Modes of Nonaxisymmetry in the Stability of Fixed Contact Line Liquid Bridges and Drops

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Fluid interfaces supported in microgravity by a helical structure are shown to have a more robust stability than more common structures such as liquid bridges. In particular, helical interfaces can take the form of infinite right circular cylinders over a broad range of configurations. In the case of a single fixed contact line support, the infinite cylinder is stable for all cases in which the pitch to diameter ratio is less than / ͱ 3 ͑more tightly coiled interfaces͒. When there are two or more equally spaced fixed contact line supports, the infinite cylinder is stable for all configurations. Furthermore, in the two support case ͑the double helix͒, stability persists for all volumes from the cylinder to zero volume, when the pitch to diameter ratio is greater than 2.082 ͑more loosely coiled interfaces͒. The equivalent to the axisymmetric Young-Laplace equation is derived for helical interfaces. Interfacial stability is determined from equilibrium branch structure following the application of Maddocks' method by Lowry and Steen ͓Proc. R. Soc. London, Ser. A 449, 411 ͑1995͔͒. Perturbations to finite wavelength disturbances are considered for the case of a single helical support. Overall stability envelopes are presented for single and multiple support cases. Limited experimental results verify the infinite length stability limit for the single helical support case.

Section: Curvature Of Nonhelicosymmetric Surfacesmentioning

confidence: 98%

Fixed contact line helical interfaces in zero gravity

Lowry

Thiessen

2007

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“…To apply in our case when χ = 0 we must adjust the contact angle, but it can easily be shown that one can always smoothly change the contact angle with a vanishing change in the surface area and volume. As lower and upper bound coincide, we get the final result that, in the flat wall case, the limit of stability is when the droplet is parallel to the pinned surface at the point of contact (apparent contact angle of π), similarly to the stability threshold for liquid bridges and sessile droplets [10,18].…”

Section: Resultsmentioning

confidence: 75%

“…The perturbation analysis can only reveal the onset of the asymmetry; to probe the mechanical properties of the asymmetric droplets Surface Evolver simulations are used in Section IV. Alternatively, other schemes [17,18], often developed for liquid bridges, might be adapted for use with the contact angle boundary condition.…”

Section: Perturbationsmentioning

confidence: 99%

“…Subsequent works [15][16][17][18] further elucidated the space of stability of these liquid bridges for which the results of Plateau is only one of many. In particular, it was similarly shown that a pinned droplet deformed by a gravitational field, rather than by compression from an upper surface, will also transition to an asymmetric shape past the point when the droplet profile is tangent to the pinning line at the point of contact [10].…”

Section: Introductionmentioning

confidence: 99%

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Buckling instability of squeezed droplets

Elfring

Lauga

2012

Motivated by recent experiments, we consider theoretically the compression of droplets pinned at the bottom on a surface of finite area. We show that if the droplet is sufficiently compressed at the top by a surface, it will always develop a shape instability at a critical compression. When the top surface is flat, the shape instability occurs precisely when the apparent contact angle of the droplet at the pinned surface is π, regardless of the contact angle of the upper surface, reminiscent of past work on liquid bridges and sessile droplets as first observed by Plateau. After the critical compression, the droplet transitions from a symmetric to an asymmetric shape. The force required to deform the droplet peaks at the critical point then progressively decreases indicative of catastrophic buckling. We characterize the transition in droplet shape using illustrative examples in two dimensions followed by perturbative analysis as well as numerical simulation in three dimensions. When the upper surface is not flat, the simple apparent contact angle criterion no longer holds, and a detailed stability analysis is carried out to predict the critical compression.

“…If primary interest were nonaxisymmetric states, these could be calculated directly using standard techniques, as has been done with single drops and bridges. 8 Energy landscapes are illustrated by filling in between equilibrium states with selected nonequilibrium states. Hence, the appropriate function space for the variational problem includes both axisymmetric and nonaxisymmetric shapes and infinitesimal and finite-amplitude disturbances from equilibria.…”

Section: ͑1͒mentioning

confidence: 99%

Liquid-bridge mediated droplet switch: A tristable capillary system

Bhandar

Steen

2005

The double-droplet switch is the simplest example of a system of capillary surfaces ͑liquid/gas interfaces at small scales͒ that demonstrates bistability. A liquid bridge placed between the droplets allows the nonlinear response to be mediated by a pressure p o maintained outside the bridge. Response diagrams that give droplet volumes versus p o are constructed through computations. The combination of the nonlinear pV responses of the bridge and the droplet switch reveals regions with markedly different behaviors depending on the control parameters. The response diagrams show regions with high sensitivity to p o , behavior dominated by the double-droplet response, and also regions with low sensitivity to p o , where the bridge response dominates. Stability is determined following the Poincaré approach with illustration using nonequilibrium energy contours ͑"landscapes"͒. The computations predict regions of hysteresis with three stable equilibria. When imperfections arising from contact-circle movement at the boundaries are included, five simultaneously stable equilibria and double hysteresis loops are predicted.