# How do trees lift water higher than 10 meters?

The atmosphere pressure is 10 meters of water (approx). This means that it is impossible to lift water higher than 10 meters with vacuum or сapillary action (on Earth, under normal conditions).

There are trees higher than 10 meters.

How do they lift water to their tops?

UPDATE

In other words: how cohesion-tension theory can be true if it apparently contradicts the laws of physics?

UPDATE 2

Atmospheric pressure helps to rise the water, not resists rising. What is resisting is water weight. When water column is 10 meters high, then atmospheric pressure can't help anymore.

Any adhesion/cohesion mechanism can't help here too, because it acts only in thin molecular layer. To transfer action force further the pressure is required, which is insufficient at 10 meters.

UPDATE 3

If we had capillary small enough to rise water to 10 meters and then we will build smaller capillary which we expect will rise water higher, we will fail. Water column will break and does not climb higher than 10 meters.

Menisci acts like small piston and can't help rising water higher than 10 meters.

UPDATE 4

Common pressure distribution in capillary is follows:

$P_0$ is atmospheric pressure. As you see, right under menisci, the pressure is lowered by $2 \sigma / R$ where $R$ is the radius of menisci and $\sigma$ is surface tension. The entire term is called "Laplace pressure". As you see, it can't supersede atmospheric pressure, because water continuity will be broken in the case.

I.e. no any menisci can rise water higher than 10 meters.

The existence of higher trees PROVES that there are some other significant mechanisms, not adhesion/cohesion, not capillary.

UPDATE 5

Current version, as I understood it, is based on a declaration, that a water, if put into thin capillary, can behave like a solid body. Particularly, it can resist tension up to minus 15 atmospheres.

This is a tensile strength of concrete, so I don't believe that without additional proofs.

I think it is just not hard to make thin tube, put water into it and check, how high it can climb.

Was it done ever?

• It seems like you are mixing up three different mechanisms/forces for moving water: 1) pressure, 2) capillary action and 3) cohesion-tension. The 10 m rule is referring specifically to pumping water using vacuum/atmospheric pressure. – fileunderwater Oct 23 '13 at 14:03
• @SuzanCioc The thing is that you do not seem very open to appreciate the complexity of water transport in a plant. There are several forces in play, and we are not talking about a single water column being sucked up 50m. As have been mentioned, capillary forces, cohesion-tension, osmosis and horizontal movement between cells in xylem are all hypothesized to contribute. – fileunderwater Oct 23 '13 at 15:06
• @SuzanCioc Also, the first update in your question could just as well be rephrased as: How can the laws of physics be true, since they are obviously contradicted by living trees?. Either your understanding of the physical laws relevant for this case are mistaken, or some very fundamental laws must be revised. That trees are transporting water to their crowns is a fact. – fileunderwater Oct 23 '13 at 15:12
• My last contribution - try this.. There is a whole literature on this topic out there, and I suggest that you explore it. – Alan Boyd Oct 23 '13 at 15:21
• @SuzanCioc Really? "The air–water interfaces in the cell walls of the leaves, where the matrix of cellulose microfibrils is highly wettable and the spacing between them results in effective pore diameters of something like 5 to 10 nm. A wettable capillary with a diameter of 2.91μm pulls on water just strongly enough to balance the 0.1 MPa atmospheric pressure, so the pressure in the water is zero. For smaller diameters, the capillary force is capable of lifting water higher than 10.33m. For example, the maximum height of a water column with a capillary diameter of 10 nm is nearly 3 km." – Amory Oct 23 '13 at 21:24

Disclaimer: This is not my field of research.

First, this is not a complete answer to our question. A nice explanation of the current hypothesis of water transport in trees (Dixon-Joly cohesion-tension theory, originally proposed 1894) can be found at The Amazing Physics of Water in Trees but also in Tyree (1997). The key points are that the stoma (leaf surface pores) are so small that the menisci can withstand huge water columns, that water has strong cohesive forces, and that water is transported using the negative pressure that is created by transpiration. The webpage linked above contains a beautiful visualization of how multitudes of stomata and menisci create strong negative pressures:

Second, much of the current discussion in the comments (an indication that the question might be a poor fit for Bio-SE?) revolves around the plausibility of the cohesion-tension theory, and specifically on whether water can sustain strong negative pressures. Caupin & Herbert (2006) review metastability and cavitation in water (in a physics journal), and contains experimental results on negative pressures in water. The paper references a large number of experiments under various experimental setups (I cannot fairly judge these). In their conclusion they state that:

Among the countless cavitation experiments, only the ones with special care about water purity can reach large negative pressures; with a variety of techniques, they all obtain Pcav around −25 MPa at room temperature (see Fig. 3 (b)), which falls far away from the theoretical value (from −120 to −140 MPa). There is a notable exception: experiments with mineral inclusions achieve −140 MPa. The large gap between these data requires special attention.

