Multispecies Diffusion: Fick’s Law Approximation
Using a Fick’s law approximation, the relative mass flux due to molecular diffusion is governed by
(3-58)
when assuming that the diffusive flux is proportional to the mole fraction gradient. If instead assuming that it is proportional to the mass fraction it becomes
(3-59)
In the equations above represents a general diffusion matrix (SI unit: m2/s) describing the diffusion of species i into the mixture. This form makes it possible to use any diffusion coefficient, matrix, or empirical model based on Fick’s law. For example, in situations when the mass transport is not dominated by diffusion, an alternative is to use the diffusion coefficients at infinite dilution,
These coefficients are typically more readily available compared to the binary diffusion diffusivities, especially for liquid mixtures.
The mixture diffusion correction described above for the mixture-averaged diffusion can also be applied in this case. Correspondingly, the resulting diffusive flux is
(3-60)
when using Equation 3-58 and
(3-61)
when instead using Equation 3-59.
When using the Fick’s Law approximation, Additional Transport Mechanisms can be accounted for in the same manner as described above for the mixture-averaged approximation.