Autophoretic locomotion in weakly viscoelastic fluids at finite P\'eclet number

In this work, we numerically investigate the dynamics of a self-propelling autophoretic Janus particle in a weakly viscoelastic fluid. The self-propulsion is achieved by an asymmetry in the properties of the surface of the Janus particle that drives a surface slip velocity and bulk flow. Here we investigate the effect of viscoelasticity on this advection-diffusion problem over a range of P'eclet and Damk"ohler numbers. Particles are found to swim faster, or slower, in viscoelastic fluids, and we show how reaction and diffusion rates affect the viscoelastic stresses that lead to changes in propulsion.