Collective diffusion

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Collective diffusion is the diffusion of a large number of particles, most often within a solvent.

Contrarly to brownian motion, which is the diffusion of a single particle, interactions between particles may have to be considered, unless the particles form an ideal mix with their solvant (ideal mix conditions correspond to the case where the interactions between the solvant and particles are identical to the interactions between particles and the interactions between solvant molecules; in this case, the particles do not interact when inside the solvant).

In case of an ideal mix, the particle diffusion equation holds true and the diffusion coefficient D the speed of diffusion in the particle diffusion equation is independent of particle concentration. In other cases, resulting interactions between particles within the solvant will amount for the following effects:

the diffusion coefficient D in the particle diffusion equation becomes dependent of concentration. For an attractive interaction between particles, the diffusion coefficient tends to decrease as concentration increases. For a repulsive interaction between particles, the diffusion coefficient tends to increase as concentration increases.
In the case of an attractive interaction between particles, particles exhibit a tendency to coalesce and form clusters if their concentration lies above a certain treshold. This is equivalent to a precipitation chemical reaction (and if the considered diffusing particles are chemical molecules in solution, then it is a precipitation).

Collective diffusion

See also