This depends on whether or not you have a vacuum in the radiometer:
The photons hitting the black side of the vanes will be absorbed transferring their momentum to the vane. Those hitting the white surface will be reflected transferring up to TWICE their momentum to the vanes.
1) In a vacuum: The above concept dominates and the white vanes trail the black vanes.
2) In a poor vacuum: the air on the black side of the vane gets heated and the air molecules give an extra "kick" to the black vane side overriding the photon momentum transfer causing the black vanes to trail. I.e. the air molecules transfer more momentum to the vane than the photons do.
Answered by:
Pete Karpius, Physics Grad Student, UNH, Durham
'The strength and weakness of physicists is that we believe in what we can measure. And if we can't measure it, then we say it probably doesn't exist. And that closes us off to an enormous amount of phenomena that we may not be able to measure because they only happened once. For example, the Big Bang. ... That's one reason why they scoffed at higher dimensions for so many years. Now we realize that there's no alternative... '