Stability and bifurcation Problems for Equilibrium States of a Liquid Bridge

The results of an investigation on the stability of a doubly connected axisymmetric equilibrium free surface pinned to the edges of two coaxial disks are presented. The general boundary of the region where the interface is stable is constructed in the plane of the parameters determining the slenderness of a liquid bridge and its relative volume. Surface forces and arbitrary (not only axisymmetric) perturbations are taken into account. The general boundary of the stability region was calculated completely in the past only for a weightless fixed-contactline liquid bridge between equal disks. The influence of axially directed gravity, isorotation and disks inequality on the evolution of this boundary has been analyzed successively. As a result, the families of the stability boundaries have been obtained for fixed-contact-line liquid bridges between equal disks in a wide range of Bond numbers, for isorotating weightless bridges between equal disks, in a wide range of Weber numbers and for weightless fixed-contact-line liquid bridges when the disk radii ratio is varied. Basing on the solution of the bifurcation problem for the critical equilibrium states, the conclusion on the results of stability losing has been made for starting system of fixed-contact line weightless bridge between equal-disks. The stability of the melt during crystal growth using the floating zone technique can be considered as a special case of the presented results. Finally as an example, for a crystal growth system using the Stepanov's method the effect of free surface unconnectivity on the stability has been investigated under zero gravity conditions

Stability of Liquid Bridges between Unequal Disks under Zero-Gravity Conditions

The stability, of axisymmetric equilibrium shapes of a liquid bridge between two coaxial disks of different radii under zero-gravity conditions is investigated. The stability regions have been evaluated for different values of the ratio of the disk radii in terms of the dimensionless parameters which characterize the length and the volume of the bridge. It has been found that disk radii unequality radically changes the upper boundary of the stability region. The analysis of the shape of marginally stable equilibrium surfaces has been carried out. Relationships between the critical values of the parameters have been deduced for some particular cases, which are of special interest for the materials purification processes and growing of single crystals by the floating zone method: for typical values of the growing angle for semiconductor materials and for liquid volumes close to that of the cylinder having a radius equal to the mean radius of the disk

Stability of an Isorotating Liquid Bridges between Equal Disks under Zero-gravity Conditions

The stability of the relative equilibrium of an isorotating axisymmetric liquid bridge between two equal‐radius coaxial disks under zero‐gravity conditions has been investigated in detail. The free surface is assumed to be pinned to the edges of the disks and in equilibrium and only perturbations compatible with this pinning are considered. In the plane of the dimensionless variables characterizing the liquid bridge length and the liquid bridge volume, the stability regions for a set of values of the Weber number have been calculated. The stability region structure and the nature of critical perturbations change when the Weber number, W, passes through the values W0 (2.05<W0<2.06) and W1 (2.44<W1<2.45). It has been found that, for W<W0, the stability region is connected, and the neutral stability may take place with respect to nonaxisymmetric perturbations as well as to axisymmetric ones. In the latter case, it has been established whether the critical axisymmetric perturbations are reflectively symmetric or reflectively antisymmetric about the equatorial plane. When the increasing Weber number passes through the value W0, the stability region breaks into two disconnected parts. The first exists for all Weber numbers larger than W0. For the states belonging to the boundary of this part, only nonaxisymmetric perturbations are critical. The second part exists only for Weber numbers between W0 and W1. Its boundary is determined by the states that may be neutrally stable to nonaxisymmetric perturbations or to axisymmetric ones. The characteristics of the shape of the neutrally stable surfaces have been calculated for a wide range of the Weber numbe

A Review on the Stability of Liquid Bridges

Errors in theAlthough early studies dealing with the stability of liquid bridges were published long time ago, these studies were mainly concerned with the stability of axisymmetric liquid bridges between parallel, coaxial, equal-in-diameter solid disks, with regard to axisymmetric perturbations. Results including effects such as solid rotation of the liquid column, supporting disks of different diameters and an axial acceleration acting parallel to the liquid column can be found in several works published in the early eighties, although most of these analysis were restricted to liquid bridge configurations having a volume of liquid equal or close enough to that of a cylinder of the same radius. Leaving apart some asymptotic studies, the analysis of non-axisymmetric effects on the stability of liquid bridges (lateral acceleration, eccentricity of the supporting disks) and other not so-classical effects (electric field) has been initiated much more recently, the results concerning these aspect of liquid bridge stability being yet scarce