Reverse osmosis perpetual motion machine

[Mapes]

"WORNG!" Salt water is around 10ppm/atm more compressible than fresh water.

Bystander, could you give a reference for this please?

 

[cesiumfrog]

It is not clear yet that the RO system will stop when it releases some amount of potential energy and settles to equilibrium. (We're all sure it does, we're just not sure how or where.)

For a dilute solution, letting $r$ be the ratio between the column height and the fundamental length scale ${i_H k_B T}({\kappa g})^{-1}$ (where $\kappa$ is the difference in mass between a solute molecule and the solvent it displaces), reverse osmosis occurs iff the concentration at the semipermeable membrane (as a fraction of the mean concentration) is less than $r$. Thus the solvent will start cycling (provided $r$>1 and that the solution is initially mixed and not yet settled), however, at equilibrium (when the Archimedean force balances the osmotic potential gradient) the concentration increases exponentially with depth and the reverse osmosis cycle halts because the concentration at the membrane is $$\frac{r}{1-e^{-r}}$$.

Not sure yet how to generalise this to non-dilute solutions.

 

[SirBrainChild]

Here is a detailed explanation: http://www.lhup.edu/~dsimanek/museum/osmosis.htm

The tone of the linked webpage is condescending at times (and starts off that way), but the information is useful.