Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $\pi/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.Comment: 24 pages, 19 figure

How do mosquito eggs self-assemble on the water surface?

This work reports a detailed numerical study of the behavior of ellipsoid-shaped particles adsorbed at fluid interfaces. Former experiments have shown that micrometer-sized prolate ellipsoids aggregate under the action of strong and long-ranged capillary interactions. The latter are due to nonplanar contact lines and to the resulting deformations of the interface in the vicinity of the trapped objects. We first consider the case of a single ellipsoid and examine in detail the influence of contact angle and ellipsoid aspect ratio on interfacial distortions. We then focus on two contacting ellipsoids and study the optimum packing configuration depending on their size and/or aspect ratio mismatch. We thoroughly explore the variety of contact configurations between both ellipsoids and provide corresponding energy maps. Whereas the side-by-side configuration is the most stable state for identical ellipsoids, we find that the mismatched pair adopts an "arrow" configuration in which a finite angle exists between the particles long axes. Such arrows are actually seen in experiments with micron-sized ellipsoids and similarly with millimeter-sized mosquito eggs. These results complement our previous work (J.C. Loudet, B. Pouligny, EPL 85, 28003 (2009)) and highlight the importance of geometrical factors to explain the morphology of aggregated structures at fluid interfaces