Effective capillary interaction of spherical particles at fluid interfaces

TL;DR

This paper analyzes the forces between spherical particles at fluid interfaces, showing conditions for long-range attraction or short-range interaction, with implications for colloidal assembly and electrostatic tuning.

Contribution

It provides a general framework for understanding capillary interactions of spherical particles, including electrostatic effects, under the superposition approximation.

Findings

Long-range attraction occurs if net force does not vanish.

Interaction is short-ranged if net force vanishes.

Electrostatic fields can tune capillary attraction.

Abstract

We present a detailed analysis of the effective force between two smooth spherical colloids floating at a fluid interface due to deformations of the interface. The results hold in general and are applicable independently of the source of the deformation provided the capillary deformations are small so that a superposition approximation for the deformations is valid. We conclude that an effective long--ranged attraction is possible if the net force on the system does not vanish. Otherwise, the interaction is short--ranged and cannot be computed reliably based on the superposition approximation. As an application, we consider the case of like--charged, smooth nanoparticles and electrostatically induced capillary deformation. The resulting long--ranged capillary attraction can be easily tuned by a relatively small external electrostatic field, but it cannot explain recent experimental observations of attraction if these experimental systems were indeed isolated.