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Fick's First Law Derivation

  1. Nov 16, 2015 #1
    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.

    Attached Files:

  2. jcsd
  3. Nov 17, 2015 #2
    There is no derivation of Fick's Law. It's empirical (from observations). The flux of a species is proportional to the concentration gradient.

  4. Nov 17, 2015 #3
    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.
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