Molecular diffusion

Molecular diffusion, often called simply diffusion, is a net transport of molecules from a region of higher concentration to one of lower concentration by random molecular motion. The result of diffusion is a gradual mixing of material. In a phase with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually result in complete mixing or a state of equilibrium.

Molecular diffusion is typically described mathematically using two Fick's laws.

Significance

Diffusion is part of transport phenomena. Of the mass transport mechanisms, molecular diffusion is known as a slower one. Molecular diffusion is generally superimposed on, and often masked by, other transport phenomena such as convection, which tend to be much faster. However, the slowness of diffusion can be the reason for its importance: diffusion is often encountered in chemistry, physics and biology as a step in a sequence of events, and the velocity of the whole chain of events is that of the slowest step. For example, the rate at which a chemical reaction progresses can be entirely limited by the rate of diffusion of reactants/products to/from the place where the reaction occurs. Diffusion of water is classified as osmosis.

The speed of diffusion can be approximately illustrated as follows (at room temperature)^[1]

In gas: 100 mm per minute;
In liquid: 0.5 mm per minute;
In solid: 0.0001 mm per minute.

The above numbers should be treated only as an illustration of the slowness of diffusion. Great differences exist in the diffusion speed between particular systems, particularly in the solid state. For example:^[1]

Hydrogen gas in solid iron at 10 °C - diffusion coefficient of 1.66x10^-13 m²/s;
Aluminum in solid copper at 20 °C - diffusion coefficient of 1.3x10^-34 m²/s.

Now, the diffusion speed is proportional to the square root of the diffusion coefficient. Therefore, hydrogen in iron diffuses over 10 orders of magnitude faster than does aluminum in copper.

In biology

In cell biology, diffusion is a main form of transport for necessary materials such as amino acids within cells.^[2]

Non-equilibrium system

Because diffusion is a transport process of particles, the system in which it takes place is not an equilibrium system (i.e. it is not at rest yet). For this reason thermodynamics and statistical mechanics are of little to no use in describing diffusion. However, there might occur so-called quasi-steady states where the diffusion process does not change in time. As the name suggests, this process is a fake equilibrium since the system is still evolving.

Types of diffusion

The spreading of any quantity that can be described by the diffusion equation or a random walk model (e.g. concentration, heat, momentum, ideas, price) can be called diffusion. Some of the most important examples are listed below.

Atomic diffusion
Brownian motion, for example of a single particle in a solvent
Collective diffusion, the diffusion of a large number of (possibly interacting) particles
Eddy diffusion
Effusion of a gas through small holes.
Electronic diffusion, resulting in electric current
Facilitated diffusion, present in some organisms.
Gaseous diffusion, used for isotope separation
Heat equation
Itō diffusion
Knudsen diffusion
Momentum diffusion, ex. the diffusion of the hydrodynamic velocity field
Osmosis is the diffusion of water through a cell membrane.
Photon diffusion
Reverse diffusion
Rotational diffusion
Self-diffusion
Surface diffusion

Metabolism and respiration rely in part upon diffusion in addition to bulk or active processes. For example, in the alveoli of mammalian lungs, due to differences in partial pressures across the alveolar-capillary membrane, oxygen diffuses into the blood and carbon dioxide diffuses out. Lungs contain a large surface area to facilitate this gas exchange process.

An experiment to demonstrate diffusion

Diffusion is easy to observe, but care must be taken to avoid a mixture of diffusion and other transport phenomena.

It can be demonstrated with a wide glass tube, paper, two corks, some cotton wool soaked in ammonia solution and some red litmus paper. By corking the two ends of the wide glass tube and plugging the wet cotton wool with one of the corks, and litmus paper can be hung with a thread within the tube. It will be observed that the red litmus papers turn blue.

This is because the ammonia molecules travel by diffusion from the higher concentration in the cotton wool to the lower concentration in the rest of the glass tube. As the ammonia solution is alkaline, the red litmus papers turn blue. By changing the concentration of ammonia, the rate of color change of the litmus papers can be changed.

Another, simpler experiment to show diffusion is to drip a drop or two of food colouring into a glass of water. At first the food colouring will be very dark and concentrated at the spot where it hit the water, but after a while it will drift apart and fill the whole glass with a lighter shade of its colour. This is the dye diffusing in the water.

References

^ ^a ^b E.L. Cussler, "Diffusion. Mass Transfer in Fluid Systems", 2nd edition, Cambridge University Press, 1997, page 1.
^ Maton, Anthea (1997). Cells Building Blocks of Life. Upper Saddle River, New Jersey: Prentice Hall. pp. 66–67. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

External links

[Cus-1] E.L. Cussler, "Diffusion. Mass Transfer in Fluid Systems", 2nd edition, Cambridge University Press, 1997, page 1.

[2] Maton, Anthea (1997). Cells Building Blocks of Life. Upper Saddle River, New Jersey: Prentice Hall. pp. 66–67. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

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