Swim pressure on walls with curves and corners

TL;DR

This paper investigates how the shape of confining walls, including curvature and corners, affects the swim pressure exerted by microswimmers, providing a framework for predicting forces on passive particles of various shapes.

Contribution

It introduces a theoretical framework to describe swim pressure on arbitrarily shaped passive particles near curved and cornered walls in active Brownian particle systems.

Findings

Derived force and torque expressions for arbitrary-shaped passive particles.

Predicted activity-induced depletion interactions between disks.

Suggested methods to optimize tracer particle shapes for high swimming velocities.

Abstract

The concept of swim pressure quantifies the average force exerted by microswimmers on confining walls in non-equilibrium. Here we explore how the swim pressure depends on the wall curvature and on the presence of sharp corners in the wall. For active Brownian particles at high dilution, we present a coherent framework which describes the force and torque on passive particles of arbitrary shape, in the limit of large particles compared to the persistence length of the swimmer trajectories. The resulting forces can be used to derive, for example, the activity-induced depletion interaction between two disks, as well as to optimize the shape of a tracer particle for high swimming velocity. Our predictions are verifiable in experiments on passive obstacles exposed to a bath of bacteria or artificial microswimmers.