# Condensate formation and multiscale dynamics in two-dimensional active suspensions

## TL;DR

This paper investigates the formation of condensates and multiscale dynamics in dense two-dimensional active suspensions, providing a justification for Navier-Stokes-based models and exploring transition scenarios from active turbulence to large-scale pattern formation.

## Contribution

It justifies one-fluid models for dense 2D active suspensions and analyzes the transition to condensate formation, including hysteresis and a low-dimensional model of the transition.

## Key findings

- Support for two non-equilibrium steady states with and without condensate
- Identification of a subcritical transition between turbulence and condensate states
- Development of a low-dimensional model capturing the transition dynamics

## Abstract

The collective effects of microswimmers in active suspensions result in active turbulence, a spatiotemporally chaotic dynamics at mesoscale, which is characterized by the presence of vortices and jets at scales much larger than the characteristic size of the individual active constituents. To describe this dynamics, Navier-Stokes-based one-fluid models driven by small-scale forces have been proposed. Here, we provide a justification of such models for the case of dense suspensions in two dimensions (2d). We subsequently carry out an in-depth numerical study of the properties of one-fluid models as a function of the active driving in view of possible transition scenarios from active turbulence to large-scale pattern, referred to as condensate, formation induced by the classical inverse energy cascade in Newtonian 2d turbulence. Using a one-fluid model it was recently shown (Linkmann et al., Phys. Rev. Lett. (in press)) that two-dimensional active suspensions support two non-equilibrium steady states, one with a condensate and one without, which are separated by a subcritical transition. Here, we report further details on this transition such as hysteresis and discuss a low-dimensional model that describes the main features of the transition through nonlocal-in-scale coupling between the small-scale driving and the condensate.