Long distance attraction between particles in a soap film

TL;DR

This study investigates the long-range, asymmetric attraction between particles in a soap film, revealing non-reciprocal interactions influenced by boundary conditions and particle positions.

Contribution

It provides the first detailed measurement and theoretical modeling of non-reciprocal forces between particles in a soap film, highlighting boundary condition effects.

Findings

Particles exhibit long-range attraction with asymmetric force magnitude and direction.

Force asymmetry can reach up to 150% depending on particle positions.

Reciprocity of forces is restored when particles are near the film center.

Abstract

Millimeter-sized particles trapped at the surface of a liquid bath attract each other through the deformation of the liquid-air interface, a phenomenon known as "the Cheerios effect". We consider here a situation similar at first sight: the interaction between two millimeter-sized particles trapped in an horizontal soap film. In this geometry, the deformation of the film due to the weight of one particle extends over the entire system size, which induces an extremely long-ranged attraction. Combined with the low viscous friction in the film, this leads to intricate particle orbits, lasting up to ten seconds before the two particles eventually collide. By tracking the particles dynamics, we measure the force exerted by each particle on the other, and we develop a theoretical model. Because the interface deformation induced by a particle depends on its position in the soap film, the attractive force has two features that fundamentally depart from classical interaction forces. The force exerted by one particle on the other differs both in direction and magnitude from the reverse interaction, with an asymmetry reaching 150% when one particle is close to the center and the other one close to the frame. Reciprocity is recovered when both particles are close to the film center. These results are a original example of non-reciprocal effective interactions due to boundary conditions.