Swimming active droplet: A theoretical analysis

Abstract

Recently, an active microswimmer was constructed where a micron-sized droplet of bromine water was placed into a surfactant-laden oil phase. Due to a bromination reaction of the surfactant at the interface, the surface tension locally increases and becomes non-uniform. This drives a Marangoni flow which propels the squirming droplet forward. We develop a diffusion-advection-reaction equation for the order parameter of the surfactant mixture at the droplet interface using a mixing free energy. Numerical solutions reveal a stable swimming regime above a critical Marangoni number M but also stopping and oscillating states when M is increased further. The swimming droplet is identified as a pusher whereas in the oscillating state it oscillates between being a puller and a pusher.