  We consider the efficiency of self-phoretic colloidal particles (swimmers) as
a function of the heterogeneity in the surface reaction rate. The set of fluid,
species, and electrostatic continuity equations is solved analytically using a
linearization and numerically using a finite-element method. To compare
spherical swimmers of different size and with heterogeneous catalytic
conversion rates, a 'swimmer efficiency' functional $\eta$ is introduced. It is
proven, that in order to obtain maximum swimmer efficiency the reactivity has
to be localized at the pole(s). Our results also shed light on the sensitivity
of the propulsion speed to details of the surface reactivity, a property that
is notoriously hard to measure. This insight can be utilized in the design of
new self-phoretic swimmers.
