A mobility based approach to transport in chiral fluids

Abstract

Chiral fluids, for which the mobility tensor has antisymmetric, off-diagonal components, exhibit transport phenomena absent in conventional systems, including interaction-enhanced diffusion and negative mobility. While these effects have been predicted theoretically and observed in simulations, their microscopic origin has remained unclear. Here, we address this question using a mobility-based nonequilibrium approach, analysing the steady-state drift of a tracer driven through an interacting chiral fluid. We show that, under strong chirality, the tracer generates a reversed density wake, in which regions of particle accumulation and depletion are inverted compared to the achiral case. This structural inversion of the wake provides a unified physical mechanism underlying both enhanced diffusion and negative mobility. Furthermore, we demonstrate that these phenomena are robust to changes in the interaction potential, highlighting their generality as a consequence of odd mobility.

Figures (4)

• Figure 1: Colour map of the particle wake generated by a tracer particle in the $(x,y)$ plane for different values of the oddness parameter $\kappa$ at area fraction $\phi = 0.1$. Panels correspond to (a) $\kappa = 0$, (b) $\kappa = 1/\sqrt{3}$, (c) $\kappa = \sqrt{3}$, and (d) $\kappa = 20$. Axes are scaled in units of the particle diametre. In (a), particles accumulate in front of the tracer and are depleted behind it relative to the driving force (green arrow). As $\kappa$ increases, this anisotropy gradually rotates, reaching $\pi$ rotation in the high chirality limit $\kappa\to \infty$. In this regime, collisions occur preferentially from behind, effectively propelling the tracer forward.
• Figure 2: (a) Reduced self-diffusion coefficient $D_{\parallel}/D_0$ as a function of the odd-parameter $\kappa$ and the host area fraction $\phi$. For $\kappa \to \infty$, the diffusion coefficient approaches $D_\parallel=D_0(1+6\phi)$ whereas for $\kappa=0$, it recovers the known hard-disk result $D_\parallel=D_0(1-2\phi)$.(b) $D_{\perp}/D_0$ as a function of $\kappa$ and $\phi$.
• Figure 3: Reduced parallel tracer velocity $v_{\parallel} /(\beta D_0 |\mathbf{f}_1|)$ as a function of the oddness parameter $\kappa$ for a a volume fraction $\phi=0.1$. (a) Values of the drift ratio $\omega$ such that the motion of the tracer particle is either enhanced or reduced by interactions with the host particles. (b) Values of $\omega$ such that the negative mobility condition $6\phi (\omega - 1) > 1$ is satisfied, and the parallel tracer velocity becomes negative as a function of oddness $\kappa$.
• Figure 4: Schematic of the weak attractive potential around a tracer particle. The potential is defined by its range $l$ and depth $y$. Particles are excluded from the hard-core region ($x <1$), experience a constant attraction in the intermediate region ($1 \le x < l+1$), and diffuse freely for $x > l+1$.