I have seen many demonstrations in lectures where people dragged around slurries of sludges of superparamagnetic "nanoparticles" with a small hand held magnet. I have never seen that nanoparticles can be separated in this way from a clear dispersion, and I believe that this is probably not possible since the magnetic force on a single, say 10 nm particle, will be very small, and Brownian motion dominates. Is there an easy way to calculate the magnetic field gradient needed for separation from dispersion?