# Nonequilibrium dynamics of mixtures of active and passive colloidal particles

## TL;DR

This paper develops a mesoscopic field theory to analyze the nonequilibrium dynamics of active and passive colloidal mixtures, predicting instabilities and cluster behaviors that align with simulations.

## Contribution

It introduces a novel field theory for active-passive colloidal mixtures and identifies two types of spinodal instabilities, including a Hopf bifurcation leading to moving clusters.

## Key findings

- Good agreement between theory and particle simulations.
- Identification of two spinodal instability types.
- Prediction of moving clusters in active-passive mixtures.

## Abstract

We develop a mesoscopic field theory for the collective nonequilibrium dynamics of multicomponent mixtures of interacting active (i.e., motile) and passive (i.e., nonmotile) colloidal particles with isometric shape in two spatial dimensions. By a stability analysis of the field theory, we obtain equations for the spinodal that describes the onset of a motility-induced instability leading to cluster formation in such mixtures. The prediction for the spinodal is found to be in good agreement with particle-resolved computer simulations. Furthermore, we show that in active-passive mixtures the spinodal instability can be of two different types. One type is associated with a stationary bifurcation and occurs also in one-component active systems, whereas the other type is associated with a Hopf bifurcation and can occur only in active-passive mixtures. Remarkably, the Hopf bifurcation leads to moving clusters. This explains recent results from simulations of active-passive particle mixtures, where moving clusters and interfaces that are not seen in the corresponding one-component systems have been observed.