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.

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

“…In previous papers 15, 16 an algorithm, based on a continuation method 17 capable of overpassing bifurcation points and turning points, was developed using a finite-difference method, and was used to obtain the bifurcation diagrams and equilibrium shapes of nonaxisymmetric liquid bridges subject to a lateral gravitational force, and to combined lateral and axial gravitational forces. In this section the algorithm is extended to liquid bridges held between noncircular disks in the presence of an axial gravitational field.…”

“…To stabilize the algorithm, a new equation needs to be included. [15][16][17] With the method modified in this way, a sequence of equilibrium shapes is obtained whether they are stable or unstable. The details of the numerical methods used to locate bifurcation and limit points in the families of equilibrium shapes are identical to those outlined elsewhere 15,16 and will not be repeated here.…”

“…III. This method was already used for analyzing stability problems of nonaxisymmetric liquid bridges held between circular disks, 15,16 but it is here adapted to the particularities imposed by the nonaxisymmetric boundary conditions. In Sec.…”

Theoretical and experimental analysis of the equilibrium contours of liquid bridges of arbitrary shape

“…7,8 Also, a finite difference scheme has been used to numerically obtain the liquid bridge contour, and the results obtained for the stability limits were in good agreement with those calculated using asymptotic techniques around the cylinder. 3 ' 4 The stability of the equilibrium configurations has also been investigated using another numerical procedure which involved solving for energy-minimizing surface configurations. 611 The results were found to be in agreement with the experimental data.…”

Stability of liquid bridges between twisted elliptical disks

“…The present paper studies a liquid bridge configuration held between two parallel and coaxial elliptic disks, analyzing the influence of the angle formed between the main axes of the disks, the excentricity of the ellipses and a gravity parallel to the disks. The stability limits and the equilibrium shapes of the configuration are calculated using a numerical method already implemented for analyzing stability problems of non-axisymmetric liquid bridges held between circular disks (Laveron-Simavilla and Perales, 1995;Laveron-Simavilla and Checa, 1997) and here adapted to the particularities imposed by the non-axisymmetric boundary conditions.…”