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The stability of axisymmetric liquid bridges spanning two equal-diameter solid disks subjected to an axial gravity field of arbitrary intensity is analyzed for all possible Uquid 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 experimental results.

Hydrothermal waves in a liquid bridge with aspect ratio near the Rayleigh limit under microgravityThe bifurcation of the solutions of the nonlinear equilibrium problem of a weightless liquid bridge with a free surface pinned to the edges of two coaxial equidimensional circular disks is examined. The bifurcation is studied in the neighborhood of the stability boundary for axisymmetric equilibrium states with emphasis on the boundary segment corresponding to nonaxisymmetric critical perturbations. The first approximations for the shapes of the bifurcated equilibrium surfaces are obtained. The stability of the bifurcated states is then determined from the bifurcation structure. Along the maximum volume stability limit, depending on values of the system parameters, loss of stability with respect to nonaxisymmetric perturbations results in either a jump or a continuous transition to stable nonaxisymmetric shapes. The value of the slenderness at which a change in the type of transition occurs is found to be ⌳ s ϭ0.4946. Experimental investigation based on a neutral buoyancy technique agrees with this prediction. It shows that, for ⌳Ͻ⌳ s , the jump is finite and that a critical bridge undergoes a finite deformation to a stable nonaxisymmetric state.

Disconnected free surfaces ͑or interfaces͒ of a connected liquid volume ͑or liquid volumes͒ occur when the boundary of the liquid volume consists of two or more separate surface components ⌫ i (iϭ1,...,m) that correspond to liquid-gas ͑or liquid-liquid͒ interfaces. We consider disconnected surfaces for which each component ⌫ i is axisymmetric and crosses its own symmetry axis. In most cases, the stability problem for an entire disconnected equilibrium capillary surface subject to perturbations that conserve the total liquid volume reduces to the same set of problems obtained when separately considering the stability of each ⌫ i to perturbations that satisfy a fixed pressure constraint. For fixed pressure perturbations, the stability of a given axisymmetric ⌫ i can be found through comparison of actual and critical values of a particular boundary parameter. For zero gravity, these critical values are found analytically. For non-zero gravity, an analytical representation of the critical values is not generally possible. In such cases, a determination of stability can be accomplished by representing all possible equilibrium surface profiles on a dimensionless ''heightradius'' diagram. This diagram is contoured with critical values of the boundary parameter. The stability diagram can, in most cases, be used to determine the stability of a disconnected surface ͑subject to perturbations that conserve the total volume͒ that is composed of components that are represented by given equilibrium profiles on the diagram. To illustrate this approach, solutions of stability problems for systems consisting of a set of sessile or pendant drops in contact with smooth planar walls or with the edges of equidimensional perforated holes in a horizontal plate are presented.

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