an autodidact meets a dilettante…

‘If I do not succeed today, I will attack [the problem] again on the morrow’

Mary Fairfax Somerville (1780-1872), mathematician, physicist, autodidact, genius

trees are so interesting… some more than others

So far my journey into this subject has proved fascinating but inconclusive, but a Veritasium video has helped me with the final solution, though it’ll still take a while to get my head around it.

There’s more than one problem involved here, as I’ve mentioned. There’s the transport problem and the ‘knowledge’ problem; how does the tree ‘know’ when it needs to bring up water, and how much to bring up?

Let’s look at transpiration again. Think of it like our perspiration. When we exercise, or even just when we’re in the sun, we sweat. The sweat then evaporates, cooling our bodies, and if we need to, we produce more sweat. It’s not conscious, we don’t have to know how much more sweat, or water, to produce, it’s just a ‘process’, no doubt a very complex one, like the process in trees and plants. However, I’ll come back to transpiration later.

Water can move up the xylem tube to the leaves of a tall tree at a maximum rate of a third of an inch per second, according to Peter Wohlleben (obviously translated into American). That’s around 2.5cms every 3 seconds, or 50cms per minute. Or 30 metres per hour. That’s rather impressive. When I told a friend about this, she said you can hear the water gushing up the trunk if you put your ear to it. Maybe that’s true.

The Veritasium video starts with another fascinating question – how can trees get so tall? And of course it’s worth noting that different species of trees have their own ‘natural’ height limits, levels of ‘bushiness’ and so forth, which is obviously affected by their particular environments as well as their genes. The tallest are around 100 metres. And one major limiting factor is that they need to transport water from roots to topmost leaves. You can’t suck water up a straw for more than ten metres, because you’ll have sucked all the air out, creating a vacuum, a pressure difference of one atmosphere. To suck the water ten times that high would create a difference of 10 atmospheres or more. So even if trees could suck somehow, the task seems impossible…

Back to transpiration – when water evaporates from the leaves, this ‘pulls up the water molecules behind it’, according to the video, though it doesn’t give an account of this ‘pulling’ mechanism, which in any case couldn’t account for the 100-metre movement, again because of the pressure limitations. Interestingly, many websites, including Wikipedia, describe transpiration as the whole process of water transportation in plants, rather than the process of evaporation and replacement in the region of the leaves, so it can be confusing. In any case the ‘pulling’ up of water to replace molecules lost in evaporation is explained by the cohesion-tension theory, as referred to in a previous post. It’s about hydrogen bonding and the adhesive and cohesive properties of water. Yet it seems miraculous that this process can explain such a vast movement against gravity. The xylem inside trees – those dead, hardened, hollowed-out cells – provide an uninterrupted column for water to pass through (the apoplastic pathway), but the distance would seem to cause pressure problems. The video discounts osmotic action, and here I have to take a quick primer on osmosis, because I don’t get it:

If there is more solute in the roots than in the surrounding soil, water would be pushed up the tree. But some trees live in mangroves where the water is so salty that osmotic pressure actually acts in the other direction, so the tree needs additional pressure to suck water in.

I don’t know why that seems counter-intuitive to me. Is it because I don’t think (sufficiently) scientifically?

Right, after a glance at a couple of videos, I think I get it. I remember the mantra that osmosis is the passage through a semi-permeable membrane (and when does a fully permeable membrane stop being a membrane?) from high to low concentration. But of course it’s the concentration of water molecules that passes from higher to lower, not the concentration of the solute. Duh. And its continued movement up the tree would have something to do with the polarity of water, its bonding properties. But anyway, osmosis isn’t the answer, as mentioned. And neither is capillary action, as explained before.

So now, to the actual explanation, which, at this moment, I certainly don’t get, but I’m going to try. It has to do with gases, liquids, vacuums, pressure and the properties of water. The video provides its final solution, so to speak, in less than two minutes of air-time, but for unscientific me, after a few viewings, it raises more questions than answers. So I’m going to analyse it bit by bit, and this may turn out to be the longest single post I’ve ever written.

