Fick's second law in cylindrical co-ordinates

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SUMMARY

This discussion focuses on the derivation of Fick's second law of diffusion specifically in cylindrical coordinates. The user seeks clarification on the intermediate steps leading to the equation related to surface diffusion in a laser-cleaned spot. References to key literature, including J. Crank's "The Mathematics of Diffusion" and a paper by S.M. George et al., are provided to support the derivation process. The conversation highlights the need for a simplified explanation suitable for those without a strong mathematical background.

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gareth
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Hi all,

Having some trouble understanding/finding the derivation of Fick's second law of diffusion in cylindrical co-ordinates.

I have attached the solution which describes the refilling of a laser cleaned spot via surface diffusion.

So basically i would like to know the intermediate steps from Fick's second law to the attached equation.

Many thanks on this one.

(PS not a mathematician as you may have guessed so please dumb it down a shade for me)

Thanks again
 

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Hi

Could you cite 17, 18, original paper?

Best Regards
 
This is a book on the mathematics of diffusion, I have had a good look at it but it still skips many steps so I can't follow the derivation.

[17] J. Crank, The Mathematics of Diffusion (Clarendon, Oxford,
1975) p. 72.

This paper basically shows the same information as the book:

[ 18] S.M. George, A.M. de Santolo and R.B. Hall, Surf. Sci. 159
(1985) L425,

Thanks for the reply.

Gareth
 

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