  We derive expressions for the photophoretic force on opaque spherical
particles in a dilute gas in the optically thick regime where the radiation
field is in local thermal equilibrium. Under those conditions, the radiation
field has a simple form, leading to well defined analytical approximations for
the photophoretic force that also consider both the internal thermal conduction
within the particle, and the effects of heat conduction and radiation to the
surrounding gas. We derive these results for homogeneous spherical particles;
and for the double layered spheres appropriate for modeling solid grains with
porous aggregate mantles. Then, as a specific astrophysical application of
these general physical results, we explore the parameter space relevant to the
photophoresis driven drift of dust in protoplanetary disks. We show that highly
porous silicate grains have sufficiently low thermal conductivities that
photophoretic effects, such as significant relative velocities between
particles with differing porosity or levitation above the midplane, are
expected to occur.

Earth and Planetary Astrophysics;Atmospheric and Oceanic Physics