  We theoretically study the active motion of self-diffusiophoretic Janus
particles (JPs) using the Onsager-Casimir reciprocal relations. The linear and
angular velocity of a single JP are shown to respectively result from a
coupling of electrochemical forces to the fluid flow fields induced by a force
and torque on the JP. A model calculation is provided for half-capped JPs
catalysing a chemical reaction of solutes at their surface, by reducing the
continuity equations of the reacting solutes to Poisson equations for the
corresponding electrochemical fields. We find that an anisotropic chemical
activity alone is enough to give rise to active linear motion of a JP, whereas
active rotation only occurs if the JP is not axisymmetric. In the absence of
specific interactions with the solutes, the active linear velocity of the JP is
shown to be related to the stoichiometrically weighted sum of the friction
coefficients (or hydrodynamic radii) of the reacting solutes. Our reciprocal
treatment further suggests that a specific interaction with the solutes is
required to observe far-field diffusiophoretic interactions between JPs, which
rely on an interfacial solute excess at the JP surface. Most notably, our
approach applies beyond the boundary-layer approximation and accounts for both
the diffusio- and electrophoretic nature of active motion.
