# What is the difference between dispersion and diffusion?

What is the difference between dispersion and diffusion? Currently I believe, that diffusion is the mixture of molecules due to Brownian motion. So I read everywhere, that it happens with magnitude of the concentration gradient, and from higher concentration to lower concentration, cf. Fick's law.

It also seems that diffusion and dispersion happens always together, and that dispersion has something to do with the concentration gradient, and that the molecule transport by dispersion is of magnitudes bigger compared to diffusion.

What I am asking is, what exactly is dispersion with regard to molecule transport?

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Dispersive mass transfer, in fluid dynamics, is the spreading of mass from highly concentrated areas to less concentrated areas. It is one form of mass transfer.

Dispersive mass flux is analogous to diffusion, and it can also be described using Fick's first law:

$$J=-E\frac{dc}{dx}$$

where c is mass concentration of the species being dispersed, E is the dispersion coefficient, and x is the position in the direction of the concentration gradient.

Dispersion can be differentiated from diffusion in that it is caused by non-ideal flow patterns (i.e. deviations from plug flow) and is a macroscopic phenomenon, whereas diffusion is caused by random molecular motions (i.e. Brownian motion) and is a microscopic phenomenon. Dispersion is often more significant than diffusion in convection-diffusion problems.

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Are vortices a potential disturbance causing dispersion? – math Mar 12 '14 at 14:35
Vortices alone can transport mass and they can definitely influence dispersive mass transfer, but I wouldn't say that they cause it. – Wojciech Mar 12 '14 at 14:52
Ok, I still don't get it: what is meant by "non-ideal flow pattern" and what is "plug flow"? It sounds to me now, like random disturbances of flow, but by what cause? – math Mar 12 '14 at 16:50
@math I added links in the answer, if it is still unclear, let me know. – Wojciech Mar 12 '14 at 17:52
Be careful when using word "turbulence" in fluid dynamics, it has a rather precise meaning. Besides that, You're pretty much right. – Wojciech Mar 13 '14 at 9:44