Fick's law of diffusion: Encyclopedia II - Fick's law of diffusion - Fick's Second Law

Fick's law of diffusion - Fick's Second Law

Fick's Second Law is used in non-steady state diffusion, i.e., when the concentration within the diffusion volume changes with respect to time.

Where

• Φ is the concentration in dimensions of [parts length^-3], [mol dm^-3]
• t is time [s]
• D is the diffusion coefficient in dimensions of [length² time^-1], [m² s^-1]
• x is the position [length], [m]

It can be derived from the First Fick's law and the material balance:

Assuming the diffusion coefficient D to be a constant we can exchange the orders of the differentiating and multiplying on the constant:

and, thus, receive the form of the Fick's equations as was stated above.

For the case of 3-dimensional diffusion the Second Fick's Law looks like:

where is the usual del operator.

Finally if the diffusion coefficient is not a constant, but depends upon the coordinate and/or concentration, the Second Fick's Law looks like:

Adapted from the Wikipedia article "Fick's Second Law", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki