Steady and oscillatory propulsion in reactive swimming droplets

Chemically reactive droplets that self-propel by generating interfacial gradients offer a simple yet powerful model for studying active matter. Understanding how interfacial reactions alter surfactant behavior and drive droplet motion is key to controlling and designing such self-propelled systems. A simplified theoretical model is developed to capture the essential mechanisms underlying this motion. While earlier models require an increase in surface tension with reaction for propulsion, the current model successfully predicts self-propulsion in systems where reaction lowers surface tension, consistent with experimental observations. A linear stability analysis is performed to identify regimes of stable static state and unstable self-propulsion, revealing both monotonic and oscillatory modes of propulsion. The transition between monotonic, oscillatory and non propulsive states is characterized by the interplay between key dimensionless parameters, including the Péclet number, relative reaction-adsorption-desorption timescales, and the fractional activity of the product surfactant. These findings advance the fundamental understanding of chemically driven active droplets and provide guiding principles for the optimal design of synthetic micro-swimmers.