The picture below is a low-effort mock-up I made showing a closed loop with uniform ambient room temperature and top-down gravity containing two species of gas—although the idea may apply equally to liquids too. The gapped rectangles ("zebra crossing") represent a molecular sieve: a filter/membrane consisting of holes large enough to allow traversal by small/light molecules (which I colored blue; e.g., helium) while blocking the passage of larger/heavier molecules (colored green; e.g., argon).

asymmetrical sieving through buoyancy

The conundrum I see here is that even though—from a macroscopic point of view—the pressure above the sieve is bound to be larger than the pressure below it; the net flow through the sieve itself should be an upward vector simply because the concentration of the blue molecules above the sieve (per volume) can be expected to be significantly lower than below it, due to its buoyancy in relation to the heavier green molecules.

If such a flow could persist —no matter how tiny—, it would have far-reaching implications. The sieve would be an embodiment of Maxwell's demon, as the system would demonstrate perpetual motion of the 2nd kind where flow and buoyancy is sustained through Brownian particle kinetics; thus causing spontaneous cooling of the environment, violating the 2nd law of (classical) thermodynamics.

Outlandish and naive of course, so please scrutinize this idea with all the skepticism it deserves? What did I overlook?

(Practically speaking, there would be significant engineering challenges involved in creating molecular sieve(s) that are defect-free with regard to not allowing any leakage of the green medium to the volume below, but techniques involving graphene oxide membranes already seem to show promising results in that area.)

  • $\begingroup$ What makes you think that smaller particles should be buoyant relative to larger ones? Buoyancy is essentially related to density. A Polyethylene terephthalate (PET) molecule can be thousands of times heavier than a mercury molecule, and yet the density of liquid mercury is ~10 times higher than that of liquid PET. It seems to me that what you have there more closely resembles osmosis, and the flow of blue particles will stop when the concentrations are equal (of course we would have to verify this with actual calculations or experiments). $\endgroup$ – user137661 Aug 20 '19 at 3:38

This perpetual motion machine fails for the same reason that all others involving the buoyant force fail. If the green molecules really can exert a buoyant force on the blue ones, that means they exert pressure, since a buoyant force is merely a difference in pressure. And a blue ball in the sieve only feels pressure in the downward direction. This one-sided pressure means you will quickly reach an equilibrium where the concentration of blue balls is greater below the sieve than above it, and the flow stops.

  • $\begingroup$ Thanks. I had similar thoughts, except that there nonetheless seems to a trap door effect in play to me. You say a blue ball in the sieve only feels pressure in the downward direction, but wouldn't it be more accurate to say blue balls in the sieve on average only feel pressure in the downward direction? If the holes are small enough to only accommodate one single blue molecule at a time, then such a single molecule will only feel any "pressure" if it collides with a green molecule upon (attempted) upper exit from the sieve — which might happen in most instances, but not in all of 'em. $\endgroup$ – Will Aug 20 '19 at 4:11
  • $\begingroup$ That’s true, but it also applies to the buoyant force. Almost exactly half of collisions will push the blue particles down, and only the tiny imbalance averages out to produce a buoyant force. Perhaps only rarely a blue ball will get blocked as it tries to go up the sieve. But the rarity of this effect is balanced by the smallness of the average buoyant force. As you increase the green ball density, both effects increase in lockstep, always allowing equilibrium. $\endgroup$ – knzhou Aug 20 '19 at 4:22
  • $\begingroup$ +1 to your answer, because I'm in full agreement about the processes you describe. I just don't quite see how equilibrium is guaranteed. Specifically, it seems to me that for any blue molecule above the sieve the probability of it sinking down to the depth of the sieve should decrease exponentially the higher a level it reaches, until it reaches a height consisting of primarily blue molecules. I'm having difficulty expressing this reasoning well in English (or any other human language) though, so I think I will program a simple physics simulation in Python just to see for myself what happens. $\endgroup$ – Will Aug 20 '19 at 7:06
  • $\begingroup$ @Will A simulation is probably the best way to go, to really get that visceral feeling that it works out. Personally, the intuition for me is to look at limiting cases: just one green molecule pretty clearly doesn't give perpetual motion, while for infinitely many tiny green molecules (which somehow are kept from going through the sieve) you just get ordinary non-stochastic pressure back, in which case you just note that the net pressure force is conservative. And then for intermediate numbers, you convince yourself that two behave just like one but twice as much, and so on. $\endgroup$ – knzhou Aug 20 '19 at 7:09

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