Eur. Phys. J. E (2014) 37: 8
https://doi.org/10.1140/epje/i2014-14008-3

Regular Article

Active polar fluid flow in finite droplets

¹ Department of Physics and Astronomy, University of Sheffield, Hicks Building, Hounsfield Road, S3 7RH, Sheffield, UK
² SUPA, School of Physics and Astronomy, University of Edinburgh, Mayfield Road, EH9 3JZ, Edinburgh, UK
³ Laboratoire de Physique Théorique et Matière Condensée, UMR 7600, Université Pierre et Marie Curie/CNRS, Paris, France
⁴ Laboratoire Jean Perrin, FRE 3231 CNRS/UPMC, 4 Place Jussieu, F-75255, Paris Cedex, France

^* e-mail: pha08caw@shef.ac.uk

Received: 24 October 2013
Revised: 17 December 2013
Accepted: 23 January 2014
Published online: 18 February 2014

Abstract

We present a continuum level analytical model of a droplet of active contractile fluid consisting of filaments and motors. We calculate the steady state flows that result from a splayed polarisation of the filaments. We account for interaction with the external medium by imposing a viscous friction at the fixed droplet boundary. We then show that the droplet has non-zero force dipole and quadrupole moments, the latter of which is essential for self-propelled motion of the droplet at low Reynolds' number. Therefore, this calculation describes a simple mechanism for the motility of a droplet of active contractile fluid embedded in a three-dimensional environment, which is relevant to cell migration in confinement (for example, embedded within a gel or tissue). Our analytical results predict how the system depends on various parameters such as the effective friction coefficient, the phenomenological activity parameter and the splay of the imposed polarisation.