A mobility based approach to transport in chiral fluids

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.

💡 Research Summary

The paper investigates transport phenomena in chiral fluids—systems whose single‑particle mobility tensor contains an antisymmetric off‑diagonal component. In two dimensions the mobility can be written as μ = μ₀(𝟙 + κ ε), where κ is a dimensionless “oddness” parameter and ε is the Levi‑Civita tensor. For κ = 0 the fluid reduces to an ordinary Brownian suspension, while κ ≠ 0 introduces a velocity component perpendicular to any applied force, a hallmark of odd (or chiral) mobility.

The authors adopt a mobility‑based nonequilibrium framework to study a tracer particle driven by a constant external force f_ext through an interacting chiral fluid. Starting from the overdamped Langevin equation v = μ f_tot, they derive a many‑body Smoluchowski equation that incorporates the antisymmetric mobility. By assuming pairwise additive interactions and focusing on the dilute limit, the problem reduces to solving a two‑body Smoluchowski equation for the steady‑state pair distribution function P_ss(rel)(r).

A perturbative expansion in the Peclet number Pe = σβ|f_ext|/2 yields a zeroth‑order equilibrium radial distribution g_eq(r) and a first‑order nonequilibrium correction g(r). For hard‑disk interactions g_eq is a Heaviside step function, and the correction satisfies Laplace’s equation ∇²g = 0 with reflecting boundary conditions at contact. The solution g(r) = (â·r̂)/r contains a vector â that depends on κ and the diffusion tensor D. As κ increases, â rotates continuously, causing the density wake around the tracer to rotate from the conventional front‑accumulation/behind‑depletion pattern to its opposite. In the strong‑chirality limit (κ ≫ 1) the wake is fully inverted.

The average interaction force exerted by the host particles on the tracer is f_int = −2ϕ D₂/(1+κ) f_ext, where ϕ is the area fraction. Consequently the total force is f_tot =