Effective field theory approach to fluctuation-induced forces between colloids at an interface

TL;DR

This paper presents an effective field theory method for calculating fluctuation-induced forces between colloids on fluid interfaces, simplifying complex integrals and enabling systematic analysis of interactions.

Contribution

It introduces an EFT framework that models particles as points, systematically incorporates size and shape effects, and facilitates efficient computation of multi-body and ground-state interactions.

Findings

Derived a complete asymptotic expansion for pair interactions.

Demonstrated efficient computation of multi-body forces.

Showcased systematic analysis of ground-state interactions.

Abstract

We discuss an effective field theory (EFT) approach to the computation of fluctuation-induced interactions between particles bound to a thermally fluctuating fluid surface controlled by surface tension. By describing particles as points, EFT avoids computing functional integrals subject to difficult constraints. Still, all information pertaining to particle size and shape is systematically restored by amending the surface Hamiltonian with a derivative expansion. The free energy is obtained as a cumulant expansion, for which straightforward techniques exist. We derive a complete description for rigid axisymmetric objects, which allows us to develop a full asymptotic expansion in powers of the inverse distance for the pair interaction. We also demonstrate by a few examples the efficiency with which multibody interactions can be computed. Moreover, although the main advantage of the EFT approach lies in explicit computation, we discuss how one can infer certain features of cases involving flexible or anisotropic objects. The EFT description also permits a systematic computation of ground-state surface-mediated interactions, which we illustrate with a few examples.