Diffusion coefficient
Diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is encountered in Fick's law and numerous other equations of physical chemistry.
The diffusivity is generally prescribed for a given pair of species and pairwise for a multi-species system. The higher the diffusivity (of one substance with respect to another), the faster they diffuse into each other. Typically, a compound's diffusion coefficient is ~10,000× as great in air as in water. Carbon dioxide in air has a diffusion coefficient of 16 mm2/s, and in water its diffusion coefficient is 0.0016 mm2/s.
Diffusivity has an SI unit of m2/s (length2 / time). In CGS units it is given in cm2/s.
The diffusion coefficient in solids at different temperatures is generally found to be well predicted by the Arrhenius equation:
where
An approximate dependence of the diffusion coefficient on temperature in liquids can often be found using Stokes–Einstein equation, which predicts that
where
The dependence of the diffusion coefficient on temperature for gases can be expressed using Chapman–Enskog theory (predictions accurate on average to about 8%):
where
For self-diffusion in gases at two different pressures (but the same temperature), the following empirical equation has been suggested:
where
The effective diffusion coefficient describes diffusion through the pore space of porous media. It is macroscopic in nature, because it is not individual pores but the entire pore space that needs to be considered. The effective diffusion coefficient for transport through the pores, De, is estimated as follows:
where
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