Trajectories of a droplet driven by an internal active device

TL;DR

This paper develops a theoretical framework to analyze how a droplet propelled by an internal active device moves along prescribed trajectories, revealing various motion patterns and dependencies on device orientation and force direction.

Contribution

It introduces a general model for droplet self-propulsion driven by internal forces along arbitrary trajectories, including complex tracks like helices, with detailed analysis of motion behaviors.

Findings

Droplet can exhibit linear, circular, or spiraling motion.

Trajectory depends on device orientation and force direction.

Unbounded motion possible even with steady forcing.

Abstract

We consider a liquid droplet which is propelled solely by internal flow. In a simple model, this flow is generated by an autonomous actuator, which moves on a prescribed trajectory inside the droplet. In a biological system, the device could represent a motor, carrying cargo and moving on a filamentary track. We work out the general framework to compute the self-propulsion of the droplet as a function of the actuating forces and the trajectory. The simplest autonomous device is composed of three point forces. Such a device gives rise to linear, circular or spiraling motion of the droplet, depending on whether the device is stationary or moving along a radial track. As an example of a more complex track we study in detail a spherical looped helix, inspired by recent studies on the propulsion of Synechococcus1 and Myxobacteria2. The droplet trajectories are found to depend strongly on the orientation of the device and the direction of the forces relative to the track with the posibility of unbounded motion even for time independent forcing.