So first it’s pointed out, by Hank in the video, that the lowest you can go, pressure-wise, is a vacuum. But that’s only for gases. So a perfect vacuum equals zero pressure. You need something to exert pressure – if there’s nothing there, no pressure:

But in a liquid you can go lower than zero pressure and actually get negative pressures. In a solid, we would think of this as tension. this means that the molecules are pulling on each other and their surroundings. As the water evaporates from the pores of the cell wall, they create immense negative pressures of -15 atmospheres in an average tree.

This negative pressure or tension idea doesn’t come easily to me, and it’s the key to the explanation. It’s certainly accepted science, though there are questions about how much negative pressure water can withstand, as this scientific paper explores, before cavitation. The negative pressure of -15 atmospheres is approximately -1.5 Mpa (megapascals). Experiments described in the scientific paper show that, depending on circumstances, liquid water can sustain far greater negative pressures than -1.5 MPa.

I might be wrong, but it seems to me that negative pressure is like pressure from within (hence tension) rather than from without. I’m going to have to accept this as true, and try and make sense of the rest of the explanation:

Think about the air-water interface at the pore [of the cell wall – is he talking about the whole xylem tube as a cell?]. There’s one atmosphere of pressure pushing in and -15 atmospheres of suction on the other side. So why doesn’t  the meniscus break? Because the pores are tiny – only 2.5 nanometers in diameter. At this scale, water’s high surface tension ensures the air-water boundary can withstand huge pressures without caving [cavitation].

So there’s an air-water boundary (the meniscus) at the pore, which presumably means the top of the column of water. But why does he call it a pore, which we usually think of as a hole, e.g. in the skin. This term isn’t explained at all, it’s just suddenly introduced. Does he mean the xylem column is 2.5 nm wide? No, the average xylem diameter is 25 to 75 micrometers, and 1 micrometer is 1,000 nanometers. In botanical terms, we think of the stomata on the underside of leaves. Is this what is meant? It seems so, from what comes next:

As you move down the tree the pressure increases up to atmospheric at the roots. So you can have a large pressure difference between the top and the bottom of the tree because the pressure at the top is so negative.

I’m still not quite sure how this might be so, and perhaps for that reason the rest of the explanation drifts away from me, though I’m sure it’s trustworthy, and it certainly helps explain why transpiration is indeed an essential part of the entire water movement explanation. But I’ll continue the explanation together with any questions I can come up with. Derek Muller, our Veritasium creator, now asks himself, shouldn’t the water boil at this high negative pressure?

Changing phase from liquid to gas (boiling) requires activation energy. What is this? It’s often defined as the minimum energy required to set off a chemical reaction:

And that can come in the form of a nucleation site like a tiny air bubble. That’s why it’s so important that the xylem tubes contain no air bubbles. Unlike a straw they’ve been water-filled from the start. This way, water remains in the metastable liquid state when it really should be boiling.

Slow down, two more terms are introduced here, a nucleation site and a metastable state. A nucleation site is basically a site where a phase change can begin, and start to spread, as in crystallisation from a solution. In order for water to boil, it has to start to boil somewhere – which is a molecular change. At this site, aka the nucleator, the opportunity for another, freer molecular arrangement (a gas) becomes available, and this will communicate itself to surrounding molecules. Okay, not the best explanation, but it helps me. For a better explanation you should go to the Khan Academy – and so should I. A metastable state, and I quote, is an excited state of an atom or other system with a longer lifetime than the other excited states. However, it has a shorter lifetime than the stable ground state. … A large number of excited atoms are accumulated in the metastable state (Optics 101).

This explains why Muller says the water high in the xylem ‘really should be boiling’, or that it should be in a gaseous state, for that would be its ground state under normal circumstances.

So that’s as far as I can go. It’s been an odyssey for me as well as it was for Muller, and I’m definitely not as sure on it as I could/should be, but I’ve made a lot of headway, and it really is amazing to think of what not only trees but the plants on my balcony ‘garden’ are doing all the time – sucking water through their bodies and into the atmosphere…