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Let's note some observations.

When water is boiled, the liquid water gains thermal energy, becomes steam, comes to the top as bubbles and burst to go into the atmosphere.

Similarly, when milk is boiled, the water turns to steam bubbles which move to the surface of the milk in the form of bubbles. But they cannot burst to the atmosphere easily because of the layer of fat on milk. The bubbles moving to the top continue to push the fat layer due to their kinetic energy. They cannot burst since they the pressure inside the bubble is less than that of the outside. When the fat layer surpasses the vessel walls, it results in the overflowing of milk.

If you boil the milk after once allowing it to boil over or removing the fat layer, the boiling will induce overflow with lesser intensity when compared to that with the the fat present. The lesser boiling over takes place because of the remaining fat in the milk.

Water does not boil over because it does not have any top layer which prevents the bursting of gas bubbles.

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Q: Why milk overflows when boiled and not water?
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