Capillary interactions among spherical particles at curved liquid interfaces

Abstract

We study the effect of interfacial curvature on the binding energy and forces exerted on small spherical particles that adsorb on an interface between two immiscible liquids. When the interface has anisotropic curvature, the constant-contact-angle condition at the particle-fluid boundary requires a deformation of the interface. Focusing on the case of an initially cylindrical interface, we predict the shape after a spherical particle binds. We then calculate the energy of adsorption and find that it depends on the shape of the interface very far from the binding site. Turning to the problem of two adsorbed spherical particles, we predict a capillary interaction that arises purely from the deformations caused by the contact-angle condition. An analogy is made between these curvature-induced capillary forces and electrostatic forces between quadrupoles in two dimensions. We conclude with a conjectured general form for the interaction of a single spherical particle with the Gaussian curvature of the underlying fluid interface, which we compare to previous work.