Mass Diffusivity - Temperature Dependence of The Diffusion Coefficient

Temperature Dependence of The Diffusion Coefficient

Typically, a compound's diffusion coefficient is ~10,000× as great in air than 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.

The diffusion coefficient in solids at different temperatures is often found to be well predicted by

where

• is the diffusion coefficient
• is the maximum diffusion coefficient (at infinite temperature)
• is the activation energy for diffusion in dimensions of
• is the temperature in units of (kelvins or degrees Rankine)
• is the gas constant in dimensions of

An equation of this form is known as the Arrhenius equation.

An approximate dependence of the diffusion coefficient on temperature in liquids can often be found using Stokes–Einstein equation, which predicts that:

where:

T₁ and T₂ denote temperatures 1 and 2, respectively

D is the diffusion coefficient (cm2/s)

T is the absolute temperature (K),

μ is the dynamic viscosity of the solvent (Pa·s)

The dependence of the diffusion coefficient on temperature for gases can be expressed using the Chapman–Enskog theory (predictions accurate on average to about 8%):

where:

• 1 and 2 index the two kinds of molecules present in the gaseous mixture
• T – temperature (K)
• M – molar mass (g/mol)
• p – pressure (atm)
• – the average collision diameter (the values are tabulated) (Å)
• Ω – a temperature-dependent collision integral (the values are tabulated but usually of order 1) (dimensionless).
• D – diffusion coefficient (which is expressed in cm2/s when the other magnitudes are expressed in the units as given above).