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)].
Highlights
The theory of active matter [1,2,3,4,5,6,7,8,9]—systems whose constituents convert a sustained supply of fuel into movement—is the framework of choice for understanding the collective behavior of motile particles
A recent perspective [45] makes a persuasive case for the study of active fluids with small but non-negligible inertia, the regime we explore here
Summary of results In this article, focusing on extensile or “pusher” [50] suspensions, we show that the introduction of inertia qualitatively alters our understanding of the viscous hydrodynamics of polar active matter, that is, flocking in fluids
Summary
The theory of active matter [1,2,3,4,5,6,7,8,9]—systems whose constituents convert a sustained supply of fuel into movement—is the framework of choice for understanding the collective behavior of motile particles. In the world of Stokesian hydrodynamics, where inertia is absent and viscosity holds sway, an ordered flock in bulk fluid is impossible [10]. This limit shapes the defining image of active suspensions as inescapably unstable, dissolving via spontaneous flow [10,11] and defect. A. Summary of results In this article, focusing on extensile or “pusher” [50] suspensions, we show that the introduction of inertia qualitatively alters our understanding of the viscous hydrodynamics of polar active matter, that is, flocking in fluids. IV with a summary, suggestions for experiment, and open questions
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