# Phoretic Interactions Between Active Droplets

## TL;DR

This paper investigates how concentration gradients mediate interactions between active droplets, revealing a diffusion-limited, repulsive force that scales with distance and is characterized by a measurable lengthscale.

## Contribution

It uncovers a regime where solute-gradients cause droplet interactions without autophoresis, providing a quantitative model of the force and its dependence on droplet size and solute concentration.

## Key findings

- Repulsive force scales as 1/r^2 between droplets
- Interaction process is diffusion-limited, not reaction rate limited
- Measured lengthscale of interaction is approximately 16 nm

## Abstract

Concentration gradients play a critical role in embryogenesis, bacterial locomotion, as well as the motility of active particles. Particles develop concentration profiles around them by dissolution, adsorption, or the reactivity of surface species. These gradients change the surface energy of the particles, driving both their self-propulsion and governing their interactions. Here we uncover a regime in which solute-gradients mediate interactions between slowly dissolving droplets without causing autophoresis. This decoupling allows us to directly measure the steady-state, repulsive force, which scales with interparticle distance as $F\sim {1/r^{2}}$. Our results show that the process is diffusion rather than reaction rate limited, and the theoretical model captures the dependence of the interactions on droplet size and solute concentration, using a single fit parameter, $l=16\pm 3$~nm, which corresponds to the lengthscale of a swollen micelle. Our results shed light on the out-of-equilibrium behavior of particles with surface reactivity.