Elastocapillary bending of microfibers around liquid droplets

Directed droplet motion along thin fibers

When microscopic droplets are placed between fibers held at a fixed angle, the droplets spontaneously move toward the apex of the fibers. The speed of the droplet motion increases both with the angle between the fibers and the distance the droplet spans across the fibers. The speed of these droplets can be described by a simple scaling relationship. Bending these fibers into a sawtooth geometry results in a droplet ratchet where cyclic motion in a fiber results in extended linear motion of the droplet, and can even be used to induce droplet mergers.

Static wetting of a barrel-shaped droplet on a soft-layer-coated fiber

A droplet can deform a soft substrate due to capillary forces when they are in contact. We study the static deformation of a soft solid layer coated on a rigid cylindrical fiber when an axisymmetric barrel-shaped droplet is embracing it. We found that elastic deformation increases with a decreasing rigid fiber radius. Significant disparities of deformation between the solid-liquid side and the solid-gas side are found when their solid surface tensions are different. When the coated layer is soft enough and the rigid fiber radius is less than the thickness of the coated layer, pronounced displacement oscillations are observed. Such slow decay of deformation with distances from the contact line position suggests a possible long-range interaction between droplets on a soft-layer-coated fiber.

Spontaneous Elastocapillary Winding of Thin Elastic Fibers in Contact with Bubbles

We study the elastocapillary interaction between flexible microfibers in contact with bubbles trapped at the surface of a liquid bath. Microfibers placed on top of bubbles are found to migrate to and wrap into a coil around the perimeter of the bubble for certain bubble-fiber size combinations. The wrapping process is spontaneous: the coil spins atop the bubble, thereby drawing in excess fiber floating on the bath. A two-dimensional microfiber coil emerges which increases the lifetime of the bubbles. A simple model incorporating surface and bending energies captures the spontaneous winding process.

Shapes of a filament on the surface of a bubble

The shape assumed by a slender elastic structure is a function both of the geometry of the space in which it exists and the forces it experiences. We explore, by experiments and theoretical analysis, the morphological phase space of a filament confined to the surface of a spherical bubble. The morphology is controlled by varying bending stiffness and weight of the filament, and its length relative to the bubble radius. When the dominant considerations are the geometry of confinement and elastic energy, the filament lies along a geodesic and when gravitational energy becomes significant, a bifurcation occurs, with a part of the filament occupying a longitude and the rest along a curve approximated by a latitude. Far beyond the transition, when the filament is much longer than the diameter, it coils around the selected latitudinal region. A simple model with filament shape as a composite of two arcs captures the transition well. For better quantitative agreement with the subcritical nature of bifurcation, we study the morphology by numerical energy minimization. Our analysis of the filament’s morphological space spanned by one geometric parameter, and one parameter that compares elastic energy with body forces, may provide guidance for packing slender structures on complex surfaces.

Electrostatic wrapping of a microfiber around a curved particle

The dynamics of the wrapping of a charged flexible microfiber around an oppositely charged curved particle immersed in a viscous fluid is investigated. We observe that the wrapping behavior varies with the radius and Young's modulus of the fiber, the radius of the particle, and the ionic strength of the surrounding solution. We find that wrapping is primarily a function of the favorable interaction energy due to electrostatics and the unfavorable deformation energy needed to conform the fiber to the curvature of the particle. We perform an energy balance to predict the critical particle radius for wrapping, finding reasonably good agreement with experimental observations. In addition, we use mathematical modeling and observations of the deflected shape of the free end of the fiber during wrapping to extract a measurement of the Young's modulus of the fiber. We evaluate the accuracy and potential limitations of this in situ measurement when compared to independent mechanical tests.

Capillary Transport of Miniature Soft Ribbons

Manipulation of soft miniature devices is important in the construction of soft robots, wearable devices, and biomedical devices. However, transport of soft miniature devices is still a challenging task, and few studies has been conducted on the subject. This paper reports a droplet-based micromanipulation method for transporting miniature soft ribbons. We show that soft ribbons can be successfully picked up and released to the target location using water droplets. We analyze the forces involved during the process numerically and investigate the influence of the width of the ribbon on the deformation. We verify that the deformation of a soft ribbon caused by elasto-capillary phenomena can be calculated using a well-known equation for calculating the deflection of a cantilever beam. The experimental and theoretical results show that the deformability of a soft miniature device during manipulation depends on its width.

Auxiliary soft beam for the amplification of the elasto-capillary coiling: Towards stretchable electronics

A flexible fiber carrying a liquid drop may coil inside the drop thereby creating a drop-on-fiber system with an ultra-extensible behavior. During compression, the excess fiber is spooled inside the droplet and capillary forces keep the system taut. During subsequent elongation, the fiber is gradually released and if a large number of spools is uncoiled a high stretchability is achieved. This mechanical behaviour is of interest for stretchable connectors but information, may it be electronic or photonic, usually travels through stiff functional materials. These high Young's moduli, leading to large bending rigidity, prevent in-drop coiling. Here we overcome this limitation by attaching a beam of soft elastomer to the functional fiber, thereby creating a composite system which exhibits in-drop coiling and carries information while being ultra-extensible. We present a simple model to explain the underlying mechanics of the addition of the soft beam and we show how it favors in-drop coiling. We illustrate the method with a two-centimeter long micronic PEDOT:PSS conductive fiber joined to a PVS soft beam, showing that the system conveys electricity throughout a 1900% elongation.

Adhesion-induced fingering instability in thin elastic films under strain

In this study, thin elastic films supported on a rigid substrate are brought into contact with a spherical glass indenter. Upon contact, adhesive fingers emerge at the periphery of the contact patch with a characteristic wavelength. Elastic films are also pre-strained along one axis before the initiation of contact, causing the fingering pattern to become anisotropic and align with the axis along which the strain was applied. This transition from isotropic to anisotropic patterning is characterized quantitatively and a simple model is developed to understand the origin of the anisotropy.

Drop-on-coilable-fibre systems exhibit negative stiffness events and transitions in coiling morphology

We investigate the mechanics of elastic fibres carrying liquid droplets. In such systems, buckling may localize inside the drop cavity if the fibre is thin enough. This so-called drop-on-coilable-fibre system exhibits a surprising liquid-like response under compression and a solid-like response under tension. Here we analyze this unconventional behavior in further detail and find theoretical, numerical and experimental evidence of negative stiffness events. We find that the first and main negative stiffness regime owes its existence to the transfer of capillary-stored energy into mechanical curvature energy. The following negative stiffness events are associated with changes in the coiling morphology of the fibre. Eventually coiling becomes tightly locked into an ordered phase where liquid and solid deformations coexist.

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

We examine the shape of droplets atop deformable thin elastomeric films prepared with an anisotropic tension. As the droplets generate a deformation in the taut film through capillary forces, they assume a shape that is elongated along the high tension direction. By measuring the contact line profile, the tension in the membrane can be completely determined. Minimal theoretical arguments lead to predictions for the droplet shape and membrane deformation that are in excellent agreement with the data. On the whole, the results demonstrate that droplets can be used as probes to map out the stress field in a membrane.