Movement of Water

There are three fundamental methods by which water can move from one  place to another: Diffusion, Bulk Flow and osmosis 

Diffusion

The passive movement of any material from an area of higher  concentration to an area of lower concentration is often called  diffusion. The basis for this movement is the kinetic energy of  individual molecules. As these molecules collide with each other they will  disperse into space, perhaps among molecules of another type. For a cell:

The rate of movement in diffusion is shown by Fick's Law:

J_s = -D_s • ΔC_s •  Δx^-1

J_s is the rate of movement or flux density usually  measured as the moles of substance s crossing a square meter of area per second.  D_s is the diffusion coefficient indicating how easily substance s  moves through the medium. If the medium is air, then the coefficient is high and  movement is rapid. In liquid, the coefficient is low and movement is slow by  comparison. ΔC_s is the concentration difference between the area of  high and area of low concentration. The negative sign indiates that the movement  is from the area of high to the area of low concentration. Δx is the distance  between the areas of high and low concentration. Another way to say all this is  that material moves faster when the substance shows good fluidity, the  concentration gradient is steeper, and the needed travel is short.

Diffusion works only over short distances

How short is short for travel? If we think about sucrose, the  transport form of photosynthate in plants, moving in a plant by diffusion, the  distance must be very short indeed. For sucrose the D_s is 0.5 •  10^-9m²s^-1, the diameter of a cell is 50 µm (=  50 • 10^-6m)...

Fick's law gives us:

t = x² • D_s^-1

Now we plug in the values above:

t = (50 • 10^-6m)² • (0.5 •  10^-9m²s^-1)^-1 = 2.5 s

So diffusion can explain a reasonably sensible rate of movement for  a sucrose molecule across a cell. But diffusion will fail to explain movement  when the distance gets larger. To test that out, imagine sucrose made in the tip  of a sugar cane leaf diffusing to the base of that leaf. That distance is about  1 meter. When you plug 1 meter in for the distance in the formula above, the  time calculates out to 32years! Now everyone knows that a sugar cane leaf  never lasts 32 years...more likely less than one year. So diffusion is too slow  to explain how sucrose gets out of a sugar cane leaf.

Many books in describing diffusion use an analogy of dropping some  dye in the corner of a swimming pool and that with time this dye would become  evenly distributed in the pool. Now you realize that this will take more than a  lifetime if the movement of the dye were due exclusively to diffusion. Obviously  these books are wrong about what moves the dye around in the pool to see it  happen in your lifetime.

Now to get really ridiculous, we can calculate the time for sugar to  diffuse from the bottom of a huge tree to its apical bud (say 70 meters). That  distance calculates out to 310,755.96 years! Even the oldest bristlecone pine  tree is "only" 5000 years, and the tallest coastal redwood must transport sugar  over even greater distances than 70 meters to get sucrose to the roots. So  diffusion will not explain sugar movement over tissue and organ  distances.

Bulk flow explains long-distance water movement

Bulk flow is the movement of a substance under influence of pressure  from an area of greater pressure to an area of lesser pressure. Rather than  individual molecules moving on the basis of their own kinetic energy, large  volumes of molecules move together in bulk. Typically we describe this movement  as through a pipe (plumbing), a tube (phloem), or a channel (river), but it  applies equally well to convection currents. Aha! this is how the dye moves in  the pool and how sugar gets from the end of a leaf to its base or from leaves to  roots.

The rate of bulk flow is shown in the Poiseuille Equation:

v = π r⁴ (8η)^-1 •  ΔΨ_p Δx^-1

The rate of flow is proportional to the fourth power of the radius  of the pipe (channel, convection current, etc.). In other words, increasing the  pipe radius by a factor of two will increase the flow rate by a factor of 16.  The rate of flow is inversely proportional to 8 times the viscosity of the  fluid. A more viscous fluid (maple syrup) will move more slowly than maple sap  in the pipe. The rate of flow is directly related to the pressure difference  between the ends of the pipe. Increasing the pressure at one end of the pipe  increases the rate of flow.

You should notice that the solute concentration has no effect on  bulk flow.

Bulk flow can obviously work in phloem and xylem as these are  basically pipes. Moreover as short plants evolved into tall trees, the xylem had  to increase the number of pipes feeding the canopy. This explains the evolution  of secondary growth. It is also not surprising that as dicots evolved into trees  with massive canopies, tracheids became eclipsed by vessels with much greater  radius. These changes help supply the water needs of a massive canopy such as  those in tropical trees.

Osmosis is the passive movement of water across a membrane

The actual movement of water through a cell membrane is the result  of two processes: diffusion and bulk flow. As you recall a membrane is the  thickness of a phospholipid bilayer. The size of a water molecule permits it to  pass through the bilayer. This would be largely a diffusion movement subject to  Fick's Law. The membrane also posesses integral proteins; the one involved with  water transport is called an aquaporin. The aquaporin protein serves as a  water-filled pipe across the membrane.

Aquaporins aremembrane pore proteins. Aquaporins arecommonly composed of four (typically) identical subunit proteins in mammals,with each monomer acting as a water channel.

Aquaporins are made up of six transmembrane α-helices arranged in a right-handed bundle, with the amino and the carboxyl termini located on the cytoplasmic surface of themembrane. Wate rmolecules traverse through the pore of the channel in single file. The presence of water channels increases membrane permeability to water.

Generally the movement of water across the membrane is not treated  by plant physiologists as either diffusion or bulk flow. Rather plant  physiologists focus upon the driving force for osmosis...energy.