Driven particles at fluid interfaces acting as capillary dipoles

TL;DR

This paper investigates the asymptotic dynamics of spherical particles driven along fluid interfaces, revealing that their capillary interactions are dipolar and decay with the fifth power of separation, influenced by particle velocity and interface deformation.

Contribution

It introduces a theoretical analysis of driven particles at fluid interfaces, showing their capillary interactions are dipolar and dominate over quadrupolar effects at moderate velocities.

Findings

Capillary interaction force is dipolar in azimuthal angle.

Interaction force decays with the fifth power of separation.

Dipolar interaction exceeds quadrupolar at moderate velocities.

Abstract

The dynamics of spherical particles driven along an interface between two immiscible fluids is investigated asymptotically. Under the assumptions of a pinned three-phase contact line and very different viscosities of the two fluids, a particle assumes a tilted orientation. As it moves, it causes a deformation of the fluid interface which is also computed. The case of two interacting driven particles is studied via the Linear Superposition Approximation. It is shown that the capillary interaction force resulting from the particle motion is dipolar in terms of the azimuthal angle and decays with the fifth power of the inter-particle separation, similar to a capillary quadrupole originating from undulations of the three-phase contact line. The dipolar interaction is demonstrated to exceed the quadrupolar interaction at moderate particle velocities.