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![]() ![]() We exploit this effect to create “hot spots” for particle assembly that have not been predicted previously, and demonstrate particle migration, orientation, and assembly at these preferred sites. Here, we extend our earlier work by showing that particles can be driven along well-defined paths at interfaces owing to interactions driven by imposed gradients in the curvature field. In our recent work, we demonstrated the alignment of rod-like particles along principle axes of curvature. Although these effects have been predicted in theory, they remain largely unexplored in experiment. Because fluid interfaces can be molded and reconfigured using pinning sites, confinement, or applied fields, curvature-driven capillary interactions are potentially powerful means to amplify the magnitude of interactions and to direct microparticle assembly. When an anisotropic particle is placed on a curved fluid interface, capillary interactions arise, as the area of the interface then depends on the particle’s orientation with respect to the principal axes and its location in a curvature gradient, resulting in torques ( 5, 14) and forces ( 5) on the particle. ![]() Therefore, it can be applied to colloids made of any material. The phenomenon is entirely controlled by the coupling between geometry and capillarity. In this work, we show that interface curvature can be employed as an external field to direct the location at which particles assemble. Assembly occurs at random locations on the interface determined by sites of initial encounter between the particles. Hence, once the particles are placed at the interface, the strength of resulting capillary interactions is fixed. At planar interfaces, the magnitude of the interaction is determined by the particle geometry, size, and surface energies. This effect, responsible for clustering of cereal in a bowl of milk ( 7), is now an important means for microparticle assembly at otherwise planar fluid interfaces, in particular for anisotropically shaped objects, which assemble with preferred orientations ( 4, 6, 8– 13). When distortions induced by neighboring particles overlap, the interfacial area decreases, resulting in capillary interactions that cause particles to attract and assemble. When particles distort an interface, spontaneous, long-range interactions occur owing to capillary energy, given by the product of the surface tension and the area of the distortion. These phenomena should be widely useful in the directed assembly of micro- and nanoparticles with potential application in the fabrication of materials with tunable mechanical or electronic properties, in emulsion production, and in encapsulation.įluid interfaces are remarkable sites for directed migration and assembly of particles ( 1– 6). We also report a repulsive interaction, in which microparticles move away from planar bounding walls along curvature gradient contours. We exploit this feature to induce migration and assembly at preferred locations, and to create complex structures. Interface curvature diverges near sharp boundaries, similar to an electric field near a pointed conductor. Trajectories and orientations are predicted by a theoretical model in which capillary forces and torques are related to Gaussian curvature gradients and angular deviations from principal directions of curvature. These interfaces present well-defined curvature fields that orient and steer particles along complex trajectories. We show this in experiments in which the shape of the interface is molded by pinning to vertical pillars of different cross-sections. Capillarity can be used to direct anisotropic colloidal particles to precise locations and to orient them by using interface curvature as an applied field.
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