Wall-induced self-diffusiophoresis of active isotropic colloids

While chemically-active homogeneous spherical particles do not undergo self-diffusiophoresis in free solution, they may do so when suspended in the vicinity of a solid boundary. We explore this possibility using a first-order kinetic model of solute absorption, where the relative magnitude of reaction to diffusion is characterized by the Damkohler number Da. When the particle is remote from the wall, it is repelled from it with a velocity that scales inversely with the square of distance. The opposite extreme, when the ratio $\delta$ of separation distance to particle size is small, results in the anomalous scaling $\delta^{\frac{\sqrt{1+2\mathrm{Da}}-1}{2}}$ of the solute concentration in the narrow gap separating the particle and wall. This irrational power may only be obtained by asymptotic matching with solute transport outside the gap. For Da$<4$ the self-propulsion speed possesses the same scaling, being set by the large pressures forming in the gap through a lubrication-type mechanism. For Da$>4$ the particle velocity is $O(\delta)$, set by the flow in the region outside outside the gap. Solute advection is subdominant to diffusion in both the remote and near-contact limits, and accordingly affects neither the above scaling nor the resulting approximations.