Anisotropies in thermal Casimir interactions: ellipsoidal colloids trapped at a fluid interface

TL;DR

This paper investigates how thermal fluctuations induce anisotropic Casimir-like forces between ellipsoidal colloids at fluid interfaces, considering both fixed and fluctuating colloid positions and orientations.

Contribution

It provides explicit expressions for the anisotropic Casimir interactions between ellipsoids, accounting for various colloid fluctuation scenarios, and highlights the transition from isotropic to anisotropic forces.

Findings

At large distances, fixed colloids experience isotropic, attractive, long-range interactions.

Including colloid fluctuations introduces anisotropy and changes the decay to a power law.

The decay power varies from 4 to 8 depending on fluctuation constraints.

Abstract

We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. In this system the restriction of the long--ranged interface fluctuations by particles gives rise to fluctuation--induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example for the Casimir effect with fluctuating boundary conditions. In the approach taken here, the Casimir interaction is rewritten as the interaction between fluctuating multipole moments of an auxiliary charge density--like field defined on the area enclosed by the contact lines. These fluctuations are coupled to fluctuations of multipole moments of the contact line position (due to the possible position and orientational fluctuations of the colloids). We obtain explicit expressions for the behavior of the Casimir interaction at large distances for arbitrary ellipsoid aspect ratios. If colloid fluctuations are suppressed, the Casimir interaction at large distances is isotropic, attractive and long ranged (double--logarithmic in the distance). If, however, colloid fluctuations are included, the Casimir interaction at large distances changes to a power law in the inverse distance and becomes anisotropic. The leading power is 4 if only vertical fluctuations of the colloid center are allowed, and it becomes 8 if also orientational fluctuations are included.