What would cause a spinning fluid to stop spinning? I once saw a demonstration where an electric current caused a drop of mercury to spin.  The drop contained bits of iron, which could be seen flowing around in a circular pattern.  As soon as the current was turned off, the spinning slowed fairly quickly.  What caused the circular motion within the drop to slow?  It seems to me that there would be very little friction within the drop, and that the motion should be similar to that of a gyroscope.  Why was this not the case?  
 A: Neuneck answer contains part of the reason, but I believe there's a stronger effect (although you'll have to tell us more on the size of the drop in the experiment to decide).
As Neuneck notes, the inertia and friction with the exterior do not scale in the same way, as one is related to mass, and therefore volume, and the other with surface area. 
I say friction with the exterior, because if the drop was undergoing "solid rotation", there is no internal friction. It happens that this was pronably not altogether the case. The drop being liquid, its shape is the one of a truncated sphere with a flat bottom part in contact with the solid substrate. (The sphere is flattened by gravity if the drop is large enough). For mercury, the contact angle is around 135° with most substrates, meaning that it looks like the drop was not wetting the solid, but it does over some surface, using the 135° above you can find that this surface is about half the section area of the drop.

The mercury in contact with the surface there is not spinning : it has zero velocity. Therefore, there is a transition layer of mercury above it which is sheared by the motion of the bulk of the drop above, in this shear region there is a quite intense dissipation due to viscosity. 
This friction is much higher than the one with air, as the viscosity of mercury is 2 orders of magnitude higher than the one of air. It is also probably much greater than the solid friction that a gyroscope at its axis or a top at its tip will feel, as the contact area is so much larger. So that's where most of the energy will be dissipated, and this will quickly eat up the momentum that, as Neuneck says, our intuition also over-estimates for small objects.
A: Friction forces seem much stronger on small objects than expected from experience. If the momentum of the moving object is not larger than the average (thermal) momentum of the surrounding material, it will get stopped quickly.
Some funghi can eject their spores at supersonic speed, but still these spores have a reach of only about 20 cm. That is because their momentum is small due to their small mass.
My guess is a similar thing is going on in your drop of mercury. The iron bits are very small and therefore do not carry a lot of momentum. What little momentum got them spinning got quickly lost in thermal noise, once the driving force was turned off.
