Branching capillary?

Medicago

Say I have a single capillary that can raise water to height H.

If I split the capillary to make another meniscus, say δ distance from the top, and both branches are of the same radius as before, will I be able to bring water up higher (i.e. could I add another H-δ high column of water to the bottom of the tube)?

If I understand correctly, the capillary force is per meniscus, so adding another meniscus should, intuitively, add more force and be able to draw up more water.


Thanks!

mfb

No, the height just depends on the diameter of the capillary at this point.
You can have more water inside, but you need more water for the same height with multiple capillaries.

Medicago

Not multiple capillaries.

ONE capillary that bifurcates at the top. Can it draw up more water than a non bifurcating capillary of the same height?

mfb

If it bifurcates, it has two branches at the top.
See my previous post.

Medicago

Well then I don't understand your answer.

I'll try to rephrase my question. I have a capillary that can draw water to height H. I bifurcated it near the meniscus to form two menisci. Can my new bifurcated capillary draw up 2H of water? Considering the radii of the two menisci are the same as the radius of the original meniscus.

mfb

Grammar indicates an amount of water, the definition of H is a height?

No, you cannot increase the height.

Medicago

Yes, a 2H column of water.

Why not? If I have another meniscus, wouldn't the force be doubled?

Andy Resnick

Generalizing your question, if you are correct then using a porous or fibrous object with many branch points would then lead to an arbitrarily large column height- since it doesn't, there is a flaw in your reasoning.

Medicago

Well the water will fail at some point. Water has a high tensile strength due to the cohesive forces between the molecules, but for some capillary height the water should give in to the tug of war between gravity and capillary forces and cavitate (or evaporate), so an infinite column of water is not possible.

I believe this is the reason why trees have a maximum height limit. Really all of this revolves around a project I'm doing on water transport in trees, and the model I propose is based on the question above.

Taking this into consideration, would you change your answer?

mfb

The force where?
Force is not a magical universal number of a system.

In addition, I think you mean a pressure difference. This will not be doubled.


It is a bit more complicated, but it is the basic concept.

Medicago

A pressure jump at the meniscus causes a force at the surface. It exists only at the surface, not along the entire column (obviously it is transferred throughout the column, but the pulling source is at the meniscus surface).


I believe this is the prime reason for the maximum height of trees. Turgor may also be involved, and also low flow velocities. Some researchers have put the height at about 120 meters tree height. If hope to show through my furcation model that water will yield when the tree is about 120 meters tall. For this I need to assume that a furcating capillary will draw up more water.

Medicago

I asked some faculty members (mechanical engineering) and no-one gave me a straight answer, but nobody said it was not valid.

Also I found it being used in an article but without explanation or reference so I guess it's trivial.

Anyway if anyone has any other ideas, I'd love to hear. thanks