Elastocapillary bending of microfibers around liquid droplets

Abstract

We report on the elastocapillary deformation of flexible microfibers in contact with liquid droplets. A fiber is observed to bend more as the size of the contacting droplet is increased. At a critical droplet size, proportional to the bending elastocapillary length, the fiber is seen to spontaneously wind around the droplet. To rationalize these observations, we invoke a minimal model based on elastic beam theory, and find agreement with experimental data. Further energetic considerations provide a consistent prediction for the winding criterion.Wetting of liquids on fibrous materials is central to a wide variety of natural and industrial phenomena such as the coalescence of wet hairs [1,2], the drying of textiles [3], the altered mechanical properties of dewy spider silk [4][5][6], the defense mechanism of a species of beetle [7], and the bundling of carbon nanotubes and nanowires during processing [8][9][10][11]. In some of these examples, the fibers are sufficiently flexible that capillary forces induce large-scale deformations -a phenomenon also observed in other geometries such as a drop contacting a flexible solid strip [12]. The bending elastocapillary length L BC = E r 3 /γ is the natural length scale that emerges when balancing elastic bending and capillarity, where E is the Young's modulus of the fiber, r is the fiber radius, and γ is the liquid-air surface tension [1,14]. A slender structure is significantly deformed by capillary forces if the length scale over which these forces act is larger than L BC [1]. To understand the wetting of fibers, several model experiments have been carried out, focusing on droplets between slender flexible structures, where material stiffness and geometry dictate the final wetting configuration [1,[15][16][17][18].Despite its simplicity, even the problem of a single droplet atop an undeformable cylinder is interesting as there are two possible equilibrium states: an axisymmetric "barrel" configuration and a non-axisymmetric "clamshell" [19][20][21][22][23]. It is then not surprising that the case of a flexible fiber interacting with a liquid is a rich subject of study, showcasing complexity and stunning examples of self-assembly [1,5,6,[24][25][26]. In a series of beautiful experiments, droplets were placed on taut elastomeric fibers, and reached the barrel configuration [5,6]. With reduced tension, capillary forces cause the fiber to buckle inside the droplet if the radius of the latter exceeds roughly L BC . As the fiber is slackened, it coils inside the droplet which acts as a windlass to maintain tension. However, for a smaller droplet-to-fiber radius ratio, or for less-wettable conditions, the clam-shell configuration may be more favourable than the barrel [23]. In such a case, a soft fiber may instead wind around the surface of a droplet without experiencing a buckling transition [1]. As argued by Roman and Bico, the reduction in surface energy upon winding exceeds the bending penalty if the droplet radius is larger than ∼ L BC . This is reminiscent of DNA molecul...

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Adhesion-induced fingering instability in thin elastic films under strain

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Liquid Droplets Act as “Compass Needles” for the Stresses in a Deformable Membrane

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