Multiple equilibria in a simple elastocapillary system

Taroni, Michele; Vella, Dominic

doi:10.1017/jfm.2012.418

Cited by 42 publications

(60 citation statements)

References 41 publications

(25 reference statements)

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“…Early investigations were motivated by applications such as liquid-jet breakup [2,3], crystal growth in microgravity [4], oil recovery [5], and paper wet strength [6]. Recently, interests have grown into areas such as elastocapillarity [7][8][9][10], contact-drop dispensing [11] with applications to scanning-probe lithography [12] and micromachined fountain-pen techniques [13]. Molecular-resolution surface patterning provides new opportunities for advanced tissue engineering [14], DNA self-assembled nanoconstructs [15], and highly sensitive protein chips [16].…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Catenoid Stability with a Free Contact Line

Akbari¹,

Hill²,

Ven³

2015

SIAM J. Appl. Math.

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“…Studies of the elasto-capillary coalescence of two elastic sheets due to capillary force of a liquid between them were made by Kim & Mahadevan (2006), , , Duprat et al (2012) and Taroni & Vella (2012). Experimental studies of elasto-capillary coalescence of multiple elastic structures include the works of Py et al (2007a), Chandra et al (2009), Pokroy et al (2009), Chandra & Yang (2010), Chiodi et al (2010), Duan & Berggren (2010), Elwenspoek et al (2010), and Kang et al (2011).…”

Section: Introductionmentioning

confidence: 99%

Elasto-capillary coalescence of multiple parallel sheets

Gat

Gharib

2013

J. Fluid Mech.

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We analyse two-dimensional clamped parallel elastic sheets which are partially immersed in liquid as a model for elasto-capillary coalescence. In the existing literature this problem is studied via minimal energy analysis of capillary and elastic energies of the post-coalescence state, yielding the maximal stable post-coalescence bundle size. Utilizing modal stability analysis and asymptotic analysis, we studied the stability of the configuration before the coalescence occurred. Our analysis revealed previously unreported relations between viscous forces, body forces, and the instability yielding the coalescence, thus undermining a common assumption that coalescence will occur as long as it will not create a bundle larger than the maximal stable post-coalesced size. A mathematical description of the process creating the hierarchical coalescence structure was obtained and yielded that the mean number of sheets per coalesced region is limited to the subset 2 N where N is the set of natural numbers. Our theoretical results were illustrated by experiments and good agreement with the theoretical predictions was observed.

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“…One common theme in these settings is the occurrence of hysteresis and rapid transitions between markedly different states, for example the zipping and unzipping of fibres by a droplet as the fibre tension or separation is varied [18]. Furthermore, theory and experiments suggest that fluid droplets are capable of significant deformation of surfaces: beams clamped at one end can be bent into contact [19,20] and two soft elastic half-spaces can be pulled together [21] by the forces of a single fluid droplet.…”

Section: Introductionmentioning

confidence: 99%

Elasto-capillary adhesion: Effect of deformability on adhesion strength and detachment

et al. 2019

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We study the interaction between capillary forces and deformation in the context of a deformable capillary adhesive: a clamped, tense membrane is adhered to a rigid substrate by the surface tension of a liquid droplet. We find that the equilibrium adhesive force for this elastocapillary adhesive is significantly enhanced in comparison to the capillary adhesion between rigid plates. In particular, the equilibrium adhesion force is orders of magnitude greater when the membrane is sufficiently deformed to contact the substrate. From a dynamic perspective, however, the formation of a fluidfilled dimple slows this approach to contact and means that stable attachment is only achieved if adhesion is maintained for a minimum time. The inclusion of a variable membrane tension (as a means of modifying the deformability) gives additional control over the system, allowing new detachment strategies to be explored.

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Multiple equilibria in a simple elastocapillary system

Cited by 42 publications

References 41 publications

Catenoid Stability with a Free Contact Line

Catenoid Stability with a Free Contact Line

Elasto-capillary coalescence of multiple parallel sheets

Elasto-capillary adhesion: Effect of deformability on adhesion strength and detachment

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