# Phoretic Interactions Generically Induce Dynamic Clusters and Wave Patterns in Active Colloids

## TL;DR

This paper presents a minimal model demonstrating that phoretic interactions in active colloids can universally induce pattern formations like waves and clusters, even at low densities, aligning with experimental observations.

## Contribution

It introduces a simplified model linking self-propulsion and phoretic interactions, revealing universal pattern formation in active colloids.

## Key findings

- Phoretic interactions induce pattern formation in dilute Janus colloids.
- Pattern types include waves and dynamic clusters.
- Universal phase diagram describes conditions for pattern emergence.

## Abstract

We introduce a representative minimal model for phoretically interacting active colloids. Combining kinetic theory, linear stability analyses, and a general relation between self-propulsion and phoretic interactions in auto-diffusiophoretic and auto-thermophoretic Janus colloids collapses the parameter space to two dimensions: area fraction and P\'eclet number. This collapse arises when the lifetime of the self-generated phoretic fields is not too short, and leads to a universal phase diagram showing that phoretic interactions {\it generically} induce pattern formation in typical Janus colloids, even at very low density. The resulting patterns include waves and dynamic aggregates closely resembling the living clusters found in experiments on dilute suspension of Janus colloids.