Piercing a liquid surface with an elastic rod: Buckling under capillary forces

Neukirch, Sébastien; Roman, Benoît; Gaudemaris, Benoît de; Bico, José

doi:10.1016/j.jmps.2006.11.009

Cited by 64 publications

(94 citation statements)

References 21 publications

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“…This result agrees with Neukirch's energetic approach to describing the geometry of an infinite soap film totally wetting a strip [10]. Here, we show how to generalise the approach to nonzero contact angles.…”

Section: Introductionsupporting

confidence: 86%

“…They appear in applications throughout biology and engineering, and include animal locomotion [1][2][3][4]; surface processing for nano-micro-applications, for example fiber coating and cleaning [5][6][7], the assembly of hairs, carbon nanotubes and biological filaments [8][9][10][11][12][13][14][15][16]; uses of AFM probes [6,17,18]; and impact of liquid jets [19].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Deformation of a free interface pierced by a tilted cylinder: Variation of the contact angle

Raufaste

Cox

2013

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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Section: Introductionsupporting

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Deformation of a free interface pierced by a tilted cylinder: Variation of the contact angle

Raufaste

Cox

2013

Colloids and Surfaces A: Physicochemical and Engineering Aspect

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“…Therefore, we approximate each plate as a rigid element with a localized bending response in an elastic hinge at the base [12]. This simplifies our analysis relative to the case of inhomogeneous bending and buckling (electronic supplementary material, appendix A) of individual plates [20,24]. The hinge elastic constant can be approximately derived from the bending response of a short cantilever by a transverse force F at its free end, with showing that the menisci can be pinned on both tips, or slip down from one or both tips.…”

Section: Collective Dynamics Of Elastic Plates (A) Experimental Obsermentioning

confidence: 99%

Elastocapillary coalescence of plates and pillars

et al. 2015

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When a fluid-immersed array of lamellae or filaments that is attached to a substrate is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together. Similarly, when hair dries it clumps together due to capillary forces induced by the liquid menisci between the flexible hairs. Building on prior experimental observations, we use a combination of theory and computation to understand the nature of this instability and its evolution in both the two-dimensional and three-dimensional setting of the problem. For the case of lamellae, we explicitly derive the interaction torques based on the relevant physical parameters. A Bloch-wave analysis for our periodic mechanical system captures the critical volume of the liquid and the 2-plate-collapse eigenmode at the onset of instability. We study the evolution of clusters and their arrest using numerical simulations to explain the hierarchical cluster formation and characterize the sensitive dependence of the final structures on the initial perturbations. We then generalize our analysis to treat the problem of pillar collapse in 3D, where the fluid domain is completely connected and the interface is a surface with the uniform mean curvature. Our theory and simulations capture the salient features of both previous experimental observations and our own in terms of the key parameters that can be used to control the kinetics of the process

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“…Although the actual postbuckling behavior is more complex [29], we will suppose, for the sake of simplicity, that lamellae with lengths exceeding L EC eventually collapse towards the base. In the case of a brush, the buckled lamellae generally hit their neighbors and merge into larger bundles.…”

mentioning

confidence: 99%

Piercing an interface with a brush: Collaborative stiffening

Chiodi¹,

Roman²,

Bico³

2010

EPL

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Abstract. -The hairs of a painting brush withdrawn from a wetting liquid self-assemble into clumps whose sizes rely on a balance between liquid surface tension and hairs bending rigidity. Here we study the situation of an immersed carpet in an evaporating liquid bath : the free extremities of the hairs are forced to pierce the liquid interface. The compressive capillary force on the tip of flexible hairs leads to buckling and collapse. However we find that the spontaneous association of hairs into stronger bundles may allow them to resist capillary buckling. We explore in detail the different structures obtained and compare them with similar patterns observed in micro-structured surfaces such as carbon nanotubes "forests".Introduction. -Everyday's life experience teaches us that wet hairs assemble into bundles. This phenomenon is however amplified at the scale of Micro-Electro-MechanicalSystems (MEMS) since surface forces tend to dominate over bulk forces when the scale is reduced. Indeed, if L is the typical size of a structure, surface forces are proportional to L, while elastic or gravity forces scale as L 2 and L 3 , respectively. Controlling 'stiction' is then a challenging issue in micro-engineering technologies since it often leads to the fatal collapse of microstructures [6][7][8]. Nevertheless, the self-assembly of micro-structures through capillary forces can also be viewed as a useful tool to build complex shapes [1][2][3][4][5]. Beyond engineering applications, surface forces may also have a strong effect on living structures. For instance, filamentous fungi living in aqueous environment have difficulty in growing their hypha through the water interface into the air. Indeed some species have to produce surfactant molecules that reduce capillary forces in order to develop the aerial structures necessary for dissemination [24].In the case of slender structures, the interaction between elasticity and interfacial forces can be defined by a typical elastocapillary length scale, L EC = B/γ ∼ Eh 3 /γ, where E is the Young modulus of the material, h and B are the thickness and the bending stiffness per unit width of the structure, respectively, and γ the liquid surface tension or the solid adhesion energy [25][26][27][28][29]. The validity of this macroscopic length scale has recently been confirmed at the scale of graphene sheets through atomistic simulations [30].In this paper we study the case of a carpet-like structure immersed in a drying liq-

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Piercing a liquid surface with an elastic rod: Buckling under capillary forces

Cited by 64 publications

References 21 publications

Deformation of a free interface pierced by a tilted cylinder: Variation of the contact angle

Deformation of a free interface pierced by a tilted cylinder: Variation of the contact angle

Elastocapillary coalescence of plates and pillars

Piercing an interface with a brush: Collaborative stiffening

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