper is the precise numerical identification of a model set of parameters for a floating object/container system which admits three distinct equilibrium configurations, two of which are local energy minimizers among pseudo-equilibrium configurations. This numerical result strongly suggests the existence of a physical system in which a circular object can be observed to float in a centrally symmetric position in two geometrically distinct configurations, i.e., at two different heights. Thus, the general dependence of observable stable equilibria on the physical parameters of the problem is both shown to be much more complicated than originally anticipated and likely to depend on additional information, e.g., the initial positioning of the floating object. We show the existence of at least one equilibrium configuration in any situation which the density of the floating object is less than that of the liquid bath. We also give a collection of conditions under which all equilibr...

On the Classification and Asymptotic Behavior of the Symmetric Capillary Surfaces

ABSTRACT We consider the symmetric solutions to the Young–Laplace equation, and its extensions past vertical points. We provide a classification of all symmetric solutions using certain families of parameters. This classification produces a unified approach to fluid interfaces in capillary tubes, sessile and pendent drops, liquid bridges, as well as exterior and annular capillary surfaces. The generating curves for symmetric solutions have asymptotes for large arclengths, and the behavior of these asymptotes is analyzed.