# Inertia drives a flocking phase transition in viscous active fluids

## TL;DR

This paper investigates how inertia influences phase transitions in viscous active fluids, revealing a critical dimensionless parameter that governs the transition from turbulence to flocking, with implications for mesoscale swimmer suspensions.

## Contribution

It introduces a dimensionless parameter R that predicts a continuous flocking transition driven by inertia in viscous active suspensions.

## Key findings

- Inertia induces a flocking phase transition in viscous active fluids.
- The transition is continuous with a growing correlation length near the threshold.
- Numerical simulations confirm the transition and steady states in 2D and 3D.

## Abstract

How fast must an oriented collection of extensile swimmers swim to escape the instability of viscous active suspensions? We show that the answer lies in the dimensionless combination $R=\rho v_0^2/2\sigma_a$, where $\rho$ is the suspension mass density, $v_0$ the swim speed and $\sigma_a$ the active stress. Linear stability analysis shows that for small $R$ disturbances grow at a rate linear in their wavenumber $q$, and that the dominant instability mode involves twist. The resulting steady state in our numerical studies is isotropic hedgehog-defect turbulence. Past a first threshold $R$ of order unity we find a slower growth rate, of $O(q^2)$; the numerically observed steady state is {\it phase-turbulent}: noisy but {\it aligned} on average. We present numerical evidence in three and two dimensions that this inertia driven flocking transition is continuous, with a correlation length that grows on approaching the transition. For much larger $R$ we find an aligned state linearly stable to perturbations at all $q$. Our predictions should be testable in suspensions of mesoscale swimmers [D Klotsa, Soft Matter \textbf{15}, 8946 (2019)].