Trapping energy of a spherical particle on a curved liquid interface

Abstract

We derive the trapping energy of a colloidal particle at a liquid interface with contact angle θ and principal curvatures c1 and c2. The boundary conditions at the particle surface are significantly simplified by introducing the shift ε of its vertical position. We discuss the undulating contact line and the curvature-induced lateral forces for a single particle and a pair of nearby particles. The single-particle trapping energy is found to decrease with the square of both the total curvature c1+c2 and the anisotropy c1−c2. In the case of non-uniform curvatures, the resulting lateral force pushes particles toward more strongly curved regions.