Weakly nonlinear dynamics of a chemically active particle near the threshold for spontaneous motion. II. History-dependent motion

Abstract

Isotropic chemically active particles can spontaneously self-propel owing to a symmetry-breaking instability when diffusion of the chemical is sufficiently weak relative to advection. This series revisits the weakly nonlinear theory describing the dynamics of such spontaneous swimmers near the instability threshold. Part II presents an extension to the general framework from part I to include unsteadiness in the form of an integral over the history of the particle motion, representing the interaction of the particle with its own chemical wake. This allows efficient simulation and theoretical analysis of fully three-dimensional unsteady problems in a range of physical scenarios.