The following videos are simulations of the 1D draining model.  All 4 simulations were run in Matlab using the same parameter values, except for the parameter lambda, which characterizes the strength of the magnetic field.

The first video shows drainage with a weak magnetic field applied.  Here gravity is still stronger, so black film forms at the top.

In the next video, there is a "medium sized" magnetic field.  Here, gravity is stronger at some heights but the magnetic force is stronger at others, and the black film begins to form in the middle.

The final video shows drainage with a strong magnetic field.  Here gravity is overcome by the magnetic force, and the black film forms at the bottom.

Parameters used: sigma=.0001, eta=X0=1, lambda=1 (1st vid), 1.9 (2nd), 5 (3rd)

Dsicretization N=200, initial configuration h(x,0)=1, and integrated to T=1000