Curvature-driven wall accumulation in chiral active particles

Abstract: We study a dilute system of non-motile chiral active particles confined in geometries ranging from straight channels to circular enclosures. Activity is introduced through chiral particle-wall interactions, modeled as tangential wall forces that generate the edge currents characteristic of chiral active matter. Remarkably, although the particles lack self-propulsion, these boundary currents induce density inhomogeneities. We show that boundary curvature drives a wall accumulation phenomenon: particles remain uniformly distributed in straight channels but accumulate near the boundaries of circular confinements. Numerical simulations and a hydrodynamic theory for the density and momentum fields consistently capture this curvature-induced wall-accumulation. These results identify boundary curvature as a fundamental control parameter for chiral edge transport and confinement-induced organization, with potential experimental relevance to spinning colloids and granular spinners.

• The paper shows that curvature alone drives steady-state accumulation of non-motile chiral particles at curved boundaries through persistent edge currents.
• Numerical simulations reveal pronounced density peaks near curved walls, with accumulation increasing with chirality and decreasing with thermal noise.
• A hydrodynamic analysis validates these findings, emphasizing the role of wall geometry as a controllable parameter in active matter systems.

Curvature-Driven Wall Accumulation in Chiral Active Particles

Overview and Motivation

This paper investigates the interplay between geometry and chirality in non-motile active matter, specifically focusing on systems where chiral forces emerge exclusively through wall-particle interactions. Unlike the commonly studied case of self-propelled chiral active particles, the work is restricted to particles lacking autonomous motility, thereby isolating the effects of chiral, non-conservative particle-wall forces. The central result demonstrates that wall curvature alone, in the presence of chiral edge currents, induces robust steady-state accumulation of particles near boundaries—a phenomenon absent in flat-walled geometries. This purely curvature-driven effect is systematically analyzed through both numerical simulations and a hydrodynamic continuum framework.

Model System and Theoretical Formulation

The setup consists of non-interacting Brownian particles moving in two dimensions and confined either by flat (straight channel) or circular (ring) walls. Each wall exerts a conservative repulsive force along the normal (implementing volume exclusion) and, crucially, an additional non-conservative, chiral force oriented tangentially to the local wall profile. The tangential component models generic chirality-inducing interactions, such as hydrodynamic flows around rotating colloids or tangential wall friction in granular spinner systems. The amplitude of this force is controlled by a parameter directly linked to the particle's chirality. Notably, the absence of bulk self-propulsion ensures that the only source of persistent motion arises from boundary-induced chiral effects.

The Langevin dynamics can be formally written as

$$m\frac{dv}{dt} = -\gamma v + \sqrt{2\gamma T}\, \xi + F^\mathrm{w} + F^\mathrm{w}_a,$$

where $F^\mathrm{w}$ is a short-range repulsive force, and $F^\mathrm{w}_a$ is a chiral tangential force decaying linearly with the wall-particle distance. The geometrical features of the wall are rigorously incorporated using a tubular (Frenet-Serret) coordinate system, efficiently separating tangential and normal components and parameterizing local curvature.

Numerical Results: Geometry-Dependent Steady States

Simulations reveal a clear dichotomy between flat and curved confinements:

• Flat Walls: Particles exhibit homogeneous steady-state distributions, with density gradients only in the narrow region of direct wall repulsion, as in passive Brownian systems.
• Curved Walls (Rings): A marked increase in the steady-state density occurs adjacent to the wall, as signaled by sharp peaks in the radial density profile. The magnitude of this accumulation grows monotonically with chirality strength and diminishes with increasing thermal noise.

The dependence on curvature is quantified by tracking the fraction of particles remaining in the bulk as a function of chirality and temperature, showing that accumulation is exclusive to the presence of finite wall curvature. In the strong chirality/low temperature regime, nearly complete depletion of bulk density can occur, concentrating all particles near the boundary.

Mechanistic Analysis: Edge Currents and Centrifugal Stabilization

The physical origin of the accumulation is attributed to chiral edge currents: particles within a narrow layer near the wall experience persistent motion tangential to the boundary due to $F^\mathrm{w}_a$. In flat geometries, tangential and normal dynamics are decoupled, preventing any sustained accumulation. However, in curved geometries, the tangential velocity around the wall induces an effective centrifugal force directed towards the wall, stabilizing particle orbits at a finite distance from the boundary and thereby establishing a nontrivial density profile.

• Temperature Effect: Thermal fluctuations counteract the orbital stabilization, enabling particles to escape into the bulk and diminishing the accumulation effect.
• Chirality Dependence: The accumulation strength is quadratic in the chiral force amplitude, as both the tangential velocity and induced centrifugal effect depend on this parameter.

Velocity distributions, conditioned on spatial regions, are nearly identical for both geometries, indicating that the curvature effect operates through a global redistribution of particles rather than local dynamical changes.

Hydrodynamic Theory and Analytical Results

A hydrodynamic theory for the coarse-grained density and velocity fields is constructed directly in the tubular coordinate system, retaining curvature-dependent contributions. In the stationary, impermeable wall limit, the theory yields closed-form expressions for both the edge currents and the wall-normal density profile. The key terms identifying curvature-induced accumulation are:

$$\frac{T}{m\gamma}\partial_n \ln \rho = -\frac{1}{\gamma m}\partial_n U^\mathrm{w} -\frac{\kappa\alpha_0^2}{(1-n\kappa)\gamma^3}(n-2n_c)^2\Theta(2n_c-n)$$

where $\kappa$ is the local curvature. The density solution explicitly predicts an accumulation peak at a finite distance from the wall, whose height and width scale with chirality, curvature, and temperature in agreement with simulation data. This curvature dependence is absent for $\kappa=0$, directly confirming that the effect is intrinsically geometric and non-existent in flat-walled systems.

Implications and Future Perspectives

Practical Implications: The findings highlight boundary curvature as a critical, tunable parameter in the organization of chiral active matter—even in the absence of bulk motility. This has consequences for the design of microfluidic devices, colloidal motors, and other systems where geometry can be harnessed to control active mass transport and accumulation.

Theoretical Outlook: Curvature-driven accumulation operates fundamentally differently from traditional motility-induced trapping at boundaries. This mechanism emerges solely from edge currents mediated by non-conservative, chirality-dependent wall forces and is amplified by geometric confinement. The continuum framework developed is readily extensible to more complex geometries, including those with non-uniform curvature or topologies.

Open Problems and Extensions:

• The present study is restricted to non-interacting (dilute) particles. Inclusion of interparticle interactions and rotational alignment could result in additional collective phenomena, such as synchronization, vortex formation, and chirality-driven phase separation, potentially modifying the accumulation behavior.
• The extension to high-density and strongly correlated chiral systems may involve incorporating shear, odd viscosity, and bulk torque densities into the hydrodynamic closure.
• Experimental systems such as spinning colloids and granular spinners provide suitable testbeds for verifying curvature-driven wall accumulation. Experimental confirmation would require high-resolution tracking of local densities and edge currents in microfabricated channels or droplets with tunable curvature.

Conclusion

This work rigorously establishes that chiral active particles, lacking self-propulsion, nevertheless accumulate near curved boundaries as a direct result of geometry-mediated edge currents. Detailed numerical and hydrodynamic analyses demonstrate that boundary curvature is a fundamental control parameter for spatial organization in chiral active matter, providing new insights for experimental realizations and theoretical extensions in the physics of nonequilibrium systems and active confinement.