Water Flow Through Conduits
Hydraulic resistance in the xylem can account for between 20-60% of the total resistance to flow of water from the soil to the air within the plant. In woody plants, most of this difference occurs in the smaller twigs and branches, where the area for conducting water is smallest.

The Hagen-Poiseuille equation can be used to model water flow through individual conduits:

where p is the value of pi, r is the radius (mm) of a xylem element of length L (mm), Y is the hydrostatic pressure difference along the segment, and n is the viscosity of water at the temperature of measurement.  [I'm sorry for the poor choice of symbols, but my editor does not permit Greek symbols in HTML!]

This equation states that flow is proportional to the fourth power of the radius. This means that small changes in diameter can have BIG changes in flow. For example, simply doubling the diameter increases flow by 16 times! (2⁴ = 16). Conversely, reducing diameter by half cuts flow down by 16 times also. This means that it is the larger diameter vessels that are critically important to water flow in plants. It also illustrates that vessels, which on average are wider than tracheids, will conduct water more easily.

The other thing that this equation tells us is that flow can be maintained at high rates, even with small diameter xylem elements, if the hydrostatic pressure gradient is large enough. Thus, plants have at least two ways to change the flow of water to their leaves: 1) increase the pressure gradient, or, 2) increase the diameter of their xylem elements, or 3) do both!).

Total flow in a plant stem would be the sum of all the conduits, thus:

This reveals some important aspects of water flow in the xylem. First, if small diameter vessels or tracheids are damaged and can not be used to move water up the stem, they will have but a small effect on total flow. Conversely, if even a few large diameter conduits are damaged, total water flow could be seriously disrupted.

Cavitation and Embolisms
Cavitation is the process by which air bubbles come out of solution because of negative pressures (tension).  When you take your hand and swish it rapidly through water and bubbles appear, or if you see bubbles in the water behind propellor blades on a boat, you are watching cavitation in action.  In plants, the same process can occur in primarily two ways: by too much tension in the xylem, which causes the water column to break (i.e. a bubble expands in a xylem element) or by freezing (ever see those bubbles in an ice cube in the tray?).  Freezing can cause air to come out of solution, and when the xylem element thaws later on, it may be cavitated due to expansion of an air bubble.

Once an element is cavitated, the xylem is said to have suffered an embolism.  Embolisms disrupt water flow and can lead to water stress in the plant, since the total flow of water to the leaves is now reduced.  It is critical to our understanding of water flow in plants that we understand how these processes occur.  First, we will discuss drought-induced embolisms, then follow that up with a discussion of freezing-induced embolisms.

Drought-Induced Embolisms
As the soil dries around a plant's roots, the ability to take up water is lowered.  Matric forces in the soil now hold the water more tightly, and a greater depression in water potential is needed to withdraw the water off the soil particles.  At the same time, transpiration is occuring from the leaves, and water continues to leave the plant, even though it is now entering at a slower rate.  This imbalance leads to a reduced water content in the plant, beginning first in the leaves, and moving progressively further down the plant back towards the roots.  As the plant continues to lose water, it's capacitance (or amount of stored water in extra-cellular spaces and cell walls diminishes.  We can watch this process happen in large trees, as the wave of tension in the xylem works its way down the trunk.  Sensitive dendrometers placed strategically at several heights on the trunk can actually measure the shrinkage on a daily basis, and we can watch the shrinkage move down to each dendrometer during the day as the water stress builds up in the tree.

Eventually, the tension in the xylem gets so great that the column begins to suffer embolisms.  Let's consider one element at a time to understand what happens.  Take a xylem element that is situated next to an airspace, or previously embolized element.  Connecting the two cells, or cell and air space, is a pit, a localized area in the cell wall that is without a secondary cell wall.  These areas normally allow for the flow of water from one cell to another, but in this case, instead of water on the other side of the functional xylem element, there is air.  This means there is an air-water meniscus that develops within the pit pore.  Since the functional xylem element is under great tension, the meniscus is pulled inward toward that cell.  But the air can not penetrate the meniscus due to surface tension (remember our first lectures?) unless the tension is so great as to exceed the ability of surface tension to keep the air out.  This can happen if the difference in pressure between the functional cell and the air space (which is essentially at atmospheric pressure) is so great that the bubble is pulled through the pores in the pit membrane.  This means that the pit pore radius exceeds the radius of curvature of the bubble.  It takes a greater pressure difference to pull a bubble through a small pore than a large one.  Once a bubble is aspirated through, the air rapidly expands due to the low pressure on that side of the meniscus.  This happens so rapidly, and with such force, that it actually makes a clicking sound which can be heard if you hold a stethoscope to a drying plant stem!  In the ultrasound range, the clickings are even easier to hear, since background noise is nearly eliminated.  Once a cell is embolized, it no longer functions to transport water.

