Numerous cell types have shown a remarkable ability to detect and move along gradients in stiffness of an underlying substrate-a process known as durotaxis. The mechanisms underlying durotaxis are still unresolved, but generally believed to involve active sensing and locomotion. Here, we show that simple liquid droplets also undergo durotaxis. By modulating substrate stiffness, we obtain fine control of droplet position on soft, flat substrates. Unlike other control mechanisms, droplet durotaxis works without imposing chemical, thermal, electrical, or topographical gradients. We show that droplet durotaxis can be used to create large-scale droplet patterns and is potentially useful for many applications, such as microfluidics, thermal control, and microfabrication.droplet control | elasticity | soft matter | wetting | mechanosensing T he control of liquids on surfaces is essential for microfluidics (1), microfabrication (2), and coatings (3-5), to name but a few applications. Wetting is typically manipulated by controlling interfacial energies (6). Heterogeneous surface chemistries have been exploited to pattern (7,8) and transport droplets (3, 9). Gradients in temperature or electric potential can drive droplet motion (3, 9). Alternatively, surface topography can control the spreading of fluids. For example, isotropically rough surfaces can exhibit superhydrophobicity (10, 11), whereas anisotropic surfaces exhibit anisotropic spreading (12) and even directed droplet transport (13-15). Here, we introduce a method to control droplets on surfaces inspired by the biological phenomenon of durotaxis-the ability of many eukaryotic cell types to move along gradients in the stiffness of their extracellular matrix (16)(17)(18)(19). Although the current explanation of durotaxis involves active sensing of matrix stiffness and actomyosin-based motility (18), we show here that even simple liquid droplets display durotaxis. Furthermore, we show that durotaxis can be exploited to achieve largescale droplet patterning. A simple theory explains how drops move toward softer parts of a substrate, and quantitatively captures the droplet distribution on patterned surfaces. Droplet durotaxis is prominent on soft substrates, which are significantly deformed by liquid surface tension (20,21).The spreading of liquid droplets on stiff, flat surfaces is primarily described by the contact angle. In equilibrium, a small droplet takes the shape of a spherical cap with uniform contact angle θ determined by Young's law: γ LV cosθ = γ SV − γ SL . Here, indices L, S, and V of interfacial energies, γ, represent liquid, solid, and vapor, respectively (6). Spontaneous droplet motion typically occurs in two main cases. First, if the actual contact angle of a droplet differs from its equilibrium contact angle, the droplet will be driven to spread/contract until it reaches its equilibrium shape (6). Second, if there is a difference between the equilibrium contact angle on either side of a droplet, the droplet will be driven toward the more wetting sid...

When a coffee drop dries on a solid surface, it leaves a ringlike deposit along the edge and this is known as the "coffee-ring effect." We find a different motion of particles repelling the coffee-ring effect in drying droplets; the motion of particles that is initially toward the edge by the coffee-ring effect is reversed toward the center by a capillary force. The reversal takes place when the capillary force prevails over the outward coffee-ring flow. We discuss the geometric constraints for the capillary force and the reverse motion. Our findings of reversal phenomena would be important in many scenarios of drying colloidal fluids.

One of the most questionable issues in wetting is the force balance that includes the vertical component of liquid surface tension. On soft solids, the vertical component leads to a microscopic protrusion of the contact line, that is, a ‘wetting ridge’. The wetting principle determining the tip geometry of the ridge is at the heart of the issues over the past half century. Here we reveal a universal wetting principle from the ridge tips directly visualized with high spatio-temporal resolution of X-ray microscopy. We find that the cusp of the ridge is bent with an asymmetric tip, whose geometry is invariant during ridge growth or by surface softness. This singular asymmetry is deduced by linking the macroscopic and microscopic contact angles to Young and Neuman laws, respectively. Our finding shows that this dual-scale approach would be contributable to a general framework in elastowetting, and give hints to issues in cell-substrate interaction and elasto-capillary problems.

Colloidal particles suspended in a fluid usually inhibit complete wetting of the fluid on a solid surface and cause pinning of the contact line, known as self-pinning. We show differences in spreading and drying behaviors of pure and colloidal droplets using optical and confocal imaging methods. These differences come from spreading inhibition by colloids confined at a contact line. We propose a self-pinning mechanism based on spreading inhibition by colloids. We find a good agreement between the mechanism and the experimental result taken by directly tracking individual colloids near the contact lines of evaporating colloidal droplets.

When a liquid drop impacts a solid surface, air is generally entrapped underneath. Using ultrafast x-ray phase-contrast imaging, we directly visualized the profile of an entrapped air film and its evolution into a bubble during drop impact. We identified a complicated evolution process that consists of three stages: inertial retraction of the air film, contraction of the top air surface into a bubble, and pinch-off of a daughter droplet inside the bubble. Energy transfer during retraction drives the contraction and pinch-off of a daughter droplet. The wettability of the solid surface affects the detachment of the bubble, suggesting a method for bubble elimination in many drop-impact applications.

A bubble reaching an air–liquid interface usually bursts and forms a liquid jet. Jetting is relevant to climate and health as it is a source of aerosol droplets from breaking waves. Jetting has been observed for large bubbles with radii of R≫100 μm. However, few studies have been devoted to small bubbles (R<100 μm) despite the entrainment of a large number of such bubbles in sea water. Here we show that jet formation is inhibited by bubble size; a jet is not formed during bursting for bubbles smaller than a critical size. Using ultrafast X-ray and optical imaging methods, we build a phase diagram for jetting and the absence of jetting. Our results demonstrate that jetting in bubble bursting is analogous to pinching-off in liquid coalescence. The coalescence mechanism for bubble bursting may be useful in preventing jet formation in industry and improving climate models concerning aerosol production.

Cavitation is a common damage mechanism in soft solids. Here, we study this using a phaseseparation technique in stretched, elastic solids to controllably nucleate and grow small cavities by several orders of magnitude. The ability to make stable cavities of different sizes, as well as the huge range of accessible strains, allows us to systematically study the early stages of cavity expansion. Cavities grow in a scale-free manner, accompanied by irreversible bond breakage that is distributed around the growing cavity, rather than being localized to a crack tip. Furthermore, cavities appear to grow at constant driving pressure. This has strong analogies with the plasticity that occurs surrounding a growing void in ductile metals. In particular we find that, although elastomers are normally considered as brittle materials, small-scale cavity expansion is more like a ductile process. Our results have broad implications for understanding and controlling failure in soft solids. arXiv:1811.00841v2 [cond-mat.soft]

The existence of maximum human lifespan remains a puzzle in aging research. Maximum human lifespan is believed to be around 125 years, whereas current demographic trends seem to show no limitation. To reconcile this contrast, the estimation of maximum human lifespan requires an adequate mathematical model. However, sparse data of available old-age mortality pattern make the estimation impossible. Here we suggest an extended Weibull model for the estimation using a proper mathematical method based on survival probability pattern. We find a tendency that survival probability is maximized in modern human survival curves. Based on such tendency, we develop an estimation method for maximum human lifespan and indeed obtain about 126 years from periodic life tables for Swedish female between 1950 and 2005. Despite uncertainty from available mortality data, our approach may offer quantitative biodemographic opportunities linking aging and survival kinetics.