Superdiffusion and antidiffusion in an aligned active suspension

TL;DR

The paper shows that imposing a uniaxial anisotropy in an active suspension produces two new linear fluxes that couple concentration and flow, yielding a flow-induced migration mechanism and a uniaxial active stress. The authors formulate Uniaxial Active Model H and predict a superdiffusive relaxation of concentration in the homogeneous phase with dynamic exponent $z = d/2$ for $d<4$, along with an early ballistic regime observed in Brownian force-dipole simulations in 3D. A diffusive instability arises when the effective diffusivity $D(\theta)$ becomes negative for a range of directions, leading to anisotropic, flow-driven phase separation; the onset scales with an active Péclet number $Pe = W/(\eta D_0 R)$ and volume fraction $\phi$. The work further explores the relevance of hydrodynamic interactions, quasi-2D confinement, and a functional Fokker-Planck framework, arguing for two new universality classes: one for the homogeneous phase and one for the onset of phase separation in the presence of uniaxial activity.

Abstract

We show theoretically that an imposed uniaxial anisotropy leads to new universality classes for the dynamics of active particles suspended in a viscous fluid. In the homogeneous state, their concentration relaxes superdiffusively, stirred by the long-ranged flows generated by its own fluctuations, as confirmed by our numerical simulations. Increasing activity leads to an anisotropic diffusive instability, driven by an active contribution to the particle current proportional to the local curvature of the suspension velocity profile.

Figures (3)

• Figure 1: (a) Schematic realization of (b) tumbling but aligned swimmers, in the form of bacteria homogeneously dispersed in a stiff nematic liquid crystal that aligns their force dipoles along its fixed $\hat{\bf z}$ axis. (c) Far-field fluid velocity field due to a swimmer.
• Figure 2: Left circles represent an initial isotropic configuration of concentration. Red arrows indicate the directions of ${\bf u}$ (a) when $\partial_\perp\partial_z u_z>0$, (b) when $\partial_z\partial_\perp u_\perp>0$, where $\perp=x$ or $y$, and the right blue blobs are the concentration distribution after advection by the red-arrow flows.
• Figure 3: Mean-Square-Displacement(MSD) of the particles, after substracting diffusive contributions, in log-log scale, (inset) in linear-linear scale after dividing by corresponding superdiffusive scaling, for different Péclet numbers.