Why doesn't the embolism travel to other cells?  The unique architecture of the xylem restricts embolisms to individual tracheids or vessels because once the bubble expands, and the cell comes to atmospheric pressure, the air is trapped within that cell by the small pit pores.  As more and more cells aspirate though, the area of functional xylem continues to decrease, and this will continue to reduce total plant water flow.  The only way the plant can continue to move water in the face of increasing resistance to flow is by lowering leaf water potentials.  This serves to increase the water potential gradient, and flow can be maintained.  However, this only works to a limited extent.  First off, remember that large diameter vessels or tracheids have a disproportionate influence on water flow, so if even just a few of those embolize, water flow is drastically lowered.  Second, there is a limit to the water potential that a leaf can tolerate, and when it becomes too low, the leaf suffers drought stress and cells may die.  The reason most plants don't have run away embolisms (if you think about it, once embolisms start, they could trigger more water stress, which would trigger more embolisms, and so on) is that the stomata on the leaf close, which reduces the loss of water from the plant.  Without that control, indeed, the plant would dry itself out!

There doesn't appear to be a strong correlation between xylem cell diameter and resistance to cavitation across species.  One might be tempted to say that angiosperms should cavitate easier than gymnosperms because they have vessels, which have wider diameters than tracheids on average, and therefore should be more prone to cavitation.  But some angiosperms are exceptionally resistant to drought (cresotebush for example can tolerate -10.0 MPa easily) while some conifers cavitate at unusually high xylem water potentials (baldcypress cavitates beginning at only -0.7 MPa!).  The crucial factor seems to be not the diameter of the xylem cell, but rather, the diameter of the pit pores.  Within a species, larger cells may have a higher probability of having larger pit pores, which might give a false impression that cavitation is correlated with cell diameter.  But across species, the correlation breaks down.  What determines pit pore sizes is an interesting area of research.

Alleviating Embolisms - How Can This Happen?
One of the perplexing problems in plant water relations is how can a plant re-establish flow in an embolized xylem element?  One way is for root pressure at night to build up enough pressure to force water back into previously embolized cells so that the water column is re-connected.  At night, when transpiration is greatly reduced, and xylem tensions are small, only small pressures are needed to fill the elements.  But surprisingly, there is strong evidence now that plants can refill their xylem while they are transpiring!!  Dr. Michelle Holbrook and her co-workers at Harvard have hypothesized that because of the geometry of the pit pores, and the way menisci form in them, that xylem might actually be able to refill even if under tension.  This exciting new development in plant water relations has certainly energized the field and many people are now looking at how this process could work.  Stay tuned!

Freezing-Induced Embolisms
When xylem sap freezes, any gases trapped in the water can come out of solution, particularly if the xylem is under negative pressure at the time.  This means that those bubbles will expand when the xylem thaws, and could result in embolisms.  This can happen either overnight, if stems freeze, or during the winter.  In this case, cell diameters seem to be more correlated with susceptibility to freezing-induced embolisms.  This may explain the predominance of conifers in the boreal zones and high elevations of mountains worldwide.  It may also explain why vines, which are angiosperms with extremely large diameter vessels, are essentially a tropical group.  The number of native vine species declines dramatically with latitude around the world, and they reach their zenith in the tropics, where freezing temperatures are not found.

Freezing-induced embolisms can be alleviated through the development of root pressures.  Grapes as we have discussed have very high root pressures, and these can be used to re-dissolve gases in the xylem and refill the cells.  Once the integrity of the water column is re-established, the cell can begin functioning again to move water from the roots to the leaves.

Efficiency of Flow vs Safety
As we have emphasized throughout this course, for every benefit there is a cost.  For plants, this pertains particularly to water flow.  Plants with large diameter conduits and larger pit pores will have higher flow rates at a given pressure gradient.  This means that if a plant keeps its stomata open, which would allow more carbon dioxide to enter for photosynthesis, it runs a risk of running out of soil water.  If it is growing in a moist soil, or with its roots underwater, this may not be so much of a problem.  But for plants that can ocassionally experience soil water stress, this could lead to the cavitation of the xylem and embolisms formation.

Conversely, plants with smaller pit pores, and smaller diameter conduits, may have to contend with much lower flow rates, but because they extract water at a lower rate, will not run out of water as fast.  Nor will they suffer cavitation at as high water potentials as plants with large pit pores.  We can see that there appears to be a trade-off between high flow capability and susceptibility to cavitation.  For plants with constant supplies of water, high flow rates and high rates of gas exchange are emphasized whereas plants in dry areas have been selected through evolution for safer xylem with smaller pit pores and greater tolerance to cavitation.  In such areas, it makes sense to select for survival measures during times of stress, when growth is limited anyway, while in areas with plentiful water, it makes more sense to grow rapidly, since competition among neighboring plants will be higher.