Einstein-Smoluchowsky law

The relation between length and time scales of diffusion, calculated from the Einstein-Smoluchowski law (Eq. 18-8), are shown in Fig. 18.11 for diffusivities between 10 10 cm2s 1 (helium in solid KC1) and 108 cm2s (horizontal turbulent diffusion in the atmosphere). Note that the relevant time scales extend from less than a millisecond to more than a million years while the spatial scales vary between 1 micrometer and a hundred kilometers. The fact that all these situations can be described by the same gradient-flux law (Eq. 18-6) demonstrates the great power of this concept. 

Does this sound familiar Yes, it should remind us of the Einstein-Smoluchowski law, Eq. 18-8. In fact, the analogy suggests that dispersion can be described by the same mathematical formalism as diffusion, that is, by the first and second Fickian laws (Eqs. 18-6 ad 18-14). We just have to replace diffusivity D by the dispersion... 

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