Anisotropic swim stress in active matter with nematic order

TL;DR

This paper extends the concept of swim pressure in active matter to an anisotropic tensor form, demonstrating how nematic order influences the anisotropic swim stress and resulting forces on boundaries.

Contribution

It introduces the tensorial swim stress for active particles with nematic order and analytically derives its form in 2D and 3D, linking anisotropic diffusivity to stress.

Findings

Anisotropic swim stress grows exponentially with external field strength.

Normal component of swim stress applies pressure on boundaries.

Normal stress difference causes net particle flow along walls.

Abstract

Active Brownian Particles (ABPs) transmit a swim pressure $\Pi^{swim}=n\zeta D^{swim}$ to the container boundaries, where $\zeta$ is the drag coefficient, $D^{swim}$ is the swim diffusivity and $n$ is the uniform bulk number density far from the container walls. In this work we extend the notion of the isotropic swim pressure to the anisotropic tensorial swim stress $\mathbf{\sigma}^{swim} = - n \zeta \mathbf{D}^{swim}$, which is related to the anisotropic swim diffusivity $\mathbf{D}^{swim}$. We demonstrate this relationship with ABPs that achieve nematic orientational order via a bulk external field. The anisotropic swim stress is obtained analytically for dilute ABPs in both 2D and 3D systems, and the anisotropy is shown to grow exponentially with the strength of the external field. We verify that the normal component of the anisotropic swim stress applies a pressure $\Pi^{swim}=-(\mathbf{\sigma}^{swim}\cdot\mathbf{n})\cdot\mathbf{n}$ on a wall with normal vector $\mathbf{n}$, and, through Brownian dynamics simulations, this pressure is shown to be the force per unit area transmitted by the active particles. Since ABPs have no friction with a wall, the difference between the normal and tangential stress components -- the normal stress difference -- generates a net flow of ABPs along the wall, which is a generic property of active matter systems.