Effects of Confinement on Free Energy of Particles at Fluid Interfaces

Guzowski, J.¹, Tasinkevych, M¹ and Dietrich, S¹

¹Max Planck Institute for Metals Research, Stuttgart, Germany

Two-dimensional colloids, formed by micron-sized particles trapped at fluid interfaces, have recently received a great deal of attention in view of the various possible applications such as controlled self-assembly, mesoscale structure formation and study of two-dimensional melting. In this work we investigate the effects of confinement and curvature on the free energy of a system composed of a particle floating at the surface of a sessile drop. Due to the presence of the substrate one has to solve the boundary value problem for the shape of the droplet, governed in the small deformation limit by the two-dimensional Helmholtz equation. To do this, we propose a capillary analogue of the image method, known from electrostatics. The full numerical minimization of the free energy agrees very well with the obtained analytical solution. We show, that the substrate provides a confining potential for the particle and that the equilibrium configuration depends on the type of the boundary conditions (pinned or free contact line). Moreover, on the contrary to the case of a flat interface, we find that the capillary interactions on a curved interface are non-monotonic, which may induce clustering in the many-particle case.