Capillary force and torque on spheroidal particles floating at a fluid interface beyond the superposition approximation.

Abstract

By means of a perturbative scheme, we determine analytically the capillary energy of a spheroidal colloid floating on a deformed fluid interface in terms of the local curvature tensor of the background deformation. We validate our results, that hold for small ellipticity of the particle and small deformations of the surface, by an exact numerical calculation. As an application of our perturbative approach, we determine the asymptotic interaction, for large separations d, between two different spheroidal particles. The dominant contribution is quadrupolar and proportional to d(-4). It coincides with the known superposition approximation and is zero if one of the two particles is spherical. The next to leading approximation, proportional to d(-8), is always attractive and independent of the orientation of the two colloids. It is the dominant contribution to the interaction between a spheroidal and a spherical colloid.