Simple model for self-propulsion of microdroplets in surfactant solution

Area of Science:

• Soft Matter Physics
• Fluid Dynamics
• Colloid Science

Background:

• Self-propulsion of liquid droplets in solutions is a key phenomenon in soft matter physics.
• Understanding droplet dynamics requires models that capture interfacial phenomena and fluid flow.
• Micellar solutions present complex environments where droplet behavior can be significantly altered.

Purpose of the Study:

• To propose a simple active hydrodynamic model for self-propelling liquid droplets in micellar solutions.
• To investigate the mechanisms of spontaneous symmetry breaking leading to droplet propulsion.
• To correlate theoretical predictions with experimental observations regarding surfactant concentration.

Main Methods:

• Development of a theoretical hydrodynamic model for droplet self-propulsion.
• Utilizing both analytical and numerical methods to study droplet dynamics.
• Analysis of flow instability modes and their contribution to propulsion.

Main Results:

• Self-propulsion emerges from the slow dissolution of inner fluid forming micelles.
• Surface generation of filled micelles is identified as the dominant propulsion mechanism.
• Marangoni stress, driven by surfactant concentration above the critical micellar concentration, causes flow instability.

Conclusions:

• The proposed model successfully explains droplet self-propulsion in micellar solutions.
• The first-order flow instability mode, through supercritical bifurcation, is the primary contributor to droplet swimming.
• The model provides a framework linking surfactant concentration to droplet propulsion dynamics.