So basically, the theoretical estimates lie at -130MPa and empirical results at -25MPa (-250 atmospheres), and water can clearly achieve large negative pressures. This would also mean that the current estimates are much larger than what is needed for the cohesion-tension theory to work (atmospheric pressure= 0.1MPa, negative pressure in water column at 50m ~ -0.5MPa).

They also have a section specifically discussing trees:

7.1. Water in nature
The law of hydrostatics teaches us that the pressure drop in a water column of 10.2 m is 0.1 MPa. This points out that negative pressures can be reached in the ascending sap of tall trees. In fact additional effects (viscous flow, drought) make the pressure in the sap negative even at smaller heights. The cohesion-tension theory, first proposed by Dixon and Jolly [56], explains that the sap column is held at the top by the meniscus in the pore of the leaves: by Laplace’s law, the meniscus curvature allows a pressure jump between the outside air pressure and the negative pressure in the sap. The trees thus contain large amounts of metastable liquids. Cavitation may sometimes occur, disrupting the liquid column and stopping the flow (xylem emboly). The complex hydraulic architecture of trees limits the damage, and strategies exist to refill the embolied xylem channels. Much work has been devoted to this topic, and is reviewed in Refs. [110,111].

There is also evidence that the risk of xylem embolism increases with tree height, and this creates a trade-off between water transport efficiency and structural adaptations to deal with embolism (Domec et al. 2008). This is for instance facilitated by the pit aperture diameter of tracheids, with apertures decreasing with height along a tree, causing increased resistance to embolism but at the same time lower water conductance. This will clearly limit the height of trees, and the paper indicates that the tallest Douglas firs are at the edge of what they can achieve.

Another recently published paper that should be relevant is 'Methods for measuring plant vulnerability to cavitation: a critical review' by Cochard et al. (2013), but I haven't had time to look closely at this. See abstract below:

Abstract:
Xylem cavitation resistance has profound implications for plant physiology and ecology. This process is characterized by a ‘vulnerability curve’ (VC) showing the variation of the percentage of cavitation as a function of xylem pressure potential. The shape of this VC varies from ‘sigmoidal’ to ‘exponential’. This review provides a panorama of the techniques that have been used to generate such a curve. The techniques differ by (i) the way cavitation is induced (e.g. bench dehydration, centrifugation, or air injection), and (ii) the way cavitation is measured (e.g. percentage loss of conductivity (PLC) or acoustic emission), and a nomenclature is proposed based on these two methods. A survey of the literature of more than 1200 VCs was used to draw statistics on the usage of these methods and on their reliability and validity. Four methods accounted for more than 96% of all curves produced so far: bench dehydration–PLC, centrifugation–PLC, pressure sleeve-PLC, and Cavitron. How the shape of VCs varies across techniques and species xylem anatomy was also analysed. Strikingly, it was found that the vast majority of curves obtained with the reference bench dehydration-PLC method are ‘sigmoidal’. ‘Exponential’ curves were more typical of the three other methods and were remarkably frequent for species having large xylem conduits (ring-porous), leading to a substantial overestimation of the vulnerability of cavitation for this functional group. We suspect that ‘exponential’ curves may reflect an open-vessel artefact and call for more precautions with the usage of the pressure sleeve and centrifugation techniques.

• Everybody get plus, but I still can't accept minus 15 atmospheres in trees. Of course I agree that metastable states can exist in principle. Will explore all this... – Suzan Cioc Oct 24 '13 at 9:48
• @SuzanCioc I agree that it is both hard to believe and really cool at the same time. However, with -15atmos you are talking about the tallest trees around. There is also a lot of evidence that at these heights trees are really on the edge of what they can achieve - see e.g. Maximum height in a conifer is associated with conflicting requirements for xylem design. – fileunderwater Oct 24 '13 at 10:04
• @SuzanCioc Also, my answer was mainly inspired by your update 5 that questioned if "...water, if put into thin capillary ... can resist tension up to minus 15 atmospheres". – fileunderwater Oct 24 '13 at 11:31

Here's Veritasium on youtube has one explanation which is same as @AlanBoyd's comment.

Meta-stable liquid can have negative pressure.

• if your are capable of translating that video into an answer, please do so. That would get my vote. @suzancioc My understanding before, re-enforced by that video, is that trees are in the amazing field of nano-hydraulics. – Atl LED Oct 23 '13 at 23:32
• So, the point of this video is that water can behave as solid body and express tension up to minus 15 atmospheres if put into small capillary. Can this point be proved by direct experiment? I don't believe it as is. Also I think, that if that would be true, it would have some subsequences. For example, if tree cut at a hight level, we should hear shot sound like taut string cut... – Suzan Cioc Oct 24 '13 at 6:16
• Please see my update. Ability to resist negative pressure is called "tensile strength". And ability to resist minus 15 atmospheres equals to tensile strength of concrete. Do you yourself believe that trees turn water into concrete? – Suzan Cioc Oct 24 '13 at 6:30
• @AtlLED I don't exclude nano hydraulics, but wish to have justified answer. – Suzan Cioc Oct 24 '13 at 6:33
• You might be interested in this reference on Henry Horatio Dixon – user1136 Oct 24 '13 at 10:24

Another disclaimer: this is not my field and I am not competent to judge the content of the paper that I am bringing to your attention.

