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Droplet motion arises in many natural phenomena, ranging from the familiar gravity-driven slip and arrest of raindrops on windows to the directed transport of droplets for water harvesting by plants and animals under dry conditions. Deliberate transportation and manipulation of droplets are also important in many technological applications, including droplet-based microfluidic chemical reactors and for thermal management. Droplet motion usually requires gradients of surface energy or temperature or external vibration to overcome contact angle hysteresis. Here, we report a new phenomenon in which a drying droplet placed on a periodically compliant surface undergoes spontaneous, erratic motion in the absence of surface energy gradients and external stimuli such as vibration. By modeling the droplet as a mass-spring system on a substrate with periodically varying compliance, we show that the stability of equilibrium depends on the size of the droplet. Specifically, if the center of mass of the drop lies at a stable equilibrium point of the system, it will stay there until evaporation reduces its size and this fixed point becomes unstable; with any small perturbation, the droplet then moves to one of its neighboring fixed points.

The Laplace pressure of a droplet placed on one side of an elastic thin film can cause significant deformation in the form of a bulge on its opposite side. Here, we show that this deformation can be detected by other droplets suspended on the opposite side of the film, leading to interaction between droplets separated by the solid (but deformable) film. The interaction is repulsive when the drops have a large overlap and attractive when they have a small overlap. Thus, if two identical droplets are placed right on top of each other (one on either side of the thin film), they tend to repel each other, eventually reaching an equilibrium configuration where there is a small overlap. This observation can be explained by analyzing the energy landscape of the droplets interacting via an elastically deformed film. We further demonstrate this idea by designing a pattern comprising a big central drop with satellite droplets. This phenomenon can lead to techniques for directed motion of droplets confined to one side of a thin elastic membrane by manipulations on the other side.

Indentation of hydrated Nafion thin films reveals that both the in-plane diffusivity of water and the intrinsic permeability of the phase-segregated network decrease dramatically with decreasing film thickness. Using pore-network theory, this decrease in diffusivity is attributed to both an increase in ionic-domain heterogeneity and a reduction in ionic-domain connectivity upon confinement.

Water transport and swelling properties of an ultrathin, selective polyamide layer with a hydrophilic polymer coating, i.e., a polymer bilayer, are studied using quartz crystal microbalance with dissipation (QCM-D). Specifically, QCM-D is used to measure the dynamic and equilibrium change in mass in a series of differential sorption experiments to determine the dependence of the apparent diffusion coefficient and equilibrium swelling of the bilayer as a function of the water vapor activity. To determine transport properties specific to the polyamide layer, sorption kinetics of the bilayer was modeled with a bilayer mass transport model. The swelling and water diffusion coefficients are interpreted according to the Painter-Shenoy polymer network swelling model and the solution-diffusion model, respectively.

A drop placed under a solid thin film causes it to bulge due to the action of liquid surface tension, Laplace pressure, difference in surface tension on two sides of the film, and gravity. Deformation is resisted by solid surface tension, bending, and in-plane stretching. For sufficiently thin films and small drops, the film mainly carries tension and the deformed configuration can be obtained simply by force balance of tensions at the contact line. In this work, we examine more closely the conditions under which this simplified situation exists. We show that generally the effect of surface tension asymmetry on two sides of the film is negligible, as is the effect of gravity on the local deformed shape. Further, we show that for sufficiently thin films, bending affects the solution only in a boundary layer near the contact region and that tensions in the films can still be estimated from force balance.

We show that a drop of liquid a few hundred microns in diameter placed under a solid, elastic, thin film (∼10 μm thick) causes it to bulge by tens of microns. The deformed shape is governed by equilibrium of tensions exerted by the various interfaces and the solid film, a form of Neumann’s triangle. Unlike Young’s equation, which specifies the contact angles at the junction of two fluids and a (rigid) solid, and is fundamentally underdetermined, both tensions in the solid film can be determined here if the liquid–vapor surface tension is known independently. Tensions in the solid film have a contribution from elastic stretch and a constant residual component. The residual component, extracted by extrapolation to films of vanishing thickness and supported by analysis of the elastic deformation, is interpreted as the solid–fluid surface tension, demonstrating that compliant thin-film structures can be used to measure solid surface tensions.

We show that a structure with a fibrillar surface terminated by a continuous film can be switched between two metastable states. The first state, in which the film is stretched between fibrils, has previously been shown to have strongly enhanced adhesion compared to an unstructured flat control. In the second state, the film collapses onto the substrate between fibrils and is held up away from the substrate at the fibrils, resulting in a surface with a periodic array of bumps with much reduced adhesion. The interface can be switched mechanically between these two states repeatedly, thus providing a means for active control of surface mechanical properties. We develop a simple model that shows what combination of parameters, such as film thickness, dimensions, and spacing between fibrils, is required for such an architecture to be metastable in each of these two states.

In this paper, we study the stability of an initially straight elastic fibril clamped at one end, while the other end is subjected to a constant normal compressive force and a prescribed shear displacement. We found the buckling load of a sheared fibril to be always less than the Euler buckling load. Furthermore, if the end of the fibril loses adhesion, then the buckling load can be considerably less. Our result suggests that the static friction of microfibre arrays can decrease with increasing normal compressive load and, in some cases, friction force can actually become negative.

We show that highly enhanced and selective adhesion can be achieved between surfaces patterned with complementary microchannel structures. An elastic material, poly(dimethylsiloxane) (PDMS), was used to fabricate such surfaces by molding into a silicon master with microchannel profiles patterned by photolithography. We carried out adhesion tests on both complementary and mismatched microchannel/micropillar surfaces. Adhesion, as measured by the energy release rate required to propagate an interfacial crack, can be enhanced by up to 40 times by complementary interfaces, compared to a flat control, and slightly enhanced for some special noncomplementary samples, despite the nearly negligible adhesion for other mismatched surfaces. For each complementary surface, we observe defects in the form of visible striations, where pillars fail to insert fully into the channels. The adhesion between complementary microchannel surfaces is enhanced by a combination of a crack-trapping mechanism and friction between a pillar and channel and is attenuated by the presence of defects.