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For self-diffusion in gases at two different pressures (but the same temperature), the following empirical equation has been suggested: [4] =, where D is the diffusion coefficient, ρ is the gas mass density, P 1 and P 2 are the corresponding pressures.
The self-diffusion coefficient of water has been experimentally determined with high accuracy and thus serves often as a reference value for measurements on other liquids. The self-diffusion coefficient of neat water is: 2.299·10 −9 m 2 ·s −1 at 25 °C and 1.261·10 −9 m 2 ·s −1 at 4 °C. [2]
Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation.
Random collisions of particles in a gas. The diffusion coefficient is the coefficient in the Fick's first law = /, where J is the diffusion flux (amount of substance) per unit area per unit time, n (for ideal mixtures) is the concentration, x is the position [length].
The diffusivity for Knudsen diffusion is obtained from the self-diffusion coefficient derived from the kinetic theory of gases: [2] = = For Knudsen diffusion, path length λ is replaced with pore diameter , as species A is now more likely to collide with the pore wall as opposed with another molecule.
D is the diffusion coefficient, which will differ from gas to gas, and from membrane to membrane, according to the size of the gas molecule in question, and the nature of the membrane itself (particularly its viscosity, temperature and hydrophobicity). φ is the concentration of the gas. x is the position across the thickness of the membrane.
The diffusion coefficient can be combined with the sorption equilibrium parameter to get the final form of the equation, where is the permeability of the membrane. The relationship being P = S D {\displaystyle P=SD}
For diffusion coefficients and thermal diffusion coefficients the picture is somewhat more complex. However, one of the major advantages of RET over classical Chapman–Enskog theory is that the dependence of diffusion coefficients on the thermodynamic factors, i.e. the derivatives of the chemical potentials with respect to composition, is ...