Migration and deformation of a droplet enclosing an active particle

TL;DR

This paper develops an asymptotic model to analyze how active particles inside deformable droplets influence shape dynamics and motility, revealing mechanisms for controlling active particle flows and droplet navigation.

Contribution

It introduces a new asymptotic solution for fluid flow around deformable droplets containing active particles, accounting for shape distortions and interfacial effects.

Findings

Offset active particles induce shape modes and displacement.

Flow patterns depend on active particle singularity types.

Surfactants can immobilize the interface and halt droplet motion.

Abstract

The encapsulation of active particles, such as bacteria or active colloids, inside a droplet gives rise to nontrivial shape dynamics and droplet motility. To understand this behavior, we derive an asymptotic solution for the fluid flow about a deformable droplet containing an active particle, modeled as a Stokes-flow singularity, in the case of small shape distortions. Offsetting of the active particle from the center of the drop breaks symmetry and leads to excitation of large number of shape modes as well as particle and drop displacement. Flows due to common singularity representations of active particles, such as Stokeslets, rotlets, and stresslets, are computed and compared to results for non-deformable droplets enclosing active particles. The effect of interfacial properties is also investigated. Surfactants adsorbed at the droplet interface immobilize the interface and arrest the droplet motion. Our results highlight strategies to steer the flows of active particles and create autonomously navigating containers.