Dynamics and instabilities of the free boundary of a two-dimensional dry active nematic aggregate

Abstract

The dynamics of a two-dimensional aggregate of active rod-shaped particles in the nematic phase with a free boundary is considered theoretically. The aggregate is in contact with a hard boundary at y = 0, a free boundary at y = H(x, t), and in the x-direction the aggregate is of infinite extension. By assuming fast relaxation of the director field, we find instabilities driven by the coupling between the deformation of the free boundary and the active stress in parameter regimes where bulk systems are stable. For a contractile aggregate, when the particles are aligned parallel to the boundaries, the system is unstable in the long wavelengths at any strength of contractility for any H, and the critical wavelength increases as H increases; when the particles are aligned perpendicular to the boundaries, the system acquires a finite-wavelength instability at a critical active stress whose strength decreases as H increases. The behavior for an aggregate with steady-state particle density ρ s , strength of active stress χ, bulk modulus ρ s β, and particles aligned perpendicular to the boundaries can be mapped to one with active stress strength − χ, bulk modulus ρ s (β − χ), and particles aligned parallel to the boundaries. The stability of an extensile aggregate can be obtained from the analysis for contractile aggregates through this mapping as well, even though the corresponding physical mechanisms for the instabilities are different. In the limit H → ∞ , the free boundary is unstable for any contractile or extensile systems in the long-wavelength limit.