Controlling the wetting behaviour of liquids on surfaces is important for a variety of industrial applications such as water-repellent coatings and lubrication. Liquid behaviour on a surface can range from complete spreading, as in the 'tears of wine' effect, to minimal wetting as observed on a superhydrophobic lotus leaf. Controlling droplet movement is important in microfluidic liquid handling, on self-cleaning surfaces and in heat transfer. Droplet motion can be achieved by gradients of surface energy. However, existing techniques require either a large gradient or a carefully prepared surface to overcome the effects of contact line pinning, which usually limit droplet motion. Here we show that two-component droplets of well-chosen miscible liquids such as propylene glycol and water deposited on clean glass are not subject to pinning and cause the motion of neighbouring droplets over a distance. Unlike the canonical predictions for these liquids on a high-energy surface, these droplets do not spread completely but exhibit an apparent contact angle. We demonstrate experimentally and analytically that these droplets are stabilized by evaporation-induced surface tension gradients and that they move in response to the vapour emitted by neighbouring droplets. Our fundamental understanding of this robust system enabled us to construct a wide variety of autonomous fluidic machines out of everyday materials.

a b s t r a c tA new technique is presented for evaluating the effective properties of linearly elastic, multi-phase unidirectional composites. Various effects on the fiber/matrix interfaces (perfect bond, homogeneously imperfect interfaces, uniform interphase layers) are allowed. The analysis of nano-composite materials based on the Gurtin and Murdoch model of material surface is also included. The basic idea of the approach is to construct a circular inhomogeneity in an infinite plane whose effects on the displacements and stresses at distant points are the same as those of a finite cluster of inhomogeneities (fibers of circular cross-section) arranged in a pattern representative of the composite material in question. The elastic properties of the equivalent inhomogeneity then define the effective elastic properties of the material. The volume ratio of the composite material is found after the size of the equivalent circular inhomogeneity is defined in the course of the solution procedure. This procedure is based on a semi-analytical solution of a problem of an infinite plane containing a cluster of non-overlapping circular inhomogeneities subjected to loading at infinity. The method works equally well for periodic and random composites and -importantly -eliminates the necessity for averaging either stresses or strains. New results for nano-composite materials are presented.

When a mixture of propylene glycol and water is deposited on a clean glass slide, it forms a droplet of a given apparent contact angle rather than spreading as one would expect on such a high-energy surface. The droplet is stabilized by a Marangoni flow due to the non-uniformity of the components' concentrations between the border and the apex of the droplet, itself a result of evaporation. These self-contracting droplets have unusual properties such as absence of pinning and the ability to move under an external humidity gradient. The droplets' apparent contact angles are a function of their concentration and the external humidity. Here we study the motion of such droplets sliding down slopes and compare the results to normal non-volatile droplets. We precisely control the external humidity and explore the influence of the volume, viscosity, surface tension, and contact angle. We find that the droplets suffer a negligible pinning force so that for small velocities the capillary number (Ca) is directly proportional to the Bond number (Bo): Ca = Bo sin α with α the angle of the slope. Lastly we study the successive shapes the droplets take when sliding at larger and larger velocities.