# Clustering instability of focused swimmers

## TL;DR

This paper investigates the hydrodynamic instabilities in focused swimmer lines, revealing that puller-type swimmers are inherently unstable while pusher-types remain stable, through analytical models.

## Contribution

It introduces a combined continuum and discrete model to analyze the instability of aligned swimmer lines, highlighting the role of hydrodynamic interactions and swimmer type.

## Key findings

- Puller swimmers are predicted to be unstable.
- Pusher swimmers are predicted to be stable.
- Analytical growth rates of instabilities are computed.

## Abstract

One of the hallmarks of active matter is its rich nonlinear dynamics and instabilities. Recent numerical simulations of phototactic algae showed that a thin jet of swimmers, obtained from hydrodynamic focusing inside a Poiseuille flow, was unstable to longitudinal perturbations with swimmers dynamically clustering (Jibuti et al., Phys. Rev. E, 90, 2014). As a simple starting point to understand these instabilities, we consider in this paper an initially homogeneous one-dimensional line of aligned swimmers moving along the same direction, and characterise its instability using both a continuum framework and a discrete approach. In both cases, we show that hydrodynamic interactions between the swimmers lead to instabilities in density for which we compute the growth rate analytically. Lines of pusher-type swimmers are predicted to remain stable while lines of pullers (such as flagellated algae) are predicted to always be unstable.