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Transport:
2.
A particle
model and factors affecting the rate of diffusion and Fick's Law of diffusion applied to biology
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INDEX
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(2A) A particle model and factors
affecting the rate of diffusion
 A particle model of diffusion in gases
and liquids:
Reminder: All fluid particles (gases or
liquids) are in constant random motion in all directions
(right picture). The picture sequence
below could represent the diffusion of
molecules or ions in cell fluids or blood stream or gases in
the lungs. Imagine the diffusion gradient from left to
right for the green particles added to the blue particles on
the left (no semi-permeable shown here, just the idea of a
concentration gradient adjacent to a cell membrane). The blue particles could we water and the green particles
could be a sugar, protein or carbon dioxide molecule. So,
for the green particles, net migration is from left to right and will continue, in
a sealed container, until all the particles are evenly
distributed (as pictured). BUT, as in living organism, if the green particles
are removed or used in some
process on the right, then net migration (net diffusion)
would continue until there was not enough green particles to
create a diffusion gradient from left to right i.e. become
evenly very dilute.
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Be
able to define diffusion as the movement of particles from an area of high
concentration to an area of lower concentration.
You experience the gas diffusion experiment (or the diffusion particle
picture above!) if somebody sprays perfume or deodorant into a room (green
particles in the diagram above!).
Even without draughts or convection, the odour will eventually
enter your nose and be detected by your sense of smell in any area of the
room.
Similarly you can smell petrol or diesel fumes throughout garage due to
the diffusion of fuel vapour molecules,
You should know that all liquid or dissolved particles have
kinetic energy and so in constant random motion in all directions and tend to spread in
all directions, BUT, on average, they will tend to migrate from a region of
higher concentration to a region of lower concentration.
The two experiments described above illustrate this random spreading, but by
the nature of the experiment design you will see initially the spreading on
average is upwards because the coloured substance starts off at the bottom of
the container where the concentration will be very high.
Note:
(i) The bigger the concentration difference between two adjacent regions, the
steeper the diffusion gradient and the faster the rate of diffusion takes in
terms of the net transfer of a particular molecule or ions (eg sugar or
sodium ions etc.).
(ii) If the system is warmer, at a higher temperature, the particles gain kinetic
energy and can on average move faster and so diffusion is faster.
(2B) Factors affecting the rate of
diffusion and Fick's Law of diffusion
The diffusion situation might be exchange of gases in the lungs or
movement of molecules and ions through a cell membrane. Three rate of
diffusion factors are described and explained in the context of transferring
substances through a membrane.
Factors affecting the rate of diffusion of particles through a
membrane - you may be talking about diffusion or osmosis and active
transport.
Expressed as how diffusion rate is increased - since that's
usually what you want in organisms!
(i) The larger the surface area
of the membrane, the greater the rate of diffusion.
This factor can also be expressed as
increase in
surface/volume ratio, so increasing the rate of substance
transfer - there is a bigger chance of a particle passing
through a given larger area.
(ii) The steeper the concentration gradient, meaning the
greater the difference between the highest concentration and the lowest
concentration area on either side of membrane, the greater the rate of
diffusion.
So, in a given time, more particles will diffuse from the area of
highest concentration to the area of lowest concentration at a
greater rate, the greater the concentration difference - more
particles available to move to area of lower concentration.
If the concentration was uniform i.e. equal on both sides of the
membrane, there would be no net diffusion - no net transfer
(ignoring active transport which can operate against a diffusion
gradient).
(iii) The shorter the distance the particles have to diffuse -
e.g. the thinner the membrane.
The shorter the time needed to transfer particles, the greater
the rate of diffusion - think of how thin membranes are!
FICK'S LAW relates factors
(i) to (iii) and states:
Rate of diffusion
(surface area x concentration difference) ÷ (diffusion distance)
(iv) Rates of transfer of substance by diffusion will
increase with increase in
temperature - the particles (molecules or ions) have more
kinetic energy and their average speed increases - e.g. particles can move in and
out of cells down diffusion gradients more rapidly.
BUT, there will be a limit e.g. in mammals, many enzyme reactions
have an optimum temperature of 37oC, and malfunction if
overheated!
Therefore, for a healthy organism at constant temperature, its
not an important factor.
 Fick's Law on the rate
of diffusion of particles relating to a membrane
Fick's Law expresses the three diffusion factors (i) to (iii)
described above in a 'proportional' mathematical formula for a thin
membrane context:
In this context Fick's Law can be stated as:
Rate of diffusion
(surface area x concentration difference)
÷
(thickness of membrane)
Diffusion rate
(factor (i) x factor (ii))
÷
factor (iii)
Rate
{(surface area) x (concentration difference - gradient)} ÷ (thickness of membrane - diffusion gradient
distance)
In terms
of the simple graph diagram above where d = ∆x =
membrane thickness:
Diffusion rate
(membrane area x
∆c)
÷
∆x
(i) A
bigger surface area of membrane - bigger
net rate of
diffusion.
If you can double or triple the surface area in an organ, you
can double or triple the rate of diffusion = rate of transfer of
substances.
This assumes a constant diffusion gradient due to constant
concentrations, same thickness of
membrane (and constant temperature).
In terms of particles, you can argue there is a bigger chance
of a particle passing through a given larger area.
(ii) A bigger concentration difference - bigger
net rate of
diffusion
For a given membrane of fixed surface area and thickness, the
bigger the difference in concentration between the two sides of
the membrane, the steeper the diffusion gradient, the faster the
particle diffusion rate.
Suppose in terms of concentrations on either side of a
membrane
(a) the concentrations were 0.05 mol/dm3
and 0.10 mol/dm3
(b) the concentrations were 0.025 mol/dm3
and 0.15 mol/dm3
concentration differences:
(a) 0.10 - 0.05 = 0.05; (b) 0.15 - 0.025
= 0.125
For a given membrane (constant surface area and
thickness) the ratio of the rates of diffusion will be
0.125/0.05 = 2.5
In other words the rate of diffusion in situation (b) is
2.5 times faster than situation (a).
This argument assumes the same thickness of membrane and
the same surface area (and constant temperature).
(iii) A
thinner membrane - bigger net rate of diffusion
Less distance for particles to travel, so less
time needed for transfer.
If you can halve the thickness of a membrane you can double
the rate of diffusion through it because you are halving the
distance and
time needed to diffuse through the membrane and for
the same concentrations you are doubling the diffusion gradient.
This assumes a constant surface area and a constant the diffusion gradient.
Some examples
of Fick's Law calculations
Ex. 1. Suppose
an exchange surface has an area 20
µm2 and a membrane thickness of 0.005
µm.
If the concentrations of a substance are 0.20 mol/dm3
and 0.05 mol/dm3 on either side of the membrane,
calculate a relative rate of diffusion.
Relative diffusion rate
surface are x concentration difference
÷
thickness of membrane
Diffusion rate
(membrane area x ∆c)
÷
∆x
Relative diffusion rate = 20 x (0.20 - 0.05) / 0.005 =
600
Ex. 2. Lets
change the values to decrease the rate of diffusion across a membrane.
Suppose an exchange surface has an area 15
µm2 and a membrane thickness of 0.010
µm.
If the concentrations of a substance are 0.15 mol/dm3
and 0.05 mol/dm3 on either side of the membrane,
calculate a relative rate of diffusion.
Relative diffusion rate
surface are x concentration difference
÷
thickness of membrane
Diffusion rate
(membrane area x ∆c)
÷
∆x
Relative diffusion rate = 15 x (0.15 - 0.05) / 0.01 =
150
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