# Dynamical Theory of the Inverted Cheerios Effect

## TL;DR

This paper develops a dynamical theory for the inverted Cheerios effect, describing how liquid drops interact on deformable substrates by considering elasticity, capillarity, and viscoelasticity, and validates it against experiments.

## Contribution

It introduces a comprehensive dynamical model for droplet interactions on deformable substrates, incorporating elasticity, capillarity, and viscoelastic effects, advancing understanding of this phenomenon.

## Key findings

- The theory accurately predicts droplet attraction and repulsion velocities.
- Both the full and simplified models agree at larger droplet separations.
- Experimental data confirms the models' validity across different conditions.

## Abstract

Recent experiments have shown that liquid drops on highly deformable substrates exhibit mutual interactions. This is similar to the Cheerios effect, the capillary interaction of solid particles at a liquid interface, but now the roles of solid and liquid are reversed. Here we present a dynamical theory for this inverted Cheerios effect, taking into account elasticity, capillarity and the viscoelastic rheology of the substrate. We compute the velocity at which droplets attract, or repel, as a function of their separation. The theory is compared to a simplified model in which the viscoelastic dissipation is treated as a localized force at the contact line. It is found that the two models differ only at small separation between the droplets, and both of them accurately describe experimental observations.