Motility of active fluid drops on surfaces

TL;DR

This paper provides a theoretical analysis of how active fluid drops can self-propel on surfaces, showing that their motility depends on internal orientation defects, shape, and surface friction, with maximal speeds linked to defect-induced splay or bend.

Contribution

It derives exact flow expressions for active fluid drops considering orientation defects, shape, and friction, revealing how these factors influence motility and speed.

Findings

Asymmetric splay or bend induces directed flow and movement.

Maximal speeds occur with interior topological defects causing splay or bend.

Drop motility is controlled by substrate friction and internal orientation profiles.

Abstract

Drops of active liquid crystal have recently shown the ability to self-propel, which was associated with topological defects in the orientation of active filaments [Sanchez {\em et al.}, Nature {\bf 491}, 431 (2013)]. Here, we study the onset and different aspects of motility of a three-dimensional drop of active fluid on a planar surface. We analyse theoretically how motility is affected by orientation profiles with defects of various types and locations, by the shape of the drop, and by surface friction at the substrate. In the scope of a thin drop approximation, we derive exact expressions for the flow in the drop that is generated by a given orientation profile. The flow has a natural decomposition into terms that depend entirely on the geometrical properties of the orientation profile, i.e. its bend and splay, and a term coupling the orientation to the shape of the drop. We find that asymmetric splay or bend generates a directed bulk flow and enables the drop to move, with maximal speeds achieved when the splay or bend is induced by a topological defect in the interior of the drop. In motile drops the direction and speed of self-propulsion is controlled by friction at the substrate.