Weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion: numerical and theoretical results

A submerged isotropic active particle (or droplet) that emits/consumes a chemical and interacts with it to drive flow via diffusio-osmotic slip (or Marangoni effects) can exhibit symmetry-breaking spontaneous motion. We simulate the dynamics of the particle with a reduced-order model, derived using a weakly nonlinear expansion near the threshold for spontaneous motion, in which the particle velocity depends on a time integral over the history of the particle motion (see preceding talk by Ory Schnitzer). Various cases are studied, including the particle interacting with a force, a wall and/or other particles, resulting in linear motion, circular motion, and more exotic dynamics such as bouncing and trapping. Results from asymptotic and linear-stability analyses are also presented.