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Well, when milk is heated in a container its temperature starts rising & water vapor bubbles rise up through it. This initially causes a little and slowly rise in level of milk. But after certain time, a point reaches when milk level starts rising rapidly & spills out if not stopped. I have observed that higher the rate of heating milk, faster this point reaches & more rapidly milk rises to spill out.

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My question is that what causes the milk to rise rapidly & spill out at a certain point of time while being heated? Is it due to rapid heat transfer or boiling of water or due to fatty foams or films become impermissible to rising vapor bubbles in bulk at a certain point while heating?

I found some answers here: How can a wooden spoon be used to prevent water from over boiling? None answered my question.

I will really appreciate any explanation answering this question.

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In pure water, the vapour bubbles that form near the bottom of the pot rise up to the top and burst, but milk (and other liquids, such as pasta water once it has starch in it from the pasta, and water with detergent added) has lower surface tension, so when the bubbles rise to the top they can form a foam.

If the liquid is heated relatively slowly then there is time for the foam to disperse at the liquid/air interface as fast as it forms. The foam can disperse either by the bubbles popping as they are exposed to the 'air' above the surface, or by the vapour in the bubble cooling and the bubble collapsing (if the surface of the liquid and surrounding air is below the liquid's boiling point).

But if it is heated too quickly then the foam doesn't disperse as fast as it collects. New bubbles are trapped below a surface layer of existing foam - because they are not exposed to the air they don't pop, and because the foam is a good insulator they don't cool so quickly and therefore don't collapse. Even if foam production is initially only slightly faster than foam dispersion there can be a runaway reaction as the gathering foam has a negative feed-back on foam dispersion.

At he same time, the foam layer now reduces evaporation from the surface of the milk, so it heats faster for the same thermal input from your stove element. The upper surface in particular will heat up rapidly as that was the region that was kept coldest by evaporation before the foam layer started to form. So the foam layer (as well as acting as negative feedback on foam dispersal) also acts as positive feedback on liquid temperature and therefore on foam production rate.

When cooking pasta - a common 'trick' to stop the pasta water from boiling over in the same way, is to add a teaspoon of oil to the water - that stops foam from forming so the feedback effect never starts.

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Milk is an emulsion of butterfat in water, having emulsifying agent as casein protein, usually there is a sheet of negative charges around fat droplets in milk emulsion, when milk is heated the charges on surfaces of droplets gets disturbed (due to collisions) causing the fats to coagulate and precipitate down the vessel causing water content in milk to rise up while fats to remain down. the same notion goes when you add some acidic substance like squeezing lemons over milk the electrolytic nature of acids causes the negative charges on surface of droplets to get neutralized by $H_+$ ions of acid (however fats don't adsorb negative anions of acid as it shows preferential adsorption), causing fats to coagulate, same principal for centrifugation when you get butter out of milk ,in this case also the negative charges over fat droplets get disturbed and fats coagulate

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