Scattering Approach for Fluctuation--Induced Interactions at Fluid Interfaces

TL;DR

This paper introduces a scattering formalism to compute fluctuation-induced interactions among colloids at fluid interfaces, accounting for boundary fluctuations, and applies it to spherical colloids to analyze multi-particle effects.

Contribution

The paper develops a general scattering approach incorporating boundary fluctuations to study colloidal interactions at fluid interfaces, extending previous methods to multi-particle systems.

Findings

The formalism reproduces known two-particle results.

Analytical expressions for three-particle interactions at large separations.

Three-body effects vary with colloid fluctuations, enhancing or diminishing attractions.

Abstract

We develop the scattering formalism to calculate the interaction between colloidal particles trapped at a fluid interface. Since, in addition to the interface, the colloids may also fluctuate in this system, we implement the fluctuation of the boundaries into the scattering formalism and investigate how the interaction between colloids is modified by their fluctuations. This general method can be applied to any number of colloids with various geometries at an interface. We apply the formalism derived in this work to a system of spherical colloids at the interface between two fluid phases. For two spherical colloids, this method very effectively reproduces the previous known results. For three particles we find analytical expressions for the large separation asymptotic energies and numerically calculate the Casimir interaction at all separations. Our results show an interesting three body effect for fixed and fluctuating colloids. While the three body effect strengthens the attractive interaction between fluctuating colloids, it diminishes the attractive force between colloids fixed at an interface.