Plants don't have hearts to pump fluids throughout their systems, so how do they generate the pressure to move water against the force of gravity from their roots to their shoots (leaves)? Capillary action (the tendency of a fluid to move through small spaces due to it's molecular constituents cohesive properties or surface tension) can explain the movement of water over small distances, but it cannot account for the large scale movement of water from the bases to the tips of tall trees like the Giant Sequoia of Redwood Forest.
Instead, it has long been thought that evaporation of water at the leaves draws water up in a long continuous column from the root, a process known as transpiration. This hypothesis was recently verified in the form of an artificial model1. Abraham Stroock and his graduate student at Cornell University built a small (10 cm) proof-of-concept tree model with artificial membranes representing roots and leaves and small "microfluidic" channels connecting them. Though small, this device demonstrates the functional capacity of the evaporation/water-column idea, and might eventually be used to test failures of this model (such as when air-bubbles intervene in the column) and to draw small amounts of water out of hard to reach places.
References:
1. Wheeler TD, Stroock AD. The transpiration of water at negative pressures in a synthetic tree. Nature, 455(7210): 208-212, 2008.
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