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Liquids often mix due to different densities, so which one should I pour first in order to have them mix properly?

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I think we are talking about viscosities here. In industry, mixing fluids with different viscosities seems to be a real problem. According to this:

Combining liquids with different viscosities can be much more difficult than combining liquids with similar physical properties. Adding a high-viscosity liquid to a low-viscosity liquid is usually easier than adding a low-viscosity liquid to a high-viscosity liquid. A low-viscosity liquid that is well-agitated can become turbulent, and the turbulence can act to disperse the high-viscosity liquid. Once the more-viscous liquid is dispersed, it can dissolve in the other liquid, eventually achieving a uniform blend.

But eggnogg-brandy is a whole different problem. link

The alcohol is an comparatively very acidic solution, so when you're first adding a milk product to it, you are exposing the milk (and the casein micelles) to a very acidic environment, and they will immediately start binding together.

The right way to do it is by pouring the nog first, and then slowly pouring in the booze while stirring. Finish up all the whisking of the cream, sugar, and eggs, and at the end, add in in the bourbon (and/or rye, rum, brandy, etc). Add acid: It's a law of the lab. In this case, it uses a high volume of fat content to give you the highest chance of clot-free success.

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