Volume 116, Number 6, December 2016
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||09 February 2017|
Clustering instability of focused swimmers
1 Department of Applied Mathematics and Theoretical Physics, University of Cambridge - Cambridge CB3 0WA, UK
2 Department of Mechanical, Electrical and Manufacturing Engineering, Loughborough University Loughborough LE11 3TU, UK
Received: 28 September 2016
Accepted: 18 January 2017
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.
PACS: 47.63.Gd – Swimming microorganisms
© EPLA, 2016
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