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Arrested development and traveling waves of active suspensions in nematic liquid crystals

Jingyi Li1, Laurel Ohm1, and Saverio E. Spagnolie1,2,*

  • *Contact author: spagnolie@math.wisc.edu
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Phys. Rev. Fluids 10, 083301 – Published 1 August, 2025

DOI: https://doi.org/10.1103/bqz4-gdvb

Abstract

Active particles in anisotropic, viscoelastic fluids experience competing stresses which guide their trajectories. An aligned suspension of particles can trigger a hydrodynamic bend instability, but the elasticity of the fluid can drive particle orientations back towards alignment. To study these competing effects, we examine a dilute suspension of active particles in an Ericksen-Leslie model nematic liquid crystal. An anchoring strength linking the active and passive media tunes the system between active suspension theory in Newtonian fluids in one limit and active nematic theory in another. For extensile active stresses, beyond a critical active Ericksen number or particle concentration, the suspension first comes into alignment, then buckles via a classical bend instability. Rather than entering the fully developed roiling state observed in isotropic fluids, the development is arrested into a steady, flowing state by fluid elasticity. Arrested states of higher wave number appear at yet larger extensile activity, and a phase transition is identified at finite anchoring strength. If the active particles are motile, the particles can surf along the bent environment of their own creation. More exotic states are also observed, including a oscillatory “thrashing” mode. Moment equations are derived, compared to kinetic theory simulations, and analyzed in asymptotic limits which admit exact expressions for the traveling wave speed and both particle orientation and director fields in the first arrested state.

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Phys. Rev. Fluids 10, 083301– Published 1 August, 2025
  • Received 28 October 2024
  • Accepted 24 June 2025
Article part of CHORUS
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