Hydrostatic forces in a bowl of cereal

Question

This morning I was eating cereal which consisted of roughly spherical pieces just shy of one centimeter in diameter. By the time I was nearly finished, the cereal pieces were floating in a monolayer on surface of the milk. I noticed that the pieces of cereal tended to group together and form a surprisingly regular hexagonal lattice. Even if I manually separated one morsel from the group, it would drift aimlessly about the bowl until it came close to the main group, and then it would once again assume a position in the lattice, and remain there. Clearly, the cereal tends to this seemingly unlikely microstate because it has lower energy, but why? What sort of hydrostatic force encourages this behavior?

Answer 1

This phenomenon has been studied by Vella and Mahadevan and written up in the American Journal of Physics (http://scitation.aip.org/content/aapt/journal/ajp/73/9/10.1119/1.1898523). It's called the Cheerios effect.

If the cereal pieces clump together away from the edges of the bowl, they gravitate toward a slight concavity in the surface caused by milk molecules attracting each other downward toward the body of water, and away from the air, as air exerts a weaker attraction on the milk molecules than they exert on each other. The resulting surface, under tension, cups slightly toward the center of the bowl. Each floating cereal piece gravitates toward the center and then creates its own slight depression in the surface, and other pieces tend to gravitate toward those depressions when they get close enough.

If the cereal clumps touching he sides of the bowl, the buoyant pieces at the sides are climbing the meniscus, caused by milk's attraction to glass or porcelain. Other pieces of cereal then gravitate toward the slight depression away from the meniscus caused by each piece floating at the side. If the milk is repelled by the sides of the bowl, cereal gravitates toward the inverse meniscus which curves downward at the sides.

The mechanism is different for small objects that are heavier than water but are supported by surface tension.

Vella and Mahadevan think that buoyancy, surface tension and the meniscus explain the cheerios effect.

The hexagonal pattern is the best arrangement to fit the most pieces of cereal into a given surface area. The hexagon is one of only three regular polygons which can tile the Euclidean plane. The other two are the triangle and the square, but they do not provide the densest arrangement of cereal.