diffusion: c s x - d s j s = difference in concentration distance diffusion coefficient flux of a...
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Diffusion:
Cs
X- Ds Js =
difference in concentration
distance
diffusion coefficient
flux of a solute in solution
=
(mass/surface area/time)
1. Diffusion
Fick (1855) discovered that the rate of solute transport is directly proportional to the concentration gradient and inversely proportional to distance traveled.
Fick’s Law describes passive movement of molecules down a concentration gradient. Substances move from high [ ] to low [ ].
Diffusion:
Cs
X- Ds Js =
difference in concentration
distance
diffusion coefficient
flux of a solute in solution
=
(mass/surface area/time)
Diffusion:
From Fick’s Law, can predict the time it takes for a substance to diffuse a particular distance
X)2
Dt ½ =
diffusion in a cell:
small molecule
. ...
. .
.. . .
....
X = 50 m
X)2
Dt ½ =
(0.00005 m)2
10-9 m2 s-1=
= 2.5 sec
Conclude: diffusion is rapid across small distances (i.e., within a cell).
Diffusion:
X)2
Dt ½ =
But … replace 50 m with 1 m and t½ becomes 24 years!
So … diffusion important only over very short distances. It can not possibly explain long distance movement within the plant.
Diffusion: describes water evaporation from stomata
.
Cwv high
Cwv low
Cwv
X- Dwv Jwv =
the driving force
the resistance
2. Bulk flow (mass flow):
movement along pressure gradients (e.g., flow in a garden hose, flow in xylem or phloem)
long distance transport in plants
volume rate of flow
driving force
~
(cm3 cm-2 s-1)
Bulk flow (mass flow):
relationship determined experimentally by Jean-Louis Poiseuille in 1840
used glass capillary tubes (d = 0.01 – 0.3 mm)
Bulk flow (mass flow): Poiseuille Equation
P
X
r2
8.Jv =
Jv volume rate of flow per unit area
r radius
viscosity
P change in hydrostatic pressure
X path length
Bulk flow (mass flow): Poiseuille Equation
P
X r2
8 Jv =
What is the pressure gradient necessary to cause flow in xylem vessels?
rearranging:
Bulk flow (mass flow): Poiseuille Equation
P
X r2
8 Jv =
picking some “reasonable” values:
r = 20 m = 0.01 g cm-1 s-1
Jv = ?
Bulk flow (mass flow): estimating sap velocity
thermocouple
voltage applied
hardwoods (large diameter vessels) like oak, ash
20-25
conifers (narrow tracheids) 2-4
m/hr
heatpulse
use 3.6 m/hr = 0.1cm/sec
Bulk flow (mass flow): Poiseuille Equation
P
X r2
8 Jv =
picking some “reasonable” values:
r = 20 m = 0.01 g cm-1 s-1
Jv = 0.1 cm s-1
Bulk flow (mass flow): Poiseuille Equation
P
X r2
8 Jv =
What is the pressure gradient necessary to cause flow in xylem vessels?
(0.1 cm s-1)(0.08 g cm-1 s-1)
(2 x 10-5)2=
= 0.2 bar m-1
0.2 bar m-1
This is the hydrostatic pressure gradient necessary to obtain flow in a horizontal tube of 20 m radius.
P = 1 bar P = 3 bar
10 m
P = -2 bar P = -4 bar
0.2 bar m-1 overcomes the frictional resistances in the tube.
Water transport in plants:
1. diffusion: within a cell or tightly localized
2. bulk flow (mass flow): long distance; no membranes crossed
3. osmosis: cell to cell, crossing membranes
0.2 bar m-1
This is the hydrostatic pressure gradient necessary to obtain flow in a horizontal tube of 20 m radius.
P = 1 bar P = 3 bar
10 m
P = -2 bar P = -4 bar
0.2 bar m-1 overcomes the frictional resistances in the tube.
10 m
Gravity effect
- 5 bars
- 8 bars
H2O at 10 m will move downward unless the force of gravity is opposed.
So … not only need 0.2 bar m-1
but also need: 0.1 bar m-1
0.3 bar m-1
to move H2O against the force of gravity and through the frictional resistance of the xylem
100 m !!
in giant Sequoia:
30 bars more negative up here
than here
(in order to move water at rates similar to that observed in transpiring plants)
i.e., 3 bars for every 10 m
Partial summary:
1. Diffusion H2O (or any substance) flows along concentration gradients from high [ ] low [ ]
Relatively rapid across short distances but can’t explain long-distance transport
Partial summary:
2. Mass flow (bulk flow)
long-distance transport in plants
flow is along pressure gradients (Poiseuille)
supports rapid movement
e.g., a transpiring sunflower leaf loses the equivalent of its entire leaf H2O content every 20 min
Water transport in plants:
3. Osmosis (van’t Hoff, 1887)
movement of a solvent (e.g., H2O) across a semi-permeable membrane
H2O will flow across membrane into solution where the chemical potential (free energy) of the H2O is lower
Water transport in plants:
3. Osmosis
flow is spontaneous in response to a driving force
high wlow w
A B
solute less concentrated
solute more concentrated
an osmotic pressure will develop in “B” = = RTCs
water
van’t Hoff1887
osmotic pressure = = RTCs
R = universal gas constantT = ° KCs = osmolality = moles of solute kg-1 H2O
plant cell sap contains ~ 0.5 2.5 mol kg-1
= RTCs
= R(293)(0.75 mol kg-1)= 18.3 bars !! (this is ~ 260 psi)
(sea water is ~ 28 bars)
VAC
CYT
i.e, the pressure on the internal wall can easily be 18 to 20 bars
This illustrates that plant cells have very substantial capacity to draw in and retain water.
Osmosis is critical in cell enlargement - expansion
role of elastic cell walls
they have sufficient structural rigidity to allow P to build up
f (concentration)
pure water
Does this raise or lower the free energy content of the H2O molecules?
add solute (e.g., sucrose)
. ...
.. ...
. .. .
.
Solutes decrease the free energy of the H2O molecules. Therefore vapor pressure is decreased.
The contribution of solutes to w is always negative (always lowers w ).
f (pressure)
VAC
CYT
+ P (i.e., turgor) on inner walls of living cells
p
w = 0
then: w = + p
w = - 12 + 4
= - 8
e.g., = -12 p = +4
f (pressure)
-P (i.e., tension or negative hydrostatic pressure) in xylem cavity and cell walls
p
w = 0
xylem
small radiisurface tension of H2Oadhesion and cohesion
give rise to negative pressures
and because the column of H2O is continuous, the -P is transmitted all the way to the roots
95% RH(-69 bars)
60% RH(-700 bars)
50% RH(-950 bars)
soil surface
.
.
.
.
water-filled pore in the soil. AA - 2 bars
- 4 bars
- 6 bars
- 8 bars
- 12 bars
- 18 bars
BB.
H2O is continuous from A B
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