A capillary surface is an interface between two fluids whose shape is determined primarily by surface tension. Sessile drops, liquid bridges, rivulets, and liquid drops on fibers are all examples of capillary shapes influenced by contact with a solid. Capillary shapes can reconfigure spontaneously or exhibit natural oscillations, reflecting static or dynamic instabilities, respectively. Both instabilities are related, and a review of static stability precedes the dynamic case. The focus of the dynamic case here is the hydrodynamic stability of capillary surfaces subject to constraints of (a) volume conservation, (b) contact-line boundary conditions, and (c) the geometry of the supporting surface.

Stability of Constrained Capillary Surfaces

A one-dimensional inviscid slice model has been used to study numerically the influence of axial microgravity on the breaking of liquid bridges having a volume close to that of gravitationless minimum volume stability limit. Equilibrium shapes and stability limits have been obtained as well as the dependence of the volume of the two drops formed after breaking on both the length and the volume of the liquid bridge. The breaking process has also been studied experimentally. Good agreement has been found between theory and experiment for neutrally buoyant systems.

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Numerical and experimental study of the dynamics of axisymmetric slender 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 difference method. In this case, the influence of the volume of the liquid column and of the residual gravity level on the first resonance has been studied, and the results compared, for the inviscid case, with other potential models, both one and three dimensional. To demonstrate the usefulness of this theoretical model in predicting the vibrational behavior of axisymmetric viscous liquid bridges, some experiments have been performed by using the neutral buoyancy technique (also known as the Plateau technique) to simulate reduced gravity conditions, with good agreement between the results of the model and experiments.

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

Cylindrical liquid bridges that are magnetically levitated in air against gravity are subjected to either axial or lateral oscillations of the total body force. It was found that the frequency of the first resonance peak is maximum when the total body force is zero and decreases with increasing total body force for both axial and lateral oscillations. The experimental results for the axially symmetric case are compared to theoretical calculations using the one-dimensional slice model.

Resonance behavior of liquid bridges under axial and lateral oscillating total body forces

It is shown that with the exception of very particular cases any tubular liquid bridge con guration joining parallel plates in the absence of gravity must change dis continuously with tilting of the plates thereby proving a conjecture of Concus and Finn Phys Fluids Thus the stability criteria that have appeared previously in the literature which take no account of such tilting are to some extent misleading Conceivable con gurations of the liquid mass following a plate tilting are characterized and conditions are presented under which stable drops in wedges with disk type or tubular free bounding surfaces can be expected As a corollary of the study a new existence theorem for H graphs over a square with discontinuous data is obtained The resulting surfaces can be interpreted as generalizations of the Scherk minimal surface in two senses a the requirement of zero mean curvature is weakened to constant mean curvature and b the boundary data of the Scherk surface which al ternate between the constants and on adjacent sides of a square are replaced by capillary data alternating between two constant values restricted by a geometrical criterion

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Liquid bridges, edge blobs, and Scherk-type capillary surfaces

A liquid column, supported by surface tension forces, can bridge the gap between two solid surfaces. When these surfaces are two parallel, coaxial, circular discs, the resulting configuration is often used to model a floating zone in melting, provided that a number of simplifying assumptions is fulfilled. Several problems which are relevant to the equilibrium and stability of liquid bridges under microgravity conditions are discussed in this paper. These problems have been selected because they are amenable to theoretical analysis while still presenting many of the most intriguing characteristics of several experiments which will be performed onboard Spacelab by use of the ESA Fluid Physics Module.

I. Da-Riva

Papers

Stability of liquid bridges