Comment on "Curvature capillary migration of microspheres" by N. Sharifi-Mood, I.B. Liu, K.J. Stebe, Soft Matter 11, 6768 (2015), arXiv:1502.01672

In a recent paper, Sharifi-Mood et al. study colloidal particles trapped at a liquid interface with opposite principal curvatures $c_{1}=-c_{2}$. In the theory part, they claim that the trapping energy vanishes at second order in $\Delta c=c_{1}-c_{2}$, which would invalidate our previous result [Phys. Rev. E 74, 041402 (2006)]. Here we show that this claim arises from an improper treatment of the outer boundary condition on the deformation field. For both pinned and moving contact lines, we find that the outer boundary is irrelevant, which confirms our previous work. More generally, we show that the trapping energy is determined by the deformation close to the particle and does not depend on the far-field.