Reynolds vs. Peclet - Finite acceleration in the Stokes regime from slowly relaxing gradients

Several models of diffusiophoretic particles exhibit spontaneous symmetry breaking - directed motion occurs even if the particle itself is isotropic. We present one such model, formulated as a system of delay differential equations. Analysis shows a critical Péclet number beyond which the stationary solution is unstable and sustained motion is possible. Beyond this critical value, simulations reveal an intermediate-Péclet regime exhibiting 'inertial' behavior - despite existing at zero Reynolds number by construction, particles do not immediately reach a steady state in response to external forces, permitting, for example, circular orbits in a central potential. In the limit of infinite Péclet number, we find that trajectories become approximately self-avoiding.