Comment on "Curvature capillary migration of microspheres" by N. Sharifi-Mood, I. B. Liu and K. J. Stebe, Soft...

In a recent paper, Nima Sharifi-Mood et al. analyzed the capillary insertion energy of a spherical colloid at the interface between a liquid and a vapor phase under equilibrium wetting conditions. They claim that, contrary to what previously found, the insertion energy would be zero up to corrections of order four in the deviatoric curvature of the interface. I show that this conclusion is incorrect and comes from the failure of the small angle approximation far from the colloid. Once this approximation is lifted, I recover the leading quadratic contribution first derived by Würger [A. Würger, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2006, 74, 041402]. This same approximation was employed by Lu Yao et al. [Lu Yao et al., J. Colloid Interface Sci., 2014, 449, 436] in the case of pinned contact lines. The resulting expression, which is used by Nima Sharifi-Mood et al. to analyze their experimental data, is off by a factor of two and misses a term quadratic in the deviatoric curvature.