Trapping energy of a spherical particle on a curved liquid interface

• We obtain the curvature-induced correction to the trapping energy.
• The energy functional is obtained from a variational principle.
• Our results are rigorous at second order in the curvature.
• The curvature anisotropy enhances trapping, whereas the mean curvature is unfavorable.

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.

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