  Self-chemophoresis is an appealing and quite successful interpretation of the
motility exhibited by certain chemically active colloidal particles suspended
in a solution of their "fuel": the particle has a phoretic response to
self-generated, rather than externally imposed, inhomogeneities in the chemical
composition of the solution. The postulated mechanism of chemophoresis is the
interaction of the particle (via an adsorption potential) with the chemical
inhomogeneities in the surrounding medium. When the range of this interaction
is much smaller than any other relevant scale in the system, the (translational
and rotational) phoretic velocities can be described in terms of a phoretic
coefficient and a slip fluid velocity at the surface of the particle. Using the
case of a spherical particle as a simple and physically insightful example,
here we exploit an integral representation of the rigid-body motion to
critically re-examine this framework. The systematic analysis highlights two
steps in the approximation: first the thin-layer approximation (very large
particle size), and subsequently a lubrication approximation (slow variation of
the adsorption potential along the tangential direction). We also discuss how
these approximations could be relaxed and the effect of this on the particle's
motion.
