  Colloidal spheres with a partial platinum surface coating perform
auto-phoretic motion when suspended in hydrogen peroxide solution. We present a
theoretical analysis of the self-propulsion velocity of these particles using a
continuum multi-component, self-diffusiophoretic model. With this model as a
basis, we show how the slip-layer approximation can be derived and in which
limits it holds. First, we consider the differences between the full
multi-component model and the slip-layer approximation. Then the slip model is
used to demonstrate and explore the sensitive nature of the particle's velocity
on the details of the molecule-surface interaction. We find a strong asymmetry
in the dependence of the colloid's velocity as a function of the level of
catalytic coating, when there is a different interaction between the solute and
solvent molecules and the inert and catalytic part of the colloid,
respectively. The direction of motion can even be reversed by varying the level
of the catalytic coating. Finally, we investigate the robustness of these
results with respect to variations in the reaction rate near the edge between
the catalytic and inert parts of the particle. Our results are of significant
interest to the interpretation of experimental results on the motion of
self-propelled particles.
