José Manuel Perales

Stability of Liquid Bridges between Equal Disks in an Axial Gravity Field

equal‐diameter solid disks subjected to an axial gravity field of arbitrary intensity is analyzed for all possible liquid volumes. The boundary of the stability region for axisymmetric shapes (considering both axisymmetric and nonaxisymmetric perturbations) have been calculated. It is found that, for sufficiently small Bond numbers, three different unstable modes can appear. If the volume of liquid is decreased from that of an initially stable axisymmetric configuration the bridge either develops an axisymmetric instability (breaking in two drops as already known) or detaches its interface from the disk edges (if the length is smaller than a critical value depending on contact angle), whereas if the volume is increased the unstable mode consists of a nonaxisymmetric deformation. This kind of nonaxisymmetric deformation can also appear by decreasing the volume if the Bond number is large enough. A comparison with other previous partial theoretical analyses is presented, as well as with available experiment...

Theoretical and experimental study of the vibration of axisymmetric viscous liquid bridges

In this paper the dynamics of axisymmetric liquid columns held by capillary forces between two circular, concentric, solid disks is considered. The problem has been solved by using a one‐dimensional model known in the literature as the Cosserat model, which includes viscosity effects, where the axial velocity is considered constant in each section of the liquid bridge. The dynamic response of the bridge to an excitation consisting of a small‐amplitude vibration of the supporting disks has been solved by linearizing the Cosserat model. It has been assumed that such excitation is harmonic so that the analysis has been performed in the frequency domain. The particular case of a cylindrical liquid bridge has been analytically studied and the transfer function has been calculated in the cases of oscillation of both disks (either in phase or in counterphase) or only of one of them. The resolution of the general formulation for a noncylindrical liquid bridge has been numerically made by using an implicit finite ...

A Review on the Stability of Liquid Bridges

Abstract Errors in the Although 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.

Liquid bridge stability data

Abstract High precision computations of the minimum volume and the corresponding shape of axisymmetric liquid bridges at rest, anchored to unequal and coaxial discs, are presented. The tables and graphs provide a standard for comparison of linearized and other approximate models, as well an aid in detecting very small departures in shape due to weak (for instance, electrostatic) forces. Relevance to crystal growth by the floating zone technique in the absence of gravity is elucidated.

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

The equilibrium shape of the liquid bridge interface is analyzed theoretically and experimentally. Both axisymmetric and nonaxisymmetric perturbations are considered. The axisymmetric deviations are those related to volume effects, the difference between the radii of the disks, and the axial forces acting on the liquid bridge. The nonaxisymmetric deviations are those due to the eccentricity of the disk and the action of lateral forces. The theoretical study is performed using three different techniques: (i) an analytical expansion around the cylindrical solution, (ii) a finite difference scheme, and (iii) an approximate numerical approach valid only for slight nonaxisymmetric deviations. The results of the three methods are compared systematically. There is a very good agreement between the analytical and the numerical approaches for contours which are close to cylindrical, and the agreement extends to configurations with only moderate deviations from cylindrical. Experiments are performed using the so-called neutral buoyancy or plateau technique. Theoretical and experimental contours are compared considering a wide range of values for the parameters characterizing the perturbations. In general, the finite difference method provides reasonably accurate predictions even for large deviations of the liquid bridge contour from cylindrical.

Equilibrium shapes of nonaxisymmetric liquid bridges of arbitrary volume in gravitational fields and their potential energy

Bifurcation diagrams of nonaxisymmetric liquid bridges subject to a lateral gravitational force and to both lateral and axial gravitational forces are found by solving the Young–Laplace equation for the interface by a finite difference method. The potential energy of the equilibrium shapes is also calculated. The results obtained show that the slenderness of the bridge determines whether the breaking of the liquid bridge subject to a lateral gravitational force leads to equal or unequal drops. The stability limits calculated are compared with the ones obtained using asymptotic techniques around the cylinder, the agreement being extremely good for a wide range of the parameters.

Experimental analysis of stability limits of capillary liquid bridges

This paper deals with the influence of axial microgravity on the stability limits of axisymmetric, cylindrical liquid columns held by capillary forces between two circular, concentric, solid disks. A fair number of experiments have been performed and both the maximum and the minimum volume of liquid that a capillary liquid bridge can withstand have been obtained as a function of the geometry of the liquid bridge and of the value of the axial microgravity acting on it. Experimental results are compared with published theoretical predictions made by other investigators and discrepancies between those results criticized.

Non-Axisymmetric Effects on Long Liquid Bridges

The stability of long liquid bridges under non-axisymmetric disturbances like a microgravitational force acting perpendicular to the liquid bridge axis or a non-coaxiality of the disks is analyzed through an asymptotic method based on bifurcation techniques. Results obtained indicate that such non-axisymmetric effects are of higher order than those produced by axisymmetric perturbations.

Stability of an isorotating liquid bridge 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...

An experimental analysis of the instability of nonaxisymmetric liquid bridges in a gravitational field

The stability limits of nonaxisymmetric liquid bridges between equal in diameter, coaxial disks have been determined experimentally. Experiments have been performed by working with very small size liquid bridges. The experimental setup allows any orientation of the liquid bridge axis with respect to the local gravity vector acceleration. By appropriately orienting the liquid bridge axis, the influence on the stability limits of both the lateral and the axial component of the acceleration acting on the liquid bridge has been investigated.