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

TL;DR

This paper critiques a recent study on colloidal particles at liquid interfaces, clarifying that the trapping energy depends on local deformation near the particle rather than the far-field, reaffirming previous results.

Contribution

The authors identify an error in the previous work's boundary condition treatment and demonstrate that the trapping energy is governed by local deformation, not the outer boundary.

Findings

Outer boundary condition is irrelevant for trapping energy.

Trapping energy depends on local deformation near the particle.

Previous results are validated despite the critique.

Abstract

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.