Mathematical Modeling of Reactive Swimming Droplets

A simple two-variable model for self propulsion of reactive swimming droplets is developed. The model is capable of predicting experimentally observed self propulsion for systems exhibiting a decrease in surface tension with reaction as well. A linear stabilityanalysis is carried out to determine stable static and unstable self-propelling regimes. It is shown that the instability can lead to both monotonic as well as oscillatory propulsion. The self-propelled motion of reactive droplets is a consequence of Marangoni flow driven by gradients in interfacial tension. While the interfacial convective transport of adsorbed surfactants stabilizes the droplet, the advective influx of free surfactants from the ambient bulk toward the interface is the key destabilizing effect. With the help of stability analysis, the role of several parameters that affect the propulsion dynamics, such as droplet size, the reaction rate, and relative activity of reactant and product surfactants, is investigated.