Capillary interactions in Pickering emulsions

TL;DR

This paper analytically calculates capillary interaction potentials for small particles on liquid droplets, revealing different behaviors for monopoles, dipoles, and quadrupoles, with implications for particle assembly at interfaces.

Contribution

It provides the first analytical expressions for capillary interactions of particles with different multipole moments on droplets, comparing these with numerical surface energy minimization.

Findings

Pair potentials show repulsion at large angles and attraction at small angles for monopoles and dipoles.

Quadrupoles do not exhibit the same change in interaction character, unlike monopoles and dipoles.

Analytical results for quadrupoles agree with numerical minimization of surface free energy.

Abstract

The effective capillary interaction potentials for small colloidal particles trapped at the surface of liquid droplets are calculated analytically. Pair potentials between capillary monopoles and dipoles, corresponding to particles floating on a droplet with a fixed center of mass and subjected to external forces and torques, respectively, exhibit a repulsion at large angular separations and an attraction at smaller separations, with the latter resembling the typical behavior for flat interfaces. This change of character is not observed for quadrupoles, corresponding to free particles on a mechanically isolated droplet. The analytical results for quadrupoles are compared with the numerical minimization of the surface free energy of the droplet in the presence of ellipsoidal particles.