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When we go to bed at home, we started to put a bowl of water on the radiator (the air gets a bit dry).

By instinct I put a soaked piece of paper (e.g. toilet paper) into the bowl and let it touch the radiator. The next morning all the water in the bowl was gone. My wife was not so sure that the paper actually had any effect. So I put two bowls of water.. one with the paper and one without. The next morning the bowl without the paper had all the water remaining and the ball with the paper was empty and the paper completely dry.

          paper
         _____ 
        /     |
\ -----/---/  |
 \ ------ /   \
  \------/     \__
------------------------- radiator

What is the physical mechanism for this "paper pump"? By how much does the temperature difference between the water and the radiator overcome the gravity force?

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How does the wick in a candle work? –  Georg Nov 26 '11 at 18:58
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up vote 4 down vote accepted

The paper absorbs water, and the adhesion energy is, per molecule, much stronger than the pull of gravity. You can make water climb up capillaries as far as the top of a tree from the bottom of the trunk, so it is not difficult to get the water to soak the paper against gravity. The paper has a large surface area, so it probably evaporated the water into the air. I don't believe it actually acts as a pump, like a siphon, to transfer water onto the surface of the radiator absent evaporation, because the water would have to detach at the radiator end in a continuous stream for this to work, setting up an actual steady state material flow, but it is an interesting question.

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""You can make water climb up capillaries as far as the top of a tree from the bottom of the trunk,"" This is rather popular, but totally wrong. No "suction" will pump higher than about 8 meters. In fact water is pumped from the roots up by pressure. Ever cut a twig of a tree esp. in springtime? Capillary forced would not pump the sap out of the cut! ""I don't believe it actually acts as a pump, like a siphon"" a siphon is not a pump! –  Georg Nov 27 '11 at 12:45
    
@Georg: You are wrong. This is not a popular misconception. You are confusing the "pressure" of sucking something up (which is by atmospheric pressure and limited to 10m height for water, a little less for denser liquids), with the capillary pressure which is by molecular adhesion, which has no height limit. There is no need for active transport of water up the trees capillaries, but there might be some nonetheless, I don't know. The paper is exactly like the tree. A siphon moves water using gravity from places of higher to lower potential, so it acts as a gravity powered pump. –  Ron Maimon Nov 27 '11 at 22:20
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