How does this osmotic system reach equilibrium?

[Exper]

TL;DR Summary

Pure water flows into salt water at the bottom due to osmosis, raising the salt water level. When it rises to the top membrane, water from the salt water diffuses back to the side with pure water, and as long as the flow continues energy can be extracted as the water falls back into the pure water.

[Mentor's note - this post has been edited to ask the interesting physics question while not falling afoul of the forum rule prohibiting discussions of perpetual motion]

On the left is pure water (blue), and on the right is concentrated salt water (green). The red walls in the middle are semipermeable membranes that let water through but not salt. The purple arrows show the way I predicted osmosis. At the bottom, the pure water would flow through the membrane into the salt water due to solute potential, and the salt water level would rise until it got to the membrane at the top. Since there would be only air on the right, water from the salt water would go through the top membrane and trickle down the ramp and drop back into the pure water on the left. The ramp is only there so that the water drips instead of running down the side of the wall. The orange circle shows where a waterwheel could be placed to get energy from the falling water.

Clearly this can't go on forever because that would lead to a perpetual motion machine that would violate the laws of thermodynamics. Somehow this system must reach a stable equilibrium in which there is no flow of water between the two sides, but how?
The only thing I can think of is maybe when the water goes left at the top it gets sucked back to the right side due to water potential, but I couldn't find anything on how water moves through a membrane if one side is concentrated and the other is empty.

 

[trurle]

The problem is what water will not trickle down the ramp because it do not pass through upper membrane. It is just another version of old perpetuum mobile based on capillary force. Electrical version based on diodes and wires also results in much confusion.

 

[Dale]

The only thing I can think of is maybe when the water goes left at the top it gets sucked back to the right side due to water potential, but I couldn't find anything on how water moves through a membrane if one side is concentrated and the other is empty.

Yes, that clearly is the problem with this device.

The only way to get the water to cross the membrane backwards is if there is a hydrostatic pressure difference that exceeds the osmotic pressure. This obviously isn't the case at the top of the column. Suppose, due to thermal motion, some water did momentarily leak across the barrier, then it would immediately be pulled back since it would be pure water and the hydrostatic pressure difference is 0 while the osmotic pressure is not.

If things worked that way then you could do reverse osmosis water purification with no pressure, simply by having the water flow away from the membrane. Osmosis doesn't work that way.

Now, if you modified the device so that the top was simply a pipe or a valve, then you could get energy out of the system. This would bring salt water into to the pure water reservoir and thereby reduce the osmotic pressure. Once the solute concentration was equalized there would be no osmotic pressure and the system would stop working. It would therefore be a chemical battery based on osmotic pressure rather than electrochemical processes.