Weakly nonlinear dynamics of self-propelling active particles #

Gunnar Peng, Ory Schnitzer

11:30 Wednesday in 4Q56.

Part of the Asymptotics in active matter session.

Abstract #

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 derive a reduced-order model for the slow dynamics of the particle near the threshold for spontaneous motion using a weakly nonlinear expansion, which involves matching a quasi-steady particle-scale solution to an unsteady diffusive remote region. The resulting amplitude equation for the particle velocity includes a term representing the interaction of the particle with its own wake in the remote region, which can be expressed as a time integral over the history of the particle motion. This allows theoretical analysis and efficient numerical simulation of fully three-dimensional problems for one or more particles in various settings.