Capillary Interactions at Curved Interfaces

Capillary Interactions at Sessile Drops Colloidal particles of intermediate wettability usually adsorb at fluid-fluid interfaces. This configuration is extremely stable against thermal fluctuations due to the very large free energy of adsorption for micron-sized particles. A quasi two-dimensional colloid structures arises at the interface, the presence of which gives rise to a novel phenomenology compared with three-dimensional colloidal structures in bulk. These physical systems provide a testbed for various fundamental questions in theoretical physics such as the Kosterlitz-Thouless scenario for two-dimensional melting. Besides the basic interest in these systems, understanding and controlling self-assembly at interfaces is of technological importance for manufacturing of electronic-papers and electrophoretic displays, separation of bacterial species and living cells, trapping of DNA and polymer particles, growth of photonic crystals, as well as extraction technologies such as flotation.

We develop a theoretical understanding of the particle-particle interactions specific to the presence of a fluid interface. The deformation of the fluid interface leads to so-called capillary forces between the particles. This effect is well known, e.g., when small corn flakes floating at the surface of milk tend to adhere at each other or at the cup wall. In these case the interface is deformed by the weight of flakes, i.e. the effects of gravity is of importance. This force spans over separations of about one millimeter, making it a rather long-ranged force between nanoparticles, in this case the gravity may be ignored completely, and other forces, like electrostatic one for example, are responsible for the deformations of interface.

Very interesting phenomenology emerges when colloidal particles are floating on the surface of a sessile droplet. In this case the capillary forces are very sensitive to the boundary conditions imposed onto the droplet contact line at the substrate. This reflects a subtle interplay between the deformations of the droplet shape, its curvature and the volume constraint. In particular, for the case of a single particle we find attraction of the particle to a free contact line and repulsion from a pinned one, also we observe a local free-energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively.
 
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