Dear Adil Mihoub,

In the parabolic diffusion model the diffusion controlled phenomena are rate-limiting.  

The parabolic diffusion equation has successfully described metal reactions in soils and soil constituents, feldspar weathering and pesticide reactions. 

The following are the two forms of the parabolic diffusion equation:

Qt/Qinf = 4/pi1/2(Dt/r2)1/2 - Dt/r2

1/t (Qt/Qinf) = 4/pi1/2(D/r2)1/2 1/t2 - D/r2

A plot of (Qt/Qinf)/t versus 1/t1/2 should give a straight line with a slope of:

4/pi1/2(D/r2)1/2 and intercept (-D/r2). Thus if r is known, D can be calculated from both slope and intercept.

Where r is the radius of the cylinder, Qt is the quantity of diffusing substance that has left the cylinder at time t, Qinf is the corresponding quantity after infinite time, and D is an "apparent" diffusion coefficient. 

For the relatively short times in most experiments, the third and subsequent terms may be ignored.

For more information on this topic, please read the attached publication.

Hoping this will be helpful,

Rafik

Many Thanks

Have a wenderfull day Rafik