Inertia drives a flocking phase transition in viscous active fluids

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)].

arXiv commentVersion of the manuscript accepted in PRX

References in corpus (45)

• The hydrodynamics of swimming microorganisms
• The Mechanics and Statistics of Active Matter
• Flocks, herds, and schools: A quantitative theory of flocking
• Spontaneous motion in hierarchically assembled active matter
• Meso-scale turbulence in living fluids
• Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles
• Fluid dynamics of bacterial turbulence
• Rheology of Active-Particle Suspensions
• Generic theory of active polar gels: a paradigm for cytoskeletal dynamics
• The 2019 Motile Active Matter Roadmap
• First-Principles Experimental Demonstration of Ferroelectricity in a Thermotropic Nematic Liquid Crystal: Spontaneous Polar Domains and Striking Electro-Optics
• Superfluid transport of information in turning flocks of starlings
• Spontaneous flow transition in active polar gels
• Defect annihilation and proliferation in active nematics
• Orientational order of motile defects in active nematics
• Defect dynamics in active nematics
• Diffusion and spatial correlations in suspensions of swimming particles
• Spontaneous symmetry breaking in active droplets provides a generic route to motility
• Topological structure and dynamics of three dimensional active nematics
• Onset of meso-scale turbulence in living fluids
• Phase Diagram of the Two-Dimensional Complex Ginzburg-Landau Equation
• Model of collective fish behavior with hydrodynamic interactions
• Data-driven quantitative modeling of bacterial active nematics
• Vorticity, Defects and Correlations in Active Turbulence
• Universal scaling of active nematic turbulence
• Collective Motion of Self-Propelled Particles with Memory
• Complex Spontaneous Flows and Concentration Banding in Active Polar Films
• Birth, Death and Flight: A Theory of Malthusian Flocks
• Characterization of the transition from defect- to phase-turbulence
• Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks
• Asymmetric exchange in flocks
• Surface tank-treading: propulsion of Purcell's toroidal swimmer
• Origins and diagnostics of the nonequilibrium character of active systems
• Activating membranes
• Polar Patterns in Active Fluids
• Hydrodynamics of polar liquid crystals
• Multi-scale statistics of turbulence motorized by active matter
• Silent Flocks
• Twist-induced crossover from 2D to 3D turbulence in active nematics
• Swimmers in thin films: from swarming to hydrodynamic instabilities
• Swimmer suspensions on substrates: anomalous stability and long-range order
• Transition in swimming direction in a model self-propelled inertial swimmer
• Spectral energy analysis of bulk three-dimensional active nematic turbulence
• Kinematics of a simple reciprocal model swimmer at intermediate Reynolds numbers
• Coarsening in the two-dimensional incompressible Toner-Tu equation: Signatures of turbulence

Cited by in corpus (14)

• Effects of inertia on conformation and dynamics of tangentially-driven active filaments
• Tuning Nonequilibrium Phase Transitions with Inertia
• Emerging mesoscale flows and chaotic advection in dense active matter
• Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles
• Defect turbulence in a dense suspension of polar, active swimmers
• Inertia drives concentration-wave turbulence in swimmer suspensions
• Microswimmers knead nematics into cholesterics
• Properties of the dissipation functions for passive and active systems
• Crossover dynamics and non-Gaussian fluctuations in inertial active chains
• Inertia-chirality interplay in active Brownian motion: exact dynamics and phase maps
• Non-reciprocal mixtures in suspension: the role of hydrodynamic interactions
• Instabilities and turbulence in extensile swimmer suspensions
• Nematic order condensation and topological defects in inertial active nematics
• Dynamical arrest in active nematic turbulence