I said above that I wouldn't make another contribution, but I found something else worth sharing in this context and which complements the answer from @fileunderwater

Wang Z et al. (2012) Capillary Rise in a Microchannel of Arbitrary Shape and Wettability: Hysteresis Loop. Langmuir 28: 16917-16926

This paper includes modelling, free energy calculations and experimentation on this problem. The maths is far beyond me, but they do come to a very interesting conclusion, namely that although a tree cannot start from a position of no liquid in the xylem and then fill up to the top it can start very small and grow beyond the height that can be maintained by simple capillary action and up to 100 m as long as the water column is never broken.

The paper is behind a paywall, but I reproduce below what is essentially the discussion section. Although this gives a flavour of the work, I must emphasise that it presents a very turgid theoretical treatment of the problem and is well worth a look.

V. IMPLICATION FOR WATER TRANSPORT TO THE TOPS OF TALL TREES Most plant physiologists accept the “cohesion-tension theory” as the explanation for the ascent of sap.26 In this qualitative theory, the move of water depends upon three important physical-chemical properties of water, which actually corre- spond to capillary rise (cohesion), cavitation (tension), and the hydrated wall (low contact angle), respectively. In this section, we focus only on the implication of the general force balance and loop hysteresis in the capillary rise of a tall tree. The height to which water in a tree rises is dependent on the size of the transport conduits. If one cuts down a tree and looks inside, the capillary dimensions of the relatively large conduits (the xylem tube) are on the order of 100 μm.27 As a result, the capillary rise is about 0.1 m. If capillary pressure alone were to explain the water rise to the treetop of a 100 m tall tree, such as the coastal redwoods of California, a capillary radius of about 100 nm is required. It was suggested that the relevant capillary dimension is the air−water interfaces in the cell walls of the uppermost leaves. The matrix of cellulose microfibrils is highly wettable, and the spacing among them yields effective pore diameters of about 10 nm. It has been pointed out that it is not necessary for the capillary to have a small bore throughout its length. Only the bore at the meniscus (i.e., in the uppermost leaf) is relevant.27 This consequence has been proved in our general expression of force balance, eq 4. Note that a microchannel containing corners or cusps on its cross section is not considered in the derivation of eq 4. Liquid filaments extend to infinity in the corners or cusps.28 Nonetheless, the elevation of the liquid column is still inversely proportional to the characteristic dimension of the cross section of the tube. For the solutions satisfying the force balance, nevertheless, there exists the issue of physical stability. A small bore at the uppermost leaf connected to a larger xylem conduit reveals the presence of a convergent micro- channel. As a consequence, multiple stable heights are possible, as described in the aforementioned analyses. However, the final state depends on the initial condition. The liquid will rise to a stable height corresponding to the larger xylem conduit if the microchannel is initially empty. In other words, the liquid will not rise of its own accord to the stable height near the top of the convergent channel because it will not be able to traverse the larger conduit of the channel. This situation is, nonetheless, stable if the liquid is sucked up to the top and then the suction is removed. How does a tall tree acquire such large negative (suction) pressures from above? As demonstrated in our experiments, the gradual rise of an initially immersed cone is able to maintain the stability of the meniscus on the top of the truncated cone as long as the force balance is satisfied. Note that the contact angle in the vicinity of the small pore mouth can be tuned up to fulfill the force balance when the microchannel is not high enough. The slow growth of the tree can be regarded as a gradual rise of the convergent channel. As long as water transport to the pores on the uppermost leaves is not interrupted throughout the entire course of the tree’s growth to 100 m, this stable height can be achieved without resorting to suction.

• Now that's an interesting one. What an approach. – Resonating Jun 24 '14 at 15:31

The following paper surveyed work on exploring water at negative pressure, from the first attempt a hundred years ago, when the largest tension reached was -3.4 MPa @ 24 degC, till the most recent measurement of water at room temperature down to -26 MPa:

http://hal.archives-ouvertes.fr/docs/00/72/64/37/PDF/Caupin-JPCondensedMatter-2012.pdf

Therefore trees can lift water higher than 10 meters because water is pulled up by negative pressure at the top (Cohesion-tension theory CTT). The tension needed to lift water to the tallest trees is -1.2MPa, which is very plausible, since it is less than the value measured a hundred years ago.