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Materials: shallow petri dish, some fluid either water with sparkles in it? or a higher viscosity fluid? some way to heat it from below uniformly. A way to heat it from above also, perhaps blow dryer. thermometer, maybe curious lighting techniques?
Method: watch water heat up, heat quickly to boil, seems to be chaos. Now heat more slowly and find temperature at which convection cells form. may have to experiment with depth of water. Now take temperature of bottom surface and air above water. now try the experiment again but this time heating both the bottom and heating the air above, do we get convection cells?
If you heat a shallow layer of water in a pan, at a low temperature you get random motions in the water molecules as they carry the heat (molecular motion) from the high temperature bottom of the pan to the low temperature surface of the water. On a macro scale what you begin to see is that the layer of water directly above the pan expands (gets warmer) and thus less dense than the layer above it and rises. This rising layer breaks up into blobs randomly. Of course if blobs are rising, blobs of water at the top must sink because they are more dense (cooler). Already the fact that these homogenous layers break up into blobs is curious math. In fact, i'm not sure we fully understand it (lookup studies of water droplets and splashes, very complex!). The breaking up of the top layer into blobs as they descend, i think is mediated in a complex way by the surface tension of the water at the top. (surface tension is the stuff that makes water creep up the edges of a container of water a millimeter or so, called the meniscus.)
As you raise the temperature of the bottom of the pan relative to the top of the water you get more random motion. at a certain temperature difference, though, these rising and falling blobs eventually arrange themselves (surprise!) into a fairly neat hexagonal array of convection cells. Warm water rises in the center of each cell and falls at the edges. This is called Benard convection (named after the first to study them, Claude Bernard). As we increase the temperature difference even more, eventually the motion becomes random again and the water begins to boil.
Two surprising things about this phenomenon are the pattern and the phase transitions. The pattern is relatively neat, most cells are the same size and mostly the same hexagonal shape. The phase transitions are like the ones we couldn't predict for water, at different stages in heating we get a different distinct story. For water it was ice, water, vapor. For sulfur, it is orthorhombic sulfur, yellow liquid, red viscous liquid, and various stages of vapor. For our shallow pan of water, it is: random conductive heating, Benard convection, roiling boil. Actually as the temperature gets hotter and hotter, the boiling goes through a few more qualitative changes.
This also happens in the extremely thin layer of atmosphere on earth. It is the beginning of weather patterns.