Stability of liquid bridges between an elliptical and a circular supporting disk

Abstract

A numerical method has been developed to determine the stability limits for liquid bridges held between noncircular supporting disks, and the application to a configuration with a circular and an elliptical disk subjected to axial acceleration has been made. The numerical method led to results very different from the available analytical solution, which has been revisited and a better approximation has been obtained. It has been found that just retaining one more term in the asymptotic analysis the solution reproduces the real behavior of the configuration and the numerical results.

Stability of liquid bridges between twisted elliptical disks

“…In a latter work (Laveron-Simavilla et al, 2003) the stability and equilibrium shapes of a liquid bridge held between a circular disk parallel and coaxial to an elliptic disk subjected to an axial acceleration was studied, it was found that in some cases both effects counteracted in the way of enlarging the stable region in the parameter plane. In this paper, the algorithm is extended to liquid bridges held between elliptic disks in the presence of a lateral acceleration in order to study the influence of the angle formed by the ellipses' main axes, the acceleration direction and the lateral Bond number.…”

“…Leaving apart non-mechanical disturbances, some works dealing with non-axisymmetric supporting disks have been published, two of them dealing with the equilibrium shapes of liquid bridges between non-circular supports (Martinez et al, 2002a,b), one dealing with the asymptotic stability of long liquid bridges between noncircular disks (Meseguer et al, 2001) and another in which the stability and the equilibrium shapes of a liquid bridge held between a circular and an elliptic disk is studied (Laveron-Simavilla et al, 2003). In the last two papers mentioned it is demonstrated that the influence on the stability limit of perturbations like an axial gravity and the existence of noncircular supporting disks can interact in the way of balancing each other.…”