Phoretic self-propulsion at finite Péclet numbers

Abstract: Phoretic self-propulsion is a unique example of force- and torque-free motion on small scales. The classical framework describing the flow field around a particle swimming by self-diffusiophoresis neglects the advection of the solute field by the flow and assumes that the chemical interaction layer is thin compared to the particle size. In this paper we quantify and characterize the effect of solute advection on the phoretic swimming of a sphere. We first rigorously derive the regime of validity of the thin-interaction layer assumption at finite values of the P\'eclet number (Pe). Within this assumption, we solve computationally the flow around Janus phoretic particles and examine the impact of solute advection on propulsion and the flow created by the particle. We demonstrate that although advection always leads to a decrease of the swimming speed and flow stresslet at high values of the P\'eclet number, an increase can be obtained at intermediate values of Pe. This possible enhancement of swimming depends critically on the nature of the chemical interactions between the solute and the surface. We then derive an asymptotic analysis of the problem at small Pe allowing to rationalize our computational results. Our computational and theoretical analysis is accompanied by a parallel study of the role of reactive effects at the surface of the particle on swimming (Damk\"ohler number).