Diffusion
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In physics, chemistry and biology, diffusion denotes the mixing of two or more substances or the net motion of a substance from an area of high concentration to an area of low concentration. The theory is that both of these result from the random motion of micro-scale individual agents (such as molecules) giving rise to net changes on the macro-scale. While originally formulated within the framework of the physical sciences, the concept of diffusion has been applied to phenomena such as the manner in which information is spread amongst a population. The chemistry definition of diffusion is the movement of a fluid from an area of higher concentration to an area of lower concentration.
Diffusion is an abstract topic and is often only explained as theoretical model. It is part of transport phenomena in general, and often accompanied by the much quicker convection (making it hard to observe 'pure' diffusion). A few examples are shown below.
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[edit] The diffusion equation
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To verify any microscopic model we may think up, we need to calculate its consequences and compare these to observation. Another way of arriving at a microscopic model is to write down a general equation and solve it mathematically (i.e. start from what you already know). This general equation, not refering to any microscopic model, is the diffusion equation
.
This equation is composed out of two true statements. One of these is the continuity equation
.
And the other Fick's law
,
where
is the flux, D is the diffusion constant, and
is the concentration of diffusing material.
The continuity equation is the mathematical equivalent to a piggybank. Your savings increase by the amount that you put in, they decrease by the amount you take out, no more and no less. Fick's law, on the other hand, was born as an empirical law which means that it describes observations and is not derived from any argument.
One general solution to the diffusion equation is a Gaussian one. This suggest an uncorrelated random walk as a microscopic model, completely in line with Robert Brown's observations.
[edit] Einstein relation
Einstein showed that 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
,
where γ is the drag coefficient (the inverse of the mobility). The Einstein relation follows directly to be
,
which is the most general expression for the diffusion coefficient, not refering to any microscopic model.
[edit] Entropy and diffusion
Diffusion increases the entropy of a system. This is nothing else than saying that diffusion is a spontaneous and irreversible process. Something can spread out by diffusing, but it won't spontaneously 'suck back in'.
[edit] In biology
In cell biology, diffusion is a main form of transport for necessary materials such as amino acids through cell membranes.[1]
[edit] No equilibrium system
Because diffusion is a transport process of particles, the system in which it takes place is no 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.
[edit] 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
- Ellusion 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 flow
- 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
- Active transport, pumping material across a cell membrane
- Pinocytosis, "cell drinking" intake of small droplets of lipids
- Phagocytosis, carrier proteins are used to transport glucose
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.
[edit] 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 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.
[edit] References
- ^ Maton, Anthea; Jean Hopkins, Susan Johnson, David LaHart, Maryanna Quon Warner, Jill D. Wright (1997). Cells Building Blocks of Life. Upper Saddle River, New Jersey: Prentice Hall, 66-67.
- Einstein, Albert (1956). Investigations on the Theory of the Brownian Movement. Dover. ISBN 0-486-60304-0.
[edit] See also
