How is Fick's First Law derived?

[yosimba2000]

How do you derive it? I'm looking for the form J = -D(dC/dX)

From the image, I am assuming left side is of higher concentration. N represents the number of molecules.

My work:

Mass balance
Net molecules in from concentration gradient =
Net = N(x) - N(x+Delta X)

Net concentration in = molecule/volume
= [N(x) - N(x+delta x)] / (A * Delta X)
= dC

And then I'm stuck! I probably went about this totally wrong.

 

[Chestermiller]

There is no derivation of Fick's Law. It's empirical (from observations). The flux of a species is proportional to the concentration gradient.

Chet

 

[MexChemE]

The best you can get is a physical statement of Fick's law and its translation to mathematical terms. Check out the first pages of section 17.1 of Transport Phenomena by BSL.