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

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 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 experimental results

Dynamics and Statics of Nonaxisymmetric Liquid Bridges

Theoretical and experimental investigation of the stability of nonaxisymmetric and nonaxisymmetric bridges contained between equal and unequal radii disks as a function of Bond and Weber number with emphasis on the transition from unstable axisymmetric to stable nonaxisymmetric shapes, are conducted. Numerical analysis of the stability of nonaxisymmetric bridges between unequal disks for various orientations of the gravity vector is performed. Experimental and theoretical investigation of large (nonaxisymmetric) oscillations and breaking of liquid bridges are also conducted

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

A numerical method has been developed to determine the stability limits for liquid bridges held between noncircular supporting disks and the application to a configuration with a circular and an elliptical disk subjected to axial acceleration has been made. The numerical method led to results very different from the available analytical solution which has been revisited and a better approximation has been obtained. It has been found that just retaining one more term in the asymptotic analysis the solution reproduces the real behavior of the configuration and the numerical results

A REVIEW ON THE STABILITY OF LIQUID BRIDGES

ABSTRACT 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

One-dimensional dynamics of nearly unstable axisymmetric liquid bridges

A general one-dimensional model is considered that describes the dynamics of slender, axisymmetric, noncylindrical liquid bridges between two equal disks. Such model depends on two adjustable parameters and includes as particular cases the standard Lee and Cosserat models. For slender liquid bridges, the model provides sufficiently accurate results and involves much easier and faster calculations than the full three-dimensional model. In particular, viscous effects are easily accounted for. The one-dimensional model is used to derive a simple weakly nonlinear description of the dynamics near the instability limit. Small perturbations of marginal instability conditions are also considered that account for volume perturbations, nonequality of the supporting disks, and axial gravity. The analysis shows that the dynamics breaks the reflection symmetry on the midplane between the supporting disks. The weakly nonlinear evolution of the amplitude of the perturbation is given by a Duffing equation, whose coefficients are calculated in terms of the slenderness as a part of the analysis and exhibit a weak dependence on the adjustable parameters of the one-dimensional model. The amplitude equation is used to make quantitative predictions of both the (first stage of) breakage for unstable configurations and the (slow) dynamics for stable configurations

Formation of beads-on-a-string structures during break-up of viscoelastic filaments

Break-up of viscoelastic filaments is pervasive in both nature and technology. If a filament is formed by placing a drop of saliva between a thumb and forefinger and is stretched, the filament’s morphology close to break-up corresponds to beads of several sizes interconnected by slender threads. Although there is general agreement that formation of such beads-on-a-string (BOAS) structures occurs only for viscoelastic fluids, the underlying physics remains unclear and controversial. The physics leading to the formation of BOAS structures is probed by numerical simulation. Computations reveal that viscoelasticity alone does not give rise to a small, satellite bead between two much larger main beads but that inertia is required for its formation. Viscoelasticity, however, enhances the growth of the bead and delays pinch-off, which leads to a relatively long-lived beaded structure. We also show for the first time theoretically that yet smaller, sub-satellite beads can also form as seen in experiments.National Science Foundation (U.S.). ERC-SOPS (EEC-0540855)Nanoscale Interdisciplinary Research Thrust on 'Directed Self-assembly of Suspended Polymer Fibers' (NSF-DMS0506941