Trapping energy of a spherical particle on a curved liquid interface

We derive the trapping energy of a colloidal particle at a liquid interface with contact angle theta and principal curvatures c(1) and c(2). The boundary conditions at the particle surface are significantly simplified by introducing the shift epsilon 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 c(1) + c(2) and the anisotropy c(1) - c(2). In the case of non-uniform curvatures, the resulting lateral force pushes particles toward more strongly curved regions. (C) 2013 Elsevier Inc. All rights reserved.