Does capillary length limit water rise in very thin capillaries?

[Medicago]

Considering very thin capillaries, such as found in wood to transport water (~100Micron), I understand that the two main factors in play are gravity and the adhesive forces between the water and the surface of the capillary tube.

I understand that gravity is proportional to volume that is (radius)^2 whereas adhesive forces are proportional to inner surface area of tube that is (radius)^1.

So for some small radius adhesive forces are stronger than gravitational pull.

However it seems as if this is independent of length. It seems that since both gravitational pull and adhesive forces, being proportional to volume and surface area, are directly proportional to some ΔL, then the length of the tube is irrelevant and the water will climb up until the tube ends. However, we still define a certain capillary length for capillaries.

Does this capillary length exist for very thin capillaries? Or would water climb indefinitely in a very thin perfect tube?

And if it does exist why would it depend on length anyway?

Thanks.

 

[Medicago]

Well I've found the answer myself.

Apparently the opposing adhesive forces act only on the meniscus!

I thought it was a shear force that acts all along the surface of the tube.

But here's another question:

If I take a tube and split it to two tubes somewhere in the middle, creating two menisci, would that raise the water higher? Considering the diameter doesn't change.

I'm simply looking into the mechanics of water transport in trees and I'm really missing some essential fluid dynamics background so I'm trying to make up for it here..

Thanks.

 

[chrisbaird]

In trees, a lot of the vertical transport is accomplished by more than pure capillary action. The evaporation (transpiration actually) of moisture out of the leaves also plays an effect. Transpiration causes low pressure at the top of the column which in effect sucks the water up the capillaries. The stomata on the leaves open and close to control transpiration, and therefore vertical flow.

 

[Medicago]

negligible in terms of pressure gradient, chris.

One can assume that gravity is balanced entirely by adhesive forces, whereas transpiration contributes to the actual flow.

 

[haruspex]

Yes, a greater length of contact for the same cross-sectional area will support a taller column of water. That's why the capillaries are narrow.
As Medicago says, capillary action draws water up until the tube is filled, but evaporation from the top makes the capillary action draw up more to keep it filled.

 

[chrisbaird]

From Wikipedia:

"In taller plants and trees however, the force of gravity can only be overcome by the decrease in hydrostatic (water) pressure in the upper parts of the plants due to the diffusion of water out of stomata into the atmosphere"