# Phoretic and hydrodynamic interactions of weakly-confined autophoretic particles

## TL;DR

This paper develops a model for weakly-confined autophoretic particles, revealing that confinement causes their chemical and hydrodynamic interactions to share the same scaling but with opposite signs, significantly affecting their collective behavior.

## Contribution

It introduces the first model for phoretic particle interactions in Hele-Shaw confinement, showing the reversal of interaction signs and analyzing collective dynamics in such environments.

## Key findings

- Phoretic and hydrodynamic interactions share the same scaling in confinement.
- Interactions are of opposite signs, affecting particle motion.
- Suspensions exhibit swirling and clustering behaviors influenced by surface properties.

## Abstract

Phoretic particles self-propel using self-generated physico-chemical gradients at their surface. Within a suspension, they interact hydrodynamically by setting the fluid around them into motion, and chemically by modifying the chemical background seen by their neighbours. While most phoretic systems evolve in confined environments due to buoyancy effects, most models focus on their interactions in unbounded flows. Here, we propose a first model for the interaction of phoretic particles in Hele-Shaw confinement and show that in this limit, hydrodynamic and phoretic interactions share not only the same scaling but also the same form, albeit in opposite directions. In essence, we show that phoretic interactions effectively reverse the sign of the interactions that would be obtained for swimmers interacting purely hydrodynamically. Yet, hydrodynamic interactions can not be neglected as they significantly impact the magnitude of the interactions. This model is then used to analyse the behaviour of a suspension. The suspension exhibits swirling and clustering collective modes dictated by the orientational interactions between particles, similar to hydrodynamic swimmers, but here governed by the surface properties of the phoretic particle; the reversal in the sign of the interaction tends to slow down the swimming motion of the particles.