(490g) Chaotic Dynamics of an Autophoretic Particle

Chemically active, or autophoretic, particles that isotropically emit or absorb solute molecules are known to undergo spontaneous self-propulsion when their activity is increased beyond a critical Péclet number (Pe). Here, we conduct numerical simulations of a spherical rigid autophoretic particle in unsteady rectilinear translation, which reveal that its motion progresses through four regimes, as Pe is increased: quiescent, steady, stirring, and chaos. The particle is stationary in the quiescent regime, and the solute profile is isotropic about the particle. At Pe = 4 the fore-aft symmetry in the solute profile is broken, resulting in its steady self-propulsion, as has been shown in previous studies. A further increase in Pe gives rise to the stirring regime at Pe ≈ 27, where the fluid undergoes recirculation, as the particle remains essentially stationary in a state of dynamic arrest. As the Péclet number is increased further, the dynamics of the particle is marked by chaotic oscillations at Pe ≈ 55 and higher, where its velocity undergoes rapid reorientations. The mean square displacement of particles in the chaotic regime exhibits a subdiffusive behavior with an apparently universal scaling exponent at long times for all values of Pe studied. However, the time-scale for the decorrelation of the self propulsion velocity decreases with an increase in Pe, and this time-scale also governs the transition in the mean square displacement from early-time ballistic to long-time subdiffusive motion.