Dripping Honey
The following mpeg movie shows a simulation of honey dripping from an inverted circular spoon. Initially flow is quite slow, but then the rate of fall increases dramatically. Most of the honey that was in the spoon forms into a drop which is connected back to the spoon surface by a thread. This drop falls faster and faster, and the thread becomes thinner and thinner, until, at some finite critical time the thread becomes infinitely long and infinitely thin.
For a more detailed description of this phenomenon see Mathematics of Honey on Toast.
Computations were done by Yvonne Stokes using the finite element method with a moving mesh. The numerical method fails close to the critical time, as can be expected.
Slumping Glass
Molten glass at temperatures of 600 to 800 degrees C is a very viscous liquid. In this state it will flow slowly under the influence of applied forces. When that force is its own weight the process is known as slumping.
Slumping is used in glass art and science, and also in the manufacturing of car windscreens, large telescope lenses, glass spectacle lenses and moulds for casting plastic spectacle lenses.
The following mpeg movies show a computer simulation of an initially flat glass disc slumping into a mould that controls its final shape. This setup is similar to that used in the manufacture of spectacle lens moulds. The initial fall of the molten glass, shown as Stage 1, is fast relative to the flow once full mould contact has occured, though in practice this may take in excess of 1 hour. Depending on the thickness of the glass relative to the depth of the mould cavity, the glass might if left long enough (in real terms for many hours or even days), eventually flow over the edge of the mould, as shown in Stage 2 of the simulation. Stage 2 shows slumping at ten times the speed of Stage 1. Notice the changing shape of the top suface of the glass disc. It is this surface that will control the shape of the plastic lenses cast from the glass mould.
This simulation was computed by Yvonne Stokes using the finite element method with a moving mesh.
Acknowledgments: The calculations were done on a Sun SPARCstation 4. The animations were done using ImageMagick also on a Sun SPARCstation 4.