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Add small amounts of milk to a bottle of coke, and you end up with a white-ish precipitate with a clear liquid on top. "The Internet" seems to agree that phosphoric acid in coke reacts with something in the milk (possibly proteins, it seems to me). The Telegraph even wrote that it is the "milk molecules" that react.

So what is the reaction(s) that takes place? I can't find any proper sources that explain this in chemical terms.

Telegraph's milk-molecule analysis: This is what happens when you add milk to coke or via the Internet Archive (without pictures).

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The phosphoric acid causes denaturation of milk proteins which precipitate out of the solution (milk is an emulsion, to be exact). The flock that is formed also adsorbs dye molecules (caramel) which is why the solution become clear.

There is nothing coke-specific about it. Any acid would denature milk just like that. And nearly any huge organic molecule would get absorbed, just like caramel dye.

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This is a bit more complicated than it seems. Milk contains about 3% protein. Most proteins are not soluble -- otherwise our bodies would dissolve when it rained! The most common type that are soluble are the albumins, which rely on their tertiary structure for solubility. Hence anything that disrupts the tertiary structure -- denatures it -- can expose hydrophobic parts of the chain, causing them to agglomerate and form a solid precipitate. In the case of milk, this process is called "curdling" and the soft solid is called "curds." It is perfectly safe to eat, in fact quite nutritious. It is the first step in making cheese, and in any case happens as soon as the milk hits your stomach acids.

Now, typical things that cause albumins to denature include heat, acidity, and concentrated salts. So, soft drinks are usually quite acidic, they cause curdling, problem solved. Hmm, almost. Actually the main protein in milk is casein, and casein is not an albumin. Its method of maintaining suspension in milk is much more complex: the casein micelle. If you are familiar with the micelles formed by detergent: these are different. They share the name because they look similar at high magnification, but definitely don't work the same way. In fact the question of how casein remains suspended in milk is an open research topic. Suffice to say, your denaturant (acid, in this case) denatures something, this disrupts the casein micelles, and they agglomerate to form delicious, nutritious, slightly not-good-looking curds.

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