Active Brownian motion of emulsion droplets: Coarsening dynamics at the interface and rotational diffusion

TL;DR

This paper models the active motion of emulsion droplets driven by surfactant phase separation, revealing coarsening dynamics and rotational diffusion behavior characteristic of active Brownian particles.

Contribution

It introduces a coupled diffusion-advection-reaction model including thermal noise to describe droplet propulsion and coarsening, extending previous work by analyzing the dynamics and fluctuations.

Findings

Coarsening occurs in two stages: slow growth then ballistic regime.

Rotational correlation time scales with inverse noise strength squared.

Droplet behaves as an active Brownian particle with predictable diffusion properties.

Abstract

A micron-sized droplet of bromine water immersed in a surfactant-laden oil phase can swim (S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13 073021 (2011)). The bromine reacts with the surfactant at the droplet interface and generates a surfactant mixture. It can spontaneously phase-separate due to solutocapillary Marangoni flow, which propels the droplet. We model the system by a diffusion-advection-reaction equation for the mixture order parameter at the interface including thermal noise and couple it to fluid flow. Going beyond previous work, we illustrate the coarsening dynamics of the surfactant mixture towards phase separation in the axisymmetric swimming state. Coarsening proceeds in two steps: an initially slow growth of domain size followed by a nearly ballistic regime. On larger time scales thermal fluctuations in the local surfactant composition initiates random changes in the swimming direction and the droplet performs a persistent random walk, as observed in experiments. Numerical solutions show that the rotational correlation time scales with the square of the inverse noise strength. We confirm this scaling by a perturbation theory for the fluctuations in the mixture order parameter and thereby identify the active emulsion droplet as an active Brownian particle.