Clustering instability of focused swimmers. (9th February 2017)

• Record Type: Journal Article
• Authors: Lauga, Eric; Nadal, Francois
• Is Part Of: Europhysics letters. Volume 116:Number 6(2016:Dec.)
• Publication Date: 2017-02-09
• Subjects: 47.63.Gd; Physics -- Periodicals; Electronic journals; 530.05
• DOI: 10.1209/0295-5075/116/64004
• Languages: English
• ISSNs: 0295-5075

Abstract

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 L. et al., Phys. Rev. E, 90, (2014) 063019). 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.