Definitions

# Diffusion

[dih-fyoo-zhuhn]

Diffusion is the net movement of particles (typically molecules) from an area of high concentration to an area of low concentration by uncoordinated random movement. In a phase with uniform temperature, absent external net forces acting on the particles, the diffusion process will eventually lead to complete mixing.

Diffusion is part of transport phenomena. Of the material transport mechanisms, diffusion is known as a slow 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 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.

The speed of diffusion can be approximately illustrated as follows (at room temperature)

• in gas: 100 mm per minute
• in liquid: 0.5 mm per minute
• in solid: 0.0001 mm per minute

## Mechanism

Diffusion is driven by random thermal motion of molecules.

Diffusion is a statistical phenomenon in that the chance of a molecule "jumping" from one volume to another depends on the number of molecules in the first volume, so molecules in volumes which have a relatively high initial concentration tend to disperse to less concentrated areas until a balance of exchange (equilibrium) is reached.

## Einstein relation

Fick's law (empirical) can be derived by noting that the flux due to diffusion only can depend on the chemical potential, and taking this potential to be that of an ideal gas. This last step is justified because the final stage of a spreading concentration may be described as an ideal gas. The result is

$mathbf\left\{J\right\} \left(mathbf\left\{r\right\} , t\right) = - frac\left\{kT\right\}\left\{gamma\right\}mathbf\left\{nabla\right\} c \left(mathbf\left\{r\right\}, t\right)$,

where $gamma$ is the drag coefficient (the inverse of the mobility). The Einstein relation follows directly to be

$D = frac\left\{kT\right\}\left\{gamma\right\}$,

which is the most general expression for the diffusion coefficient, not referring to any microscopic model.

## Entropy and diffusion

Diffusion increases the entropy of a system. In other words, diffusion is a spontaneous and irreversible process. Something can spread out by diffusing, but it won't spontaneously 'suck back in'. Thermodynamically, diffusion is a process to lower the free energy of the system, to increase the entropy. That is, diffusion is driven by gradients of the chemical potential rather than gradients of the chemical concentration, implying that diffusion, under certain circumstances, may occur against a concentration gradient.

## In biology

In cell biology, diffusion is a main form of transport for necessary materials such as amino acids through cell membranes.

## Non equilibrium system

Because diffusion is a transport process of particles, the system in which it takes place is a non 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.

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.

## Experiments 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 tubed 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 way to demonstrate diffusion is to drop a drop of ink by dropper into a glass of water. One can see the ink spreads slowly from the initial region where the ink first encountered the water surface, to everywhere in the glass. This is because the dye molecules in the ink diffuses from the high concentration region to other lower concentration regions.

## References

• Einstein, Albert (1956). Investigations on the Theory of the Brownian Movement. Dover.