Self-diffusiophoresis with bulk reaction

Catalytic motors, which self-propel in a liquid due to an inhomogeneous surface reaction, constitute an important illustration of active matter in a non-biological context. Prevailing models of the associated self-diffusiophoretic transport assume a chemical reaction at the boundary of the swimmer. We here address the more realistic scenario where that reaction is balanced by a homogeneous reaction in the bulk. The associated diffusive transport of solute, described by two Damk\"ohler numbers, exhibits a boundary-layer topology which is not encountered in the prevailing models.