Atakpup (yes, there is such a person — he's my 14 year old son) asked me this a few months ago, and I haven't been able to puzzle it out; help me please, SMP:

Capillary action causes many liquids, including water, to rise in (very) small tubes, pulled by intermolecular forces between the liquid and the walls of the tube. There's a limit, of course: For every liquid, tube composition, and tube diameter, there's a maximum height to which the liquid will rise.

'pup and I have talked about this so he knows the above and we've observed it a bit. So a few months ago he asks: Why couldn't we build an apparatus with many (many, many) such tubes, and take a little water out the top of them, put it into a waterwheel+generator or some other mechanism for extracting useful energy as it falls back to earth, and do it either over and over or continuously and have the whole thing run perpetually?

Obviously this can't work. The energy that lifts the water comes from somewhere, and it isn't created, and ... well, around this point I get stuck.

So ... what's wrong with this idea? Not the practicality of it (obviously even if he were right — and note, I'm not saying he is, he's obviously wrong), we're talking about a tiny amount of energy for any reasonably conceivable implementation. But I have a hard time explaining why it couldn't produce any energy at all.

btw, I know this is similar to various perpetual motion waterwheels that have been proposed for centuries (or millennia?). Those are easy to debunk. This one's harder, at least for me, because the energy that is lifting the water isn't coming from the mechanism itself, it's just ... sort of there, in a sense.

OK, enough rambling to try to disguise that I'm embarrassed that I can't just see it myself.

The water rises because there is an attraction between the water molecules and the walls of the tube. There is no gain in energy as the water rises because of that attraction, the gain in energy due to height is balanced by the decrease due to the molecular attraction. To put the water into a position where it would fall you have to pull it away from the tube, which would require the same amount of energy that it gains by its slight increase in height.

Thinking of it another way, when the water rises in the tiny tube it actually goes downhill in a total energy point of view, even though it rises in the gravitational field.

Where does the energy to do that come from?

You can basically construct this with a paper towel and a cup of water. Dip the towel into the water so that it starts to take up water. The water will rise up to the top of the towel, but it won't drip unless the end of the towel is lower than the top of the water.

I suspected it had something to do with the extraction-from-the-tubes part of the apparatus, but I hadn't thought of the energy required actually to pull the liquid away. Should have. Thanks.

OK, there we go. Move along, nothing to see here.

Hahahaahah AtakDog you non-omniscient FOOL!!! The cat (errr Dog?) is out of the bag! Now I know you don't know everything, MUHAHAAHAHAAHAHAH. Well, I guess it's ok not to know something every 1 in 40,000 posts or something.

I used to think about this a lot in middle school, I always wondered what would happen if the top of the capillary tubes all contacted a glass rod or something and then the whole apparatus was titled a few degrees such that gravity would allow the drops to roll down the glass rod. I suspect the drops wouldnt actually transfer to the rod in the way they do in my mind

I had similar thoughts. For example, if you had a large number of capillary tubes and the ends were close enough together so that the little bulge from the water tension would cause them to touch, the would eventually coalesce into a droplet that will fall under its own weight. The problem (I think) is that there is no bulge. At the end of the capillary tube, I don't think the water actually sticks out at all, kind of like this picture:

http://van.physics.illinois.edu/qa/listing.php?id=2219

The bold is exactly correct. There is no bulge. The center of the water column is always lower than the water at the walls in the capillary effect scenario. To get a bulge you need pressure to raise the center above the water at the walls.

I also had another idea, which was that you could have a portal on the side of the tube that you could open and if you could get the water to spill out of it, then you can imagine a very, very tall tube, and the only energy you need to put into the system is opening and closing the portal.

But the trick would be to figure out a way to have capillary action pull the water up, and the have it "let go" upon opening the portal.

These were fun thought experiments.

There is an energy problem in opening the portal. To open the portal you have to create an open surface for the water. Breaking the interaction between the portal wall and the water would require overcoming the same force that pulled the water up in the first place. It would take work to open the portal against that affinity for water.

I suspect it's possible to prove that, in classical physics, perpetual motion using gravity and intermolecular forces is impossible.

It certainly takes work to open the door, but I don't think that's where the problem is. You can just drill a hole in the side of it to let the water leak out instead of thinking of a mechanical door or something like that. The amount of energy required to drill the hole does not depend on the height of the water column. So if you build a very tall water column that is able to store more energy (as gravitational potential energy) compared to the amount of energy required to drill the hole, then you could* get the energy out of the system.

* But of course, you can't.

If you drill the hole, will water leak out?

We have to be very clear here. If you drill a hole below the level of the water without any surface interaction, then of course it pours out. The energy you get is the energy due to lifting the water to make the column in the first place.

What gets complicated is the drilling of a hole in the wall above the water's level before the capillary effect occurs. The drill is a problem also because the material of the drill could have a surface interaction with the water which would wick it out as it punctures through the glass.

Imagine that the glass has a precut plug being held in place. If the plug was below the pre-capillary water level, then you would have to push on it to hold it in place because the static pressure of the water would try to push it out to create a hole. But if it was above the pre-capillary level but was wetted as the capillary effect of the water pulls the water up, then you would have to pull on it to hold it in place. The water interaction would be pulling it in slightly as the water is pulled up the sides of the container. If you let go, the plug would fall into the container and the water would drop back below the hole, pulled by gravity and the surface tension of the water in the center.

What happens if you lift the tube out of the source water? Does the water in the tube just stick in there rather than flow out the bottom of the tube? If so, how do they get the water out of the tube? With a little plunger?


PairTheBoard