Nonlinear dynamics of a chemically-active drop: From steady to chaotic self-propulsion

Area of Science:

• Soft Matter Physics
• Chemical Hydrodynamics
• Nonlinear Dynamics

Background:

• Chemically active drops spontaneously self-propel in solutions, displaying varied trajectories including straight, helical, and chaotic paths.
• Understanding the fundamental mechanisms governing these complex dynamics is crucial for controlling active matter systems.

Purpose of the Study:

• To develop a minimal axisymmetric model for spherical active drops to elucidate the origins of diverse self-propulsion dynamics.
• To investigate the roles of diffusiophoresis, the Marangoni effect, and advection in generating steady and chaotic motion.

Main Methods:

• Development of a minimal axisymmetric model incorporating diffusiophoresis and the Marangoni effect.
• Numerical investigation of fully coupled hydrodynamic and advection-diffusion equations.
• Linear stability analysis to determine instability thresholds.

Main Results:

• Simple interface properties and mobility mechanisms can lead to both steady self-propulsion and chaotic behavior.
• Strong surfactant advection, particularly for larger drops, can destabilize steady motion, leading to spontaneous stopping and symmetric flow.
• Increased advection relative to diffusion can induce chaotic oscillations, with instability thresholds dependent on the balance between diffusiophoresis and the Marangoni effect.

Conclusions:

• The interplay between diffusiophoresis, the Marangoni effect, and nonlinear surfactant advection governs the complex dynamics of active drops.
• Diffusiophoresis promotes instabilities, influencing both motionless and moving drop behaviors.
• This model provides a framework for understanding and potentially controlling the emergent behaviors of active droplets.