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Concept
Mass diffusivity
Summary
Diffusivity, mass diffusivity or diffusion coefficient is usually written as the proportionality constant between the molar flux due to molecular diffusion and the negative value of the gradient in the concentration of the species. More accurately, the diffusion coefficient times the local concentration is the proportionality constant between the negative value of the mole fraction gradient and the molar flux. This distinction is especially significant in gaseous systems with strong temperature gradients. Diffusivity derives its definition from Fick's law and plays a role in 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 dimensions of length2 / time, or m2/s in SI units and cm2/s in CGS units.
The diffusion coefficient in solids at different temperatures is generally found to be well predicted by the Arrhenius equation:
where
D is the diffusion coefficient (in m2/s),
D0 is the maximal diffusion coefficient (at infinite temperature; in m2/s),
EA is the activation energy for diffusion (in J/mol),
T is the absolute temperature (in K),
R ≈ 8.31446 J/(mol⋅K) is the universal gas constant.
An approximate dependence of the diffusion coefficient on temperature in liquids can often be found using Stokes–Einstein equation, which predicts that
where
D is the diffusion coefficient,
T1 and T2 are the corresponding absolute temperatures,
μ is the dynamic viscosity of the solvent.
Official source
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