Stability of Constrained Capillary Surfaces

Bostwick, Joshua; Steen, Paul H.

doi:10.1146/annurev-fluid-010814-013626

Cited by 120 publications

(117 citation statements)

References 136 publications

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“…As a result, the destabilizing effect of gravity can be weakened or even canceled altogether. A similar mechanism of stabilization has been observed experimentally using the radiation pressure of acoustic waves [20] and a surrounding flow of a different fluid [21,25]. This paper has the following structure.…”

Section: Introductionsupporting

confidence: 64%

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Stability of a liquid bridge under vibration

Benilov

2016

Phys. Rev. E

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We examine the stability of a vertical liquid bridge between two vertically vibrating, coaxial disks. Assuming that the vibration amplitude and period are much smaller than the mean distance between the disks and the global timescale, respectively, we employ the method of multiple scales to derive a set of asymptotic equations. The set is then used to examine the stability of a bridge of an almost cylindrical shape. It is shown that, if acting alone, gravity is a destabilizing influence, whereas vibration can weaken it or even eliminate altogether. Thus, counter-intuitively, vibration can stabilize an otherwise unstable capillary structure.

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Section: Introductionsupporting

confidence: 64%

“…(2) by changing u →ū. Equation (33) can be simplified using the incompressibility conditions (25) and (27), and thus becomes ∂ū ∂T…”

Section: B the First Ordermentioning

confidence: 99%

Stability of a liquid bridge under vibration

Benilov

2016

Phys. Rev. E

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“…This can be deduced for systems with a variational structure 2 by representing the potential energy with respect to all dynamically accessible configurations: There are more possible configurations with less potential energy for less-constrained equilibrium states and, therefore, more possible modes of instability 41,45,46 . Applications of these concepts to contact-line constraints, which are of interest to contact-drop dispensing, have been discussed in recent reviews [47][48][49] . By definition, CAH is a relationship between the surface wettability and contact-line constraint on non-ideal surfaces and, thus, is expected to influ- Figure 4: Pinned-to-free contact-line transition scenarios to be examined for stability loss of liquid bridges on surfaces with CAH.…”

Section: Stability-constraint Relationship: Overviewmentioning

confidence: 99%

Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis

Akbari

Hill

2016

Soft Matter

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We study the stability and breakup of liquid bridges with a free contact line on surfaces with contact-angle hysteresis (CAH) under zero-gravity conditions. Non-ideal surfaces exhibit CAH because of surface imperfections, by which the constraints on three-phase contact lines are influenced. Given that interfacial instabilities are constraintsensitive, understanding how CAH affects the stability and breakup of liquid bridges is crucial for predicting the drop size in contact-drop dispensing. Unlike ideal surfaces on which contact lines are always free irrespective of surface wettability, contact lines may undergo transitions from pinned to free and vice-versa during drop deposition on non-ideal surfaces. Here, we experimentally and theoretically examine how stability and breakup are affected by CAH, highlighting cases where stability is lost during a transition from a pinned-pinned (more constrained) to pinned-free (less constrained) interface-rather than a critical state. This provides a practical means of expediting or delaying stability loss. We also demonstrate how the dynamic contact angle can control the contact-line radius following stability loss. *

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“…All equilibrium surfaces outside the MSR are unstable. A summary of Myshkis's method is given by Bostwick and Steen [31].…”

Section: Theorymentioning

confidence: 99%

Catenoid Stability with a Free Contact Line

Akbari¹,

Hill²,

Ven³

2015

SIAM J. Appl. Math.

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Contact-drop dispensing is central to many small-scale applications, such as direct-scanning probe lithography and micromachined fountainpen techniques. Accurate and controllable dispensing required for nanometerresolved surface patterning hinges on the stability and breakup of liquid bridges. Here, we analytically study the stability of catenoids pinned at one contact line with the other free to move on a substrate subject to axisymmetric and non-axisymmetric perturbations. We apply a variational formulation to derive the corresponding stability criteria. The maximal stability region and stability region are represented in the favourable and canonical phase diagrams, providing a complete description of catenoid equilibrium and stability. All catenoids are stable with respect to nonaxisymmetric perturbations. For a fixed contact angle, there exists a critical volume below which catenoids are unstable to axisymmetric perturbations. Equilibrium solution multiplicity is discussed in detail, and we elucidate how geometrical symmetry is reflected in the maximal stability and stability regions.

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Stability of Constrained Capillary Surfaces

Cited by 120 publications

References 136 publications

Stability of a liquid bridge under vibration

Stability of a liquid bridge under vibration

Liquid-bridge stability and breakup on surfaces with contact-angle hysteresis

Catenoid Stability with a Free Contact Line

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