Chaotic dynamics of an autophoretic particle

R. Kailasham, Aditya S. Khair

Published 2022-03-03Version 1

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 P\'{e}clet 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 $Pe\approx27$, where the fluid undergoes recirculation, as the particle remains essentially stationary in a state of dynamic arrest. As the P\'{e}clet number is increased further, the dynamics of the particle is marked by chaotic oscillations at $Pe\approx55$ 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 swimming 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.