The curved kinetic boundary layer of active matter

TL;DR

This paper analytically derives the swim pressure distribution and forces on arbitrarily shaped bodies in active matter, accounting for boundary curvature effects on the kinetic boundary layer.

Contribution

It extends previous models by providing an analytical solution for the boundary layer on curved surfaces in active matter systems.

Findings

Derived the swim pressure distribution on curved boundaries.

Quantified the effect of boundary curvature on swim pressure.

Provided a general scaling law for curvature effects on swim pressure.

Abstract

The finite reorient-time of swimmers leads to a finite run length $\ell$ and the kinetic accumulation boundary layer on the microscopic length scale $\delta$ on a non-penetrating wall. That boundary layer is the microscopic origin of the swim pressure, and is impacted by the geometry of the boundary [Yan \& Brady, \textit{J. Fluid. Mech.}, 2015, \textbf{785}, R1]. In this work we extend the analysis to analytically solve the boundary layer on an arbitrary-shaped body distorted by the local mean curvature. The solution gives the swim pressure distribution and the total force (torque) on an arbitrarily shaped body immersed in swimmers, with a general scaling of the curvature effect $\Pi^{swim}\sim\lambda\delta^2/L$.