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For those who have either read the book, or watched the movie "The BFG", you would know Frobscottle as a green drink the giant uses, and has bubbles fizzing "in the wrong way", which is downwards. Assuming the bubbles to be filled with air, and that gravitational force on the bubble is greater than buoyant force, does this imply Frobscottle is less dense than air? Furthermore, is a liquid possible that is less dense than air?

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It implies that the author made it up without worrying about physics. If Frobscottle was less dense that air, it wouldn't stay in a cup. It would float like a helium balloon.

There is a liquid less dense than air, but it is nothing you could put air bubbles in. It is 3 monolayers of $He^3$ adsorbed on graphite at temperatures below 80 milliKelvin. First, the liquid is only 3 atoms deep. Second, air freezes solid at that temperature.

See http://www.u-tokyo.ac.jp/en/utokyo-research/research-news/lowest-density-liquid-in-nature/ and https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.235306.

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Why assume that the bubbles are air? A mixture of xenon and oxygen in a bottle of water pressurized lower than the critical point of xenon might result in bubbles that sink. The BFG could maintain low pressure by sucking the Frobscottle out via a straw with a one-way valve.

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