Relative Flux And Fick’s Law

Relative Flux and Fick’s Law

If the only transfer relative to a fixed frame is convection, i.e., if simply [pic], then convection would be the only mechanism for mass transfer. However, we knowfrom experience that there is a transfer of species relative to, for example, the mass average velocity, especially when there is a concentration gradient. From our previous discussion, for example,[pic]
is the mass flux relative to the mass average velocity. Then the specie balance equation,

[pic]
or
[pic]
can be interpreted in the following manner:net convective transport out/unit volume
rate of production per unit volume
[pic]net relative transfer out per unit volume
rate of accumulation per unit volume



Binary Systems (A&B)

From kinetictheory it is known that

[pic] .
Here

[pic], the relative activity on a molar basis,
and
[pic] .

(In going from the [pic] to the [pic] formulation the following identities were used:[pic]

[pic]

There are many other forms for the flux equation. The basic problem is to deduce from experimental evidence or theory what state properties [pic] depends on and what is thefunctional form. Fick’s law relates the relative flux to the concentration gradient similar to Fourier’s law of heat conduction and is referred to as a constitutive relationship. Since a contiuum approach isbeing used herein, the specific form of the constitutive relationship cannot be obtained directly.
Other equivalent forms are:

[pic]











Flux Gradient Fick’s Law[pic] [pic] [pic]


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