Yogurt liquefies when stirred cold because the physical structure of the protein network, which gives yogurt its thickness, is disrupted. This disruption releases the whey (liquid) that was previously held within the network.
Yogurt's characteristic thick texture comes from a network of proteins, primarily casein, that have coagulated during the fermentation process. The bacteria in yogurt produce lactic acid, which lowers the pH of the milk. This lower pH causes the casein proteins to denature and aggregate, forming a three-dimensional network that traps water and other components, resulting in a semi-solid gel.
When you stir yogurt, especially when it's cold, you're physically breaking apart this delicate protein network. The bonds holding the protein structure together are weakened, and the water (whey) that was trapped within the network is released. Because the network is damaged, it can no longer hold the liquid as effectively, leading to a thinner, more liquid consistency. The colder temperature can exacerbate this effect because the proteins are less flexible and more prone to breaking under stress.
Think of it like a sponge. When the sponge is intact, it holds water. But if you tear the sponge apart, it can no longer hold as much water, and the water will be released. Similarly, stirring yogurt breaks down its protein 'sponge,' releasing the whey.
To minimize liquefaction, stir yogurt gently and avoid over-stirring. Allowing yogurt to warm slightly before stirring can also help, as the proteins will be more flexible and less prone to breaking.