Active polar fluid flow in finite droplets

TL;DR

This paper develops an analytical model for active contractile fluid droplets, revealing how internal polarisation and external friction influence their steady-state flow and motility, relevant to cell migration in confined environments.

Contribution

It introduces a continuum analytical model linking filament polarisation, external friction, and active stresses to droplet motility, providing insights into cell migration mechanisms.

Findings

Droplet exhibits non-zero force dipole and quadrupole moments.

Self-propulsion depends on polarisation splay and external friction.

Analytical predictions match parameter variations affecting motility.

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 the interaction with an arbitrary 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 3D 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.