If I take thick oil to mean what I think it does, this should be a very viscous fluid, so Reynolds number, which relates inertial forces to viscous forces should be so small as to not be applicable. I think in the purely linear viscous regime, that good solutions exist. My first guess would be that you need the same number of rotations to achieve the same degree of mixing, so 20RPM should probably achieve the same rate of mixing per unit of time. Of course for the smaller barrel, you may be able to run it faster and have the process take less time.
If you have a way to measure the quality of mixing, you might be able to experiment with it. Perhaps the density difference between two samples of the oil. My assumption of number of rotations comes from assuming the geometry is what matters, i.e. the free surface is roughly horizontal, and the flow pattern is the same as you change size/rotation speed. Obviously at some rotation speed, the flow will be too slow so the the free surface (air bubble) may simply be carries around the barrel, so I'm guessing there is a max rotation rate, and I'm not sure how that scales with size/viscosity.