Bifurcation of chemically driven self-propelled droplets on a surfactant-adsorbed surface based on spreading coefficients

Abstract

The bifurcation of the self-propelled motion of a reactive fluid on a solid surface is of fundamental interest in the haptotaxis of cells, cellular adhesion, and the energy conversion of active matter. Changes in the wettability of a solid surface due to chemical reactions are significantly related to bifurcation, with the thermodynamic factors primarily accounting for the substrate–droplet interaction energy, and the kinetic factors determining the time constant of the formation of the wettability gradient. However, no quantitative experiments have been performed to elucidate bifurcation with consideration of the time-dependent change in the wettability under nonequilibrium conditions with the purpose of determining the contributions of the thermodynamic and kinetic factors to droplet motion. In this study, we systematically varied the wettability of a surfactant-adsorbed solid surface by adjusting the pH of the surrounding fluid and quantitatively investigated the relationship between bifurcation, which arrests self-propelled droplet motion, and the spreading coefficient that determine the disjoining pressure. The size-dependent droplet velocity is consistent with the indications of a model that considers the kinetic factors of the relevant chemical reactions. In addition, bifurcation occurred when the sign of the thermodynamically determined dispersive component of the spreading coefficient changed, corresponding to a change in the direction of the disjoining pressure. Our analysis of the time-dependent spreading coefficient has the potential for contributing to the elucidation of various bifurcation phenomena induced by a change in the wettability gradient through consideration of both the thermodynamic and kinetic factors of the relevant chemical and physical reactions.