Curvature-induced capillary interaction of spherical particles at a liquid interface.

We consider a liquid interface with different principal curvatures +/-c and find that the mere presence of a spherical particle leads to a deformation field of quadrupolar symmetry; the corresponding "capillary quadrupole moment" is given by the ratio of the particle size and the curvature radius. The resulting pair interaction of nearby particles is anisotropic and favors the formation of aggregates of cubic symmetry. Since the single-particle trapping energy depends quadratically on curvature with a negative prefactor, a curvature gradient induces a lateral force that pushes the particles towards strongly curved regions of the interface. As an illustration we discuss the effects occurring on a catenoid.