Singular density correlations in chiral active fluids in three dimensions

TL;DR

The paper demonstrates that three-dimensional chiral active fluids with a common torque exhibit anisotropic and singular density fluctuations in homogeneous states. Through a particle model of 3D chiral ABPs and a Dean-based fluctuating hydrodynamic theory, it reveals that density fluctuations are amplified along the torque direction while becoming hyperuniform in the plane perpendicular to the torque as persistence increases. The static structure factor $S(\mathbf{q})$ is shown to be singular at the origin with direction-dependent scaling, and the theory provides a qualitative match to simulations, including anisotropic patterns and hyperuniform exponents. These findings extend hyperuniformity concepts to 3D chiral active matter and offer theoretical tools for understanding anisotropic nonequilibrium fluids, with potential experimental realizations in helical swimmers and related systems.

Abstract

We investigate density fluctuations in three-dimensional chiral active fluids by using a simple model of helical self-propelled particles. Helical motion is generated by a constant angular velocity (or chiral torque) acting on the self-propelled force. The chiral torque is assumed to have the same direction and magnitude for all particles. Due to the helical nature of the particle motion, the system is generically anisotropic even when it is spatially homogeneous. Numerical simulations demonstrate that the helicity induces an anisotropic pattern and a singularity in the static structure factor (the density correlation function in Fourier space) in the low-wavenumber limit. Moreover, the system in the limit of infinite persistence time exhibits hyperuniformity in the direction perpendicular to the chiral torque, while giant density fluctuations emerge along the parallel direction. We then construct a fluctuating hydrodynamic theory for the system to describe the singular behavior. A linear analysis of the resulting equations yields an analytical expression for the static structure factor, which qualitatively agrees with our numerical findings.

Figures (5)

• Figure 1: (a) Schematic illustration of the model of a helical self-propelled particle. The illustration shows the case of $\bm{\Omega} = (0, 0, \Omega)$ and zero noise. The top panel depicts the motion in three dimensions, and the bottom panel shows its projection onto the $x$-$y$ plane. (b) Typical trajectories of a single free particle for various rotational diffusion constants. The chiral torque is fixed as $\bm{\Omega} = (0, 0, \Omega)$ with $\Omega = 0.4$. Time is measured in units of $\tau = \sigma / v_0$.
• Figure 2: (a) The local density distribution $P(\rho)$ at $D = 0$. In this figure, $\rho$ denotes the local density. The vertical dotted line indicates the mean density $\rho = 0.5$. (b) A typical particle configuration in the steady state at $D = 0$, $\rho = 0.5$, and $R = 1$. The color represents the azimuthal angle $\phi_j$ of the orientation vector $\bm{e}_j$, defined as $\bm{e}_j = (\sin\theta_j \cos\phi_j, \sin\theta_j \sin\phi_j, \cos\theta_j)$, where $\theta_j$ is the zenith angle. Cross-sectional particle configurations with thickness $\sigma$ in (c) the $x$-$y$ plane at $z = L/2$ and (d) the $x$-$z$ plane at $y = L/2$.
• Figure 3: Contour plots of the static structure factor $S(\bm{q})$ at $D = 0$ and $R = 1$ (or $\Omega = 1$). The upper panels show $S(\bm{q})$ in the $q_x$-$q_z$ plane obtained from (a) numerical simulations and (b) theoretical analysis. The lower panels show $S(\bm{q})$ in the $q_x$-$q_y$ plane obtained from (c) numerical simulations and (d) theoretical analysis.
• Figure 4: The static structure factor $S(\bm q)$ obtained from the numerical simulation at $D=0$ on (a) the $q_z$-axis and (b) the $q_x$-axis. The dashed-dotted lines in (b) represent the predictions of the linearized theory. (c) and (d) show the static structure factor $S(\bm q)$ in the $q_x$-$q_z$ plane at $R=1$ and $D = 0$. (c) $S(q_x,0,q_z)$ as a function of $q_z$ for various $q_x$. (d) $S(q_x,0,q_z)$ as a function of $q_x$ for various $q_z$.
• Figure 5: Static structure factor obtained from the numerical simulation at $\rho=0.5$ and $R =1$. Panels (a) and (b) show the static structure factor on the $q_z$ and $q_x$-axis for various $D$, respectively. In panel (a), the black dashed line represents $q_z^{-1}$ as a guide for the eye. The black dashed line in panel (b) is proportional to $q_x^{2}$.