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Challenge Question: Why does the shape of the water sheet affect the direction of the Marangoni convection?
Challenge Answer: Heat weakens surface tension, so water gets pulled away from the heat source. But to maintain the film, water has to replace it (or it breaks like at the end). So should the water move away along the edges, to be replaced by water from the center, or should it be the other way around? Water heats faster where it is thinner, so there's a preference to move away from the heat along the thinner water path. In the convex case, that's along the edge. In the concave case, that's toward the center.
Challenge Winner: Katie Smith of Honolulu, HI