Self-propelled, chemically-powered colloidal locomotors are swimmers designed to transverse small scale landscapes in a range of applications involving micropumping, sensing and cargo transport. Applications can require that the locomotors navigate precisely prescribed pathways, in which case onboard steering mechanisms are incorporated into the engine design. We demonstrate, through numerical simulation how boundaries can simply and passively guide locomotors to move along their surfaces. As a model system we choose an engine design in which a spherical Janus colloid coated with a symmetrical catalyst cap converts fuel in a continuous liquid phase into a product solute on one side of the colloid. The solute is repelled from the colloid through a short range interaction in a thin layer around the particle which is much smaller than the swimmer radius. The concentration gradient which develops because of the asymmetric production on the active Janus side creates a slip velocity in the layer which propels the swimmer in the direction opposite to the cap (self-diffusiophoresis). Previous research has demonstrated that diffusiophoretically-driven Janus swimmers reaching a planar wall can, for a range of active cap areas, rotate to a configuration in which the active side is partially inclined from the wall and the locomotor skims at a constant separation distance. In this configuration, the net diffusiophoretic propulsive torque balances the hydrodynamic torque resulting from the wall proximity, and the net diffusiophoretic force normal to the wall is equal to zero. The propulsive force along the surface balances the hydrodynamic resistance, allowing the colloid to skim. This represents the simplest form of passive guidance.
Here we investigate the more complicated example of boundary guidance in which the swimmer skimming along a planar wall encounters a second wall which intersects the first. We use a boundary integral method to compute the resulting colloid trajectory as a function of the size of the active cap area and the intersection angle. We find that torques exerted on the swimmer arising from the hydrodynamic interaction with the wall and the diffusiophoretic propulsive force cause the colloid to rotate from its stable skimming configuration. We develop criteria, as a function of the intersection angle and cap size , to describe when the colloid resumes skimming along the intersecting boundary, or rebounds from the wall breaking the boundary guidance.