  We have studied microparticle migration on curved fluid interfaces in
experiment and derived an expression for the associated capillary energy $E$
for two cases, i.e., pinned contact lines and equilibrium contact lines, which
differ from expressions derived by others in the literature. In this problem, a
particle of radius $a$ makes a disturbance in a large domain characterized by
principal radii of curvature $R_1$ and $R_2$. Since $a$ is smaller than all
associated geometric and physico-chemical length scales, analysis calls for a
singular perturbation approach. We recapitulate these concepts, identify
conceptual errors in the Comments about our work, and provide evidence from
experiment and simulation that supports our view.
