On Floating Equilibria in a Laterally Finite Container
Date
2016-08
Authors
Treinen, Ray
McCuan, John
Journal Title
Journal ISSN
Volume Title
Publisher
Society for Industrial and Applied Mathematics
Abstract
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 an object can be observed to float in a centrally symmetric position in two geometrically distinct configurations, i.e., at two different heights. The numerical calculation relies on a fairly involved theoretical framework which can also be used to show uniqueness of equilibrium configurations for other parameters. 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. In addition to providing a basis for numerical results, the theoretical framework developed here leads to two rigorous general results. The first is the existence of at least one equilibrium configuration when the density of the floating object is less than that of the liquid bath. The second is that all such equilibrium interfaces must project simply onto the base of the container.
Description
Keywords
floating objects, capillarity, Mathematics
Citation
Treinen, R., & McCuan, J. (2016). On floating equilibria in a laterally finite container. SIAM Journal on Applied Mathematics, 78(1), pp. 551-570.