# Model microswimmers in channels with varying cross section

## TL;DR

This paper develops an analytical framework to understand how microswimmers behave in channels with varying cross sections, revealing how geometry and swimming mechanism influence accumulation and rectification.

## Contribution

It extends the Fick--Jacobs approach to microswimmers in corrugated channels, providing new insights into their distribution and rectification based on swimmer type and channel geometry.

## Key findings

- Microswimmer accumulation at walls depends on swimming mechanism and channel shape.
- Effective equations describe swimmer distribution along channels with weak corrugation.
- Asymmetric channels induce rectification of microswimmers, influenced by swimmer type.

## Abstract

We study different types of microswimmers moving in channels with varying cross section and thereby interacting hydrodynamically with the channel walls. Starting from the Smoluchowski equation for a dilute suspension, for which interactions among swimmers can be neglected, we derive analytic expressions for the lateral probability distribution between plane channel walls. For weakly corrugated channels we extend the Fick--Jacobs approach to microswimmers and thereby derive an effective equation for the probability distribution along the channel axis. Two regimes arise dominated either by entropic forces due to the geometrical confinement or by the active motion. In particular, our results show that the accumulation of microswimmers at channel walls is sensitive to both, the underlying swimming mechanism and the geometry of the channels. Finally, for asymmetric channel corrugation our model predicts a rectification of microswimmers along the channel, the strength and direction of which strongly depends on the swimmer type.