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  • Open Access

Order by Inertia in Spinning Active Matter: Holey Fluids and Spin-Textured Crystals

Camille Jorge1,2 and Denis Bartolo1,*

  • *Contact author: denis.bartolo@ens-lyon.fr
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Phys. Rev. X 16, 041034 – Published 6 November, 2026

DOI: https://doi.org/10.1103/xyym-pjh7

Abstract

Active matter sustains emergent flows at the expense of preserving structural order. The feedback between structure and viscous flows typically disrupts crystalline and liquid-crystalline organization by amplifying the very deformations they generate. Yet this destabilizing paradigm has recently been challenged by experiments showing that inertial fluid flows can stabilize few-body bound states of active spinners. Whether inertial active matter can sustain genuine cohesion and order at the many-body level, however, remains elusive. Here we investigate two-dimensional assemblies of macroscopic spinners operating at high Reynolds number and uncover two phase transitions leading to the emergence of a dilute percolating fluid and a dense spin-textured crystal. At low density, inertial flows generate two competing interactions: anisotropic attractions and transverse Magnus forces that continuously break and reconfigure bonds. Together they drive a percolation transition toward a dynamically rearranging holey liquid reminiscent of the empty-liquid states observed in equilibrium patchy colloids. At high density, the feedback between spin alignment and particle positions suppresses transverse rearrangements and yields a first-order transition toward a spin-ordered crystal. Our results demonstrate that, beyond the overdamped limit, hydrodynamic feedback can promote rather than destroy collective order, revealing a distinct regime of many-body active matter governed by inertial flows.

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Popular Summary

Active matter is driven from within by units capable of autonomous motion. At small scales, where viscous forces dominate, active flows typically destabilize ordered structures. Here, we explore a regime of active matter in which inertia plays an organizing role at the many-body level. We experimentally investigate a suspension of macroscopic spinning particles that stir the surrounding fluid at high Reynolds numbers and show that the inertial flows produced by the spinners organize the system into collective phases with remarkable structure. Using quantitative measurements of particle and spin correlations, and hydrodynamic modeling, we show that these phases emerge from the interplay between directional pumping flows, which attract particles along their spin axis, and transverse Magnus forces, which continuously rearrange their bonds. The findings reveal a previously unexplored regime of active matter in which inertia promotes collective organization, establishing new connections between active matter, inertial hydrodynamics, and nonequilibrium phase transitions.

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Phys. Rev. X 16, 041034– Published 6 November, 2026
  • Received 18 May 2026
  • Accepted 22 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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