capillary action nanotubes in space elevator?

crazy idea i just had while appreciating the nice trees near me... nanotubes can be made that have tiny holes allowing capillary action to carry water up, against gravity... this obviously wouldn't be on a first space elevator built, but if anyone decided that having two would be good, wouldn't it be sweet to get water sent straight up the elevator with NO energy cost whatsoever? rate would be slow, but recycling technology is pretty damn good so you wouldn't ever really lose any unless you made it into fuel.

Great yes, but not really possible.

The altitude to which water rises under the capillary effect is determined by:

h = [2* sigma * cos(theta)] / (rho * g * r)

Where sigma is the surface tension of the liquid (0,0728 J/m for water), theta is the surface contact angle (20° for water), rho is the density (1 kg/m^3) and g is the acceleration (9,81 m/s^2 near the ground), and finally r is the tube radius.
If you put in r=1nm, unless I've made a mistake, you get an altitude of 28km. So you'd need over a thousand transfer stations for renewed capillary effect. Also, to have a flow - i.e. to be able to draw water out of your capillary tubes at the top - you'd still have to put in energy.

It might turn out to be a low-energy solution (there are many if's involved there), but certainly not free.

There is also the problem of avoiding that the water freezes.

ah i thought it was more of a rate than a height that was limited. for some reason i doubt the water freezing would be that big of a concern inside of a <=1nm tube, since you can't exactly fit that many molecules through something that size. i do know it's small enough that quantum mechanics is relevant so classical analogues may not apply.

anyways sigma is "the liquid-air surface tension (J/m² or N/m)" I don't know how this changes in vacuum, or what conditions inside a nanotube elevator would be like. but 28km is only 3 orders of magnitude from what you need, and lower transfers (280km maybe) would be possible with an injection of energy, so you never know. of course since it's only linear in sigma that might be too much to ask, again i don't know how sigma is related to pressure.

What about putting a charge on the water (adding a few ions) then running power up the nanotube to drag the water up with it? That way you get water and electricity at the top.

interesting idea. but i don't think it would work. while you could induce a magnetic field, i don't think you could get the water to follow it with just a few ions, not to mention that at 1nm you have to think of atoms discretely so adding ions doesn't really charge your water. besides, when water and electricity come into contact, it usually results in electrolysis. while i like the idea of feeding hydrogen and oxygen up the elevator, i don't like the idea of them both being in the same place and not already bonded. that being said in a 1nm tube you wouldn't exactly have enough space for a violent reaction but still.

there is probably some quantum property one could take advantage of that would make this possible. alas it is well beyond me to think of.

Hey,

It might be a bit off topic but since you guys seem to have knowledge of the possibility of the working of this idea I am going to ask here.

I want to use capillary concept to transfer water through nanotubes. THe height is not as much lower than the ambition in this topic, to be exact around 6 meters. I know the diameter is important for the capillary force. So thats when i thought of nanotubes.
I want to transfer water to the roof of a building so we get free energy at the top. (I know it is not much and it is probably slow)This water can then be used to flush toilets etc. Do you guys think this is practicly possible to make it efficient?
Maybe to strengthen the effect i want to use a vacuum like happens within trees by evaporation.
You guys have any ideas of how such a vacuum can be created without costing energy?
I thought this idea was insane but now i read this post for transporting it to outer space anything seems possible

Thanks in advance,
Elmar

I found this F. Caupin(2008):
A curious student might ask
whether this relation makes sense when the value of R
is of atomic dimensions. For example, the formula yields
Hmacro ≃ 30 km for the case of water at 20C and R =
0.5 nm. Such a value of H seems both immeasurably large
and unreliable, since the derivation applies macroscopic
laws outside of their regime of validity. Moreover, at a
height of 30 km, the pressure of the hypothetical water
would be about twice the cavitation limit of water [2],
Pcav ≃ −140 MPa, so the water would be ultra-unstable.
Nevertheless, motivated by the student’s question, one can
ask a related question: using more accurate, microscopic
physics, what is the maximum possible value of H for a
specified fluid?

I didn't understand the whole article because I never studied physics at this level. But theoretical it is possible to rise to much higher heights. I think because of electrical forces or so. You can read the article when you search on google. They mention heights up to 190km for H2O

Reference: Absolute limit for the capillary rise of a fluid
Frederic Caupin (2008)

If someone could elaborate to make it comprehensible for me I would be very greatful.