Effect of a lateral gravitational field on the nonaxisymmetric equilibrium shapes of liquid bridges held between eccentric disks and of volumes equal to those of cylinders

Abstract

Bifurcation diagrams of nonaxisymmetric cylindrical volume liquid bridges held between nonconcentric circular disks subject to a lateral gravitational force are found by solving the Young-Laplace equation for the interface by a finite difference method. In the absence of lateral gravity, the primary family of liquid bridges that starts with the cylinder when the eccentricity of the disks, e, is zero first loses stability at a subcritical bifurcation point as e increases. Further loss of stability is experienced by the already unstable primary family as a turning point is encountered at yet higher values of the eccentricity. However, the introduction of lateral gravity gl changes entirely the structure of the solutions in that instability always occurs at a turning point with respect to e no matter how small the magnitude of gl. The stability limits calculated are compared with the ones obtained using asymptotic techniques by taking as base solution the cylinder of slenderness Λ=π.