  We study the diffusiophoretic self-propulsion of a colloidal catalytic
particle due to a surface chemical reaction in a vicinity of a solid wall.
Diffusiophoresis is a chemico-mechanical transduction mechanism in which a
concentration gradient of an interacting solute produces an unbalanced force on
a colloidal particle and drives it along the gradient. We consider a spherical
particle with an axisymmetric reacting cap covering the polar angle range $0\le
\theta\le \theta_{cap}$ in the presence of a repulsive solute, near an infinite
planar wall, and solve the coupled solute concentration and Stokes equations,
using a mixture of numerical and analytic arguments. The resulting particle
trajectory is determined by $\theta_{cap}$ and the initial orientation of the
symmetry axis with respect to the plane. At normal incidence the particle
initially moves away from or towards the wall, depending on whether the cap
faces towards or away, respectively, but even in the latter case the particle
never reaches the wall due to hydrodynamic lubrication resistance. For other
initial orientations, when $\theta_{cap}\le 115^{\circ}$ the particle either
moves away immediately or else rotates along its trajectory so as to cause the
active side to face the wall and the particle to rebound. For higher coverage
we find trajectories where the particle skims along the wall at constant
separation or else comes to rest. We provide a phase diagram giving the nature
of the trajectory (repulsion, rebound, skimming or stationary) as a function of
$\theta_{cap}$ and the initial orientation.
