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I had this idea of an osmotic pump way back in high school and I never got a satisfactory answer if it would work. If I had this configuration:

osmotic pump

Would it continually pump water up given ambient heat so long as the bottom reservoir is full?

EDIT To explain what is happening, there is pure water in each of the dark blue reservoirs, saline in the cyan containers (same concentration of saline in each container) and a semipermeable membrane at the bottom and near the top of each container.

The pure water in each reservoir would be sucked up into each container directly above it due to osmotic pressure (high water concentration flows to lower water concentration), and then dumped out at the top also due to osmotic pressure (saline to air which is almost 0% water concentration). Since the membrane is not permeable to salt, only the water is released from the container into the next higher reservoir.

NOTE that the membrane at the top of each saline container doesn't touch the pure water in the reservoir it empties into. I'm also thinking that the saline containers may have to be completely filled with extra osmotic pressure to spare to counteract the pure water that sticks to the outside of the upper membrane and cause a reverse osmosis effect. Other possible tricks relying on surface tension and gravity might also aid in pulling the water away from the membrane. END EDIT

If enough were stacked, would this allow for transporting water higher than the maximum that trees can transport (about 138m according to this article)?

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It is tough to understand what is happening. If you could provide a more detailed explanation of your setup, it would help. –  udiboy1209 Aug 24 '13 at 16:05
    
Added further explanation. –  Adrian Aug 24 '13 at 16:13
    
How is it dumped out at the top due to osmotic pressure? The semi-permeable membrane separetes what at the top where water is dumped? –  udiboy1209 Aug 24 '13 at 16:49
    
It is dumped out into the air (~0% water concentration) and then falls into the reservoir. The main problem I've thought of is trying to get the pure water from sticking next to the semipermeable membrane. Since it is 100% water concentration, it would impede the water transport across the membrane. –  Adrian Aug 24 '13 at 16:54
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@Adrian that dictionary definition does not go into enough depth to get the concept across. Please read up on "perpetual motion machines of the second kind." These are machines that take energy from the environment in the form of heat and turn it into work. They are just as impossible as perpetual motion machines of the first kind, which is what your link describes. In general it is a bad idea to rely on dictionary definitions for physics concepts - you should check Wikipedia at the very least, and preferably also a good text book. –  Nathaniel Aug 25 '13 at 6:40

2 Answers 2

It won't work. It is true that a semi-permeable membrane can raise a column of salt water until the pressure (due to the column) matches the osmotic pressure across the semi-permeable membrane.

The problem comes at the top of each level: how do you envision that water gets out of the salt column into the next higher pool?

If the fresh water in the upper pool actually touches the membrane at the top of the column, it will flow into the column, increasing the water level, increasing the pressure at the bottom, forcing water down into the bottom pool. Thus you end up draining the upper pool into the lower one.

If it doesn't actually touch the membrane, you seem to be assuming that for some reason water will drip out. But it won't. If you have a film of water on the other side of the membrane, the osmotic pressure will suck it into the saline. (In fact, water will be sucked into the saline from the air, as the vapor pressure above the membrane will be lower than the vapor pressure above water, creating net flow of water into the saline.)

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Yes, I was thinking that the problem would most likely occur at the top membrane. I tried to show in the diagram that the upper water reservoir doesn't allow the water to touch the membrane. Your last paragraph is a concern though. An idea would be get the saline to entirely fill the container with osmotic pressure to spare. If the lower membrane is deep enough in it's pool, the water would tend to leave through the upper membrane. This might be augmented by somehow pulling the water away from the membrane using some surface tension and gravity tricks. Possible? –  Adrian Aug 25 '13 at 5:55
    
@Adrian - No, not possible, due to conservation of energy. You can verify by working out the effective pressure for this new scheme (that is, water will go in at the upper membrane, as the inward pressure there will be stronger than at the bottom). –  Rex Kerr Aug 25 '13 at 9:46

A quick sanity test for this sort of idea is this: "if it worked, could I use it to construct a perpetual motion machine?" In this case, yes, you could - all you need to do is let the water flow back down from the top reservoir to the bottom again, via a waterwheel, and you'd have an endless source of work without putting any energy into the system. This means that your idea breaks the first or second law of thermodynamics somewhere along the way, and the only remaining task is to figure out where exactly this happens.

The problem in this case is that you're relying on the air being "almost 0% water concentration" (i.e. this machine is only supposed to work on dry days, when it's not very humid.) You're expecting that when the water moves out of the upper membranes it will stay in a liquid phase and drip down into the reservoirs below.

However, when the water molecules move from region of liquid water into a region of dry air, they don't stay liquid but become vapour. We call this evaporation. Whether water can evaporate through the membrane depends on the balance between the vapour pressure of water in the air and the osmotic pressure of water in the solution. If the air is dry then water molecules will indeed move out (very slowly) from the upper membranes, but they will turn into water vapour. They won't condense back into the upper reservoirs, because the air is dry and doesn't want to give up that moisture. In fact, the upper reservoir will be losing water to evaporation itself, at a much faster rate.

So when the air is dry enough for water to pass through the upper membranes, all that will happen is that the water in all of the reservoirs will evaporate. You will not see an accumulation of water in the upper reservoir.

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