378
9 Bioenergetics
plant leaf cells is controlled by stomate guard cells that expand or contract by water
osmosis. Osmotic pressure in plant cells from ground water helps to keep plant
stems stiff. Since our cells have a salinity greater than fresh water, when we bathe
or swim in fresh water, there will be an intake of water through our skin into our
cells. If we attempt to satiate our thirst with salt water, the effect in our gut is likely
to be a loss of water, not a gain. Within protozoans, contractile vacuoles take up
water by osmosis, and then discharge their contents through the cell wall, relieving
the cell of built-up osmotic pressure.
9.20 Diffusion
Suppose there is a concentration gradient of small particles in a solution, such as
macromolecules in water. These particles are in constant motion from thermal collisions. If there is a concentration of such particles, there is a statistical probability
that thermal collisions will spread the particles from higher density regions to lower
density regions. We measure the density of particles by their concentration C (in
number per unit volume). The flux of those particles moving by diffusion is denoted
J D and is defined by the net number of particles which pass through a fixed small
area per unit time per unit area. The particles will diffuse with some average speed
we will denote by v D . This is not individual speeds of particles, but the speed of the
macromolecules drifting through the water averaged over times large compared to
the time between collisions with the background water molecules. The flux of these
macromolecules will then satisfy
J D = Cv D .
(9.143)
Now we should expect that the diffusing particles should drift toward regions of
lesser concentration, with a flux proportional to the gradient of that concentration.
This is Fick’s Law:
(J D ) x = −D
∂C
∂x
(9.144)
where (J D ) x is the net particle flux in the direction x. Fick’s Law defines the particle
diffusion constant D. It is an analog of the rate at which heat flows across a thermal
gradient. (See Sect. 9.5.) In three dimensions, Fick’s law reads
J D = −D ∇C ,
(9.145)
incorporating the expected fact that diffusion occurs in the direction of the largest
gradient of the concentration, and toward lower concentration.
Conservation of particle number means that the net change per unit time in
particle number in a layer of fluid of thickness dx is determined by the net flux
9 Bioenergetics
plant leaf cells is controlled by stomate guard cells that expand or contract by water
osmosis. Osmotic pressure in plant cells from ground water helps to keep plant
stems stiff. Since our cells have a salinity greater than fresh water, when we bathe
or swim in fresh water, there will be an intake of water through our skin into our
cells. If we attempt to satiate our thirst with salt water, the effect in our gut is likely
to be a loss of water, not a gain. Within protozoans, contractile vacuoles take up
water by osmosis, and then discharge their contents through the cell wall, relieving
the cell of built-up osmotic pressure.
9.20 Diffusion
Suppose there is a concentration gradient of small particles in a solution, such as
macromolecules in water. These particles are in constant motion from thermal collisions. If there is a concentration of such particles, there is a statistical probability
that thermal collisions will spread the particles from higher density regions to lower
density regions. We measure the density of particles by their concentration C (in
number per unit volume). The flux of those particles moving by diffusion is denoted
J D and is defined by the net number of particles which pass through a fixed small
area per unit time per unit area. The particles will diffuse with some average speed
we will denote by v D . This is not individual speeds of particles, but the speed of the
macromolecules drifting through the water averaged over times large compared to
the time between collisions with the background water molecules. The flux of these
macromolecules will then satisfy
J D = Cv D .
(9.143)
Now we should expect that the diffusing particles should drift toward regions of
lesser concentration, with a flux proportional to the gradient of that concentration.
This is Fick’s Law:
(J D ) x = −D
∂C
∂x
(9.144)
where (J D ) x is the net particle flux in the direction x. Fick’s Law defines the particle
diffusion constant D. It is an analog of the rate at which heat flows across a thermal
gradient. (See Sect. 9.5.) In three dimensions, Fick’s law reads
J D = −D ∇C ,
(9.145)
incorporating the expected fact that diffusion occurs in the direction of the largest
gradient of the concentration, and toward lower concentration.
Conservation of particle number means that the net change per unit time in
particle number in a layer of fluid of thickness dx is determined by the net flux