Effect of cohesion and tensile strength on the working of siphons

Question

My understanding of siphons is that air pressure is able to lift (because of lower pressure at the top of the siphon) the liquid up the shorter arm and then gravity pulls it down the longer arm.

However, siphons can work in vacuum under special conditions. Wikipedia states that the liquid siphons because of cohesion and tensile strength provided the liquid is pure, degassed and the surface (of the tube) is clean. For example, in this YouTube video, based on this paper (not free), they use a fluid with strong intermolecular attractions.

The pressure explanation tells that the diameter of the tubes is immaterial. However, it seems that if tension is the driving force behind the siphon, then the diameter should have an effect on the working of the siphon simply because with a larger diameter I have more liquid to pull the liquid from the other side.

But increasing the diameter of the shorter arm surely cannot pull the liquid from the lower reservoir to the higher one, right? What effect does the diameter of the tube have, if we stick to the cohesion explanation, in vacuum?

Incidentally, if the liquid consists of long molecules like polyethylene glycol, could it be siphoned in the opposite direction. And if there is a possibility of the liquid being siphoned in the opposite direction, either because of its long molecules or because of high cohesion, can that effect be evened out by the effect of pressure (which pushes it from the higher reservoir to the lower one)?

EDIT: Let me try to make things precise. Let's say we have a top reservoir A, a bottom reservoir B.

1. While siphoning from A to B, usually pressure and gravity drive the system. If the liquid under consideration was highly cohesive, can cohesive forces, perhaps in the absence of air pressure, slow down or reverse the flow? What happens if the shorter arm has a large diameter? Here I expect the cohesive forces pulling the liquid in the longer arm to increase, thereby decreasing the flow.
2. If we try to siphon from B to A, then under ordinary circumstances, the liquid will just fall back to B, except perhaps a few drops falling into A, after which air fills the pipe. But if the liquid is highly cohesive (or has long molecules), can it be siphoned, perhaps in vacuum, from B to A? In this second setting, gravity will try to drive the flow from A to B, so could it be cancelled by cohesion pulling the liquid from B to A?

It seems impossible that the liquid should be able to go from B to A without someone just sucking everything out of B into A.

As an aside, just a small clarification. Under ordinary circumstances, if A and B were at the same level and I attempted to siphon water, say, from A to B, it will just stay in the pipe without falling on any side, right? Like sucking on a straw and closing the top before the liquid falls.

Answer 1

If we have two reservoirs with a tube joining them gravity will tend to make the levels in the two reservoirs the same. In a siphon the tube rises higher than the levels in the reservoirs, so the liquid must rise before it falls again. Some force other than gravity is needed to force the liquid to rise.

In a conventional siphon this force is air pressure, which can raise water to a height of about 10 metres. If the siphon tube goes higher than 10 metres there will be a space containing only water vapour formed at the top of the tube, and no water will flow through the tube.

If a liquid with strong intermolecular attractions is used instead of water it is these attractions (instead of air pressure) which provide the force that raises the liquid from the top reservoir to the top of the tube.

Note also the capillary siphon, (a wet string replacing the tube) where it is capillary forces that raise water over the top of container A.

All the above are driven by gravity, ie the energy to raise the water or other fluid comes from the gravitational potential energy of the falling liquid. The siphon can be thought of as a way of transferring the energy from the falling liquid to the rising liquid. A larger diameter tube offers less resistance, so it would increase the flow. This is true even if it is larger on the rising side; a larger mass moves more slowly and the potential energy rise is the same as the P. E. fall for the falling fluid moving more quickly over the same height on the other side of the tube.

As you correctly said, if the levels are the same on both sides the water will just stay in the tube and the levels will stay the same.

There are other sources of energy which could conceivable be used in a siphon-like experiment. One possible candidate is surface tension.

If the surface tension of a fluid is strong enough then it might in principle be able to overcome gravity. You would need a liquid that can form large drops with height of similar size to the size of the siphon. Water has a high surface tension compared with most liquids, but I don't believe it would work in a normal-sized apparatus, except perhaps in micro-gravity.

This device would be driven by the liquid trying to reduce its total surface area. The direction of flow would depend on how much liquid was already in each container, the relative heights of the liquid in the reservoirs, the shapes of the reservoirs and the amount of attraction between the liquid and the containers and tube.