Heterogeneity-Induced Oscillations in Active Nematics

One of the defining features of active nematics is that above a critical activity the quiescent state becomes unstable to a distorted, flowing one. We show that spatial variations in activity can fundamentally change the nature of this instability, affecting the symmetry of the unstable mode and producing spontaneous oscillations. We analytically identify a dynamical system for the evolution of the odd and even director modes, with the leading-order coefficients dependent on the activity profile, allowing a quantitative connection between the spatially-heterogeneous activity and dynamics, which we verify numerically. In the context of constant gradients in activity, we determine a phase diagram for the active response and highlight how variation of the activity profile causes the oscillations to vary from almost harmonic to relaxational. Our results indicate a novel route to spatio-temporal structure in active nematics and suggest experiments on controllable light-activated systems.

💡 Research Summary

Active nematics are nonequilibrium fluids whose constituent particles generate internal stresses proportional to an activity parameter ζ. In the canonical theory, ζ is taken to be spatially uniform; when ζ exceeds a critical value ζc the quiescent, uniformly aligned state becomes linearly unstable, giving rise to spontaneous flow, defect proliferation and eventually active turbulence. Houston et al. ask a fundamentally different question: how does a spatially varying activity field ζ(z) modify the onset of flow and the nature of the ensuing dynamics?

The authors work in a planar channel of thickness d with homeotropic anchoring (θ=0) at the walls and no‑slip flow. Using the Ericksen–Leslie equations for a flow‑aligning nematic (ν=−1) they derive a single scalar evolution equation for the director angle θ(z,t):

∂tθ = K/γ ∂z²θ + (1−ν cos2θ)/(2 µ)