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Matlab code for numerical solving of evolution equation
In this problem, we study the draining of a soap-film with magnetic nanoparticles, under the influence of a magnetic field. We consider the following experiment: form a cylindrical soap-bubble between two parallel plates. On the top plate place a strong bar magnet (field strength >1000 G). If there are no magnetic forces present, the soap-film will drain under the influence of gravity. Due to the effects of marginal regeneration, elements of "black film", which are much thinner than the bulk film and appear invisible to the eye, form in the film and move upwards. Hence the film appears to disappear from the top down. Adding the magnet above the film provides a magnetic pressure in the opposite direction as gravity. If the magnetic force is strong enough, the draining is "reversed", and the film disappears from the bottom up. The video below demonstrates this "reverse draining":
In the following video, a ring of black film sits in the middle of the cylinder. Rotating the square magnet alters the field lines and thus the shape of the film:
The draining process is far more complicated and interesting on a molecular level. The following video shows a regular soap-film draining in a flat configuration filmed under a floursecent light. Film thickness may be inferred by color
This video show reverse draining under flourescent lighting
In the next video, a band of black film has formed in the middle of the cylinder. The film undergoes turbulent motion as some thicker film is pulled to the upper ring and some thicker film falls to the lower ring.
Try to explain this pattern formation...

[DEM] I am going to post a link to thoughts/comments/questions for useful papers
| Source Name | Page # | Quote |
| Encyclopedia of Stars | 44, 46 | "The stars are the heavens" |
In this problem, we place a magnet near a magnetic soap-film. The magnetic field creates an attraction between the film and the magnet, and induces a competition between magnetic and elastic forces. In similar problems with electrostatics, the "pull-in" phenomenon, at which the Coulomb attraction overcomes the elastic restoring force, occurs for every geometry. In the magnetic problem, "pull-in" may or may not occur, based on the geometry.
Below is a video in which a half bubble on a plate is deflected towards a magnet above. The video shows the instability that occurs at the critical distance between magnet and bubble.
During the remainder of the spring semester, Derek, Regan, and John are meeting in the lab
starting at 11 AM.
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