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If we put water and gasoline in a bottle, and shake it, it is not necessary to wait too long to see the two liquids separated, with the water below.

I can understand that the potential gravitational energy of that stable configuration is smaller than the opposite (with the water above). If $M>m$ and $H>h \implies MH + mh > Mh + mH$ because $M(H-h)>m(H-h)$. So a configuration with the heavier body below is energetically more favorable.

But what is the kinetic mechanism? How exactly the denser fluid goes down? What makes this example still more complicated is that an average gasoline molecule (say $C_8H_{18}$) is heavier than a water molecule. It was discussed here, but without study the kinetics.

A simpler model could be a ball pit, with two types of balls of the same size, but the red ball heavier than the blue one. If we put some layers of blue balls in the pit and after that some layers of the red one, and shake it by some vibrational device, can we expect to gradually invert the layers? It was discussed here, but the focus was entropy, not kinetic mechanism. My interest is how Newton's Laws explain the swap process.

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  • $\begingroup$ Let me guess. You have never had a course in fluid mechanics? $\endgroup$ – Chet Miller Jun 6 at 1:06
  • $\begingroup$ @ChetMiller yes, but I don't remember of this case being discussed. The Archimedes principle refers to a solid, or something with a defined shape in a liquid. $\endgroup$ – Claudio Saspinski Jun 6 at 15:28
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Gasoline on bottom scenario is also equilibrium, but unstable. Small perturbation will cause inbalance of buoyancy forces on the interface. This is a Rayleigh-Taylor instability.

If you shake the container vigorously, you may end up in creating numbers of small droplets of gasoline - a colloidal mixture. In such case surface tension will keep the droplets from merging. If they become small enough, the brownian motion of particles will keep them from drowning/going up.

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In the case of water and gasoline you have to compare the macroscopic densities rather than individual molecular weight. As for a layer of heavier balls remaining on top of lighter ones, their mutual static friction can maintain the condition. Vibration can cause the static friction to become kinetic friction which would allow less resistance to movement against each other.

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