# Self-propulsion of an active polar drop

## TL;DR

This paper analyzes how active polar drops spontaneously break symmetry and self-propel due to active stresses, revealing mechanisms and differences between contractile and extensile stresses, including chaotic motion under extensile stress.

## Contribution

It provides an analytical theory explaining the active stress-induced instability and self-propulsion in polar drops, complementing previous numerical observations.

## Key findings

- Both contractile and extensile stresses cause instability and propulsion.
- Extensile stress leads to chaotic motion of the drop.
- Analytical model explains symmetry breaking mechanisms.

## Abstract

We investigate the self-propulsive motion of a drop containing an active polar field. The drop demonstrates spontaneous symmetry breaking from a uniform orientational order into a splay or bend instability depending on the types of active stress, namely, contractile or extensile, respectively. We develop the analytical theory of the mechanism of this instability, which has been observed only in numerical simulations. We show that both contractile and extensile active stress result in the instability and self-propulsive motion. We also discuss asymmetry between contractile and extensile stress, and show that extensile active stress generates chaotic motion even under a simple model of the polarity field coupled with motion and deformation of the drop.