Examples of Non-Uniqueness of the Equilibrium States for a Floating Ball

Treinen, Ray

doi:10.4236/ampc.2016.67019

Cited by 4 publications

(1 citation statement)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also showed in [MT13] that at least two equilibria can be expected, one a local minimum for energy and another a local maximum among a one parameter family of pseudo-equilibria, which will be defined below. Numerical calculations described in [Tre16] also suggested that this situation prevails with some generality as the physical parameters are varied.…”

Section: Introductionmentioning

confidence: 88%

On Floating Equilibria in a Laterally Finite Container

McCuan¹,

Treinen²

2018

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 88%

On Floating Equilibria in a Laterally Finite Container

McCuan¹,

Treinen²

2018

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

A Floating Cylinder on an Unbounded Bath

Chen

Siegel

2018

J. Math. Fluid Mech.

View full text Add to dashboard Cite

In this paper, we reconsider a circular cylinder horizontally floating on an unbounded reservoir in a gravitational field directed downwards, which was studied by Bhatnargar and Finn 1 in 2006. We follow their approach but with some modifications. We establish the relation between the total energy E T relative to the undisturbed state and the total force F T , that is,where h is the height of the center of the cylinder relative to the undisturbed fluid level. There is a monotone relation between h and the wetting angle φ 0 . We study the number of equilibria, the floating configurations and their stability for all parameter values. We find that the system admits at most two equilibrium points for arbitrary contact angle γ, the one with smaller φ 0 is stable and the one with larger φ 0 is unstable. The initial model has a limitation that the fluid interfaces may intersect. We show that the stable equilibrium point never lies in the intersection region, while the unstable equilibrium point may lie in the intersection region.

show abstract

Bifurcation of a partially immersed plate between two parallel plates

Zhou

Zhang

2017

J. Fluid Mech.

View full text Add to dashboard Cite

The three-plate system in which a vertical plate is located between two spaced parallel plates partially immersed in an infinite water bath in a downward gravity field is considered. With different contact angles and distance between the plates on both sides, the force profiles of the middle plate in this three-plate system are investigated using the Young–Laplace equation in two dimensions, and five non-trivial qualitative force profiles are found to possibly depend on the contact angles and the distance. The study is then extended to the qualitative changes of stability and behaviours in the system, and the striking properties related to the bifurcation theory come to light. Results show that, for different contact angles, there are at most eight possible bifurcation diagrams where the distance between the plates on both sides is chosen as the bifurcation parameter. By analysing the force profile of the middle plate in each of the eight bifurcation diagrams, the stabilities of the equilibria of the plate can be obtained. The number and the stabilities of equilibria will change when the bifurcation parameter passes the critical value.

show abstract

Examples of Non-Uniqueness of the Equilibrium States for a Floating Ball

Cited by 4 publications

References 30 publications

On Floating Equilibria in a Laterally Finite Container

On Floating Equilibria in a Laterally Finite Container

A Floating Cylinder on an Unbounded Bath

Bifurcation of a partially immersed plate between two parallel plates

Contact Info

Product

Resources

About