  A standard approach to propulsion velocities of autophoretic colloids with
thin interaction layers uses a reciprocity relation applied to the slip
velocity. But the surface flux (chemical, electrical, thermal, etc.), which is
the source of the field driving the slip is often more accessible. We show how,
under conditions of low Reynolds number and a field obeying the Laplace
equation in the outer region, the slip velocity can be bypassed in velocity
calculations. In a sense, the actual slip velocity and a normal field
proportional to the flux density are equivalent for this type of calculation.
Using known results for surface traction induced by rotating or translating an
inert particle in a quiescent fluid, we derive simple and explicit integral
formulas for translational and rotational velocities of arbitrary spheroidal
and slender-body autophoretic colloids.
