Fick's second law in cylindrical co-ordinates

In summary, the conversation is about understanding and deriving Fick's second law of diffusion in cylindrical coordinates. The person asking for help has attached a solution that shows the refilling of a laser cleaned spot via surface diffusion and wants to know the intermediate steps from Fick's second law to the attached equation. They also request for the original papers to be cited. Another person suggests a book on the mathematics of diffusion and mentions a relevant paper. The person seeking help thanks them and provides additional information about the paper.
  • #1
gareth
189
0
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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  • #2
Hi

Could you cite 17, 18, original paper?

Best Regards
 
  • #3
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
 

1. What is Fick's second law in cylindrical coordinates?

Fick's second law in cylindrical coordinates is a mathematical equation that describes the diffusion of particles in a cylindrical system. It is a variation of Fick's second law, which is a fundamental equation in the field of diffusion that explains how particles move from areas of high concentration to areas of low concentration.

2. What is the difference between Fick's second law and Fick's second law in cylindrical coordinates?

The main difference between the two equations is the shape of the system being studied. Fick's second law applies to diffusion in a two-dimensional system, while Fick's second law in cylindrical coordinates applies to a three-dimensional cylindrical system. This means that the cylindrical coordinates equation takes into account the radial and axial coordinates in addition to the concentration gradient.

3. How is Fick's second law in cylindrical coordinates derived?

Fick's second law in cylindrical coordinates is derived from the more general equation of Fick's second law by taking into account the cylindrical symmetry of the system. This involves converting the Cartesian coordinates in the original equation to cylindrical coordinates, and then applying the chain rule to obtain the final equation.

4. What are the applications of Fick's second law in cylindrical coordinates?

Fick's second law in cylindrical coordinates has many practical applications in fields such as chemical engineering, biology, and materials science. It can be used to study the diffusion of molecules in cylindrical systems such as chemical reactors, biological cells, and porous materials. This equation is also helpful in designing and optimizing processes that involve diffusion, such as drug delivery systems and membrane filtration.

5. Are there any limitations to Fick's second law in cylindrical coordinates?

Like any mathematical model, Fick's second law in cylindrical coordinates has its limitations. It assumes that the diffusion process is linear and that the system is in steady-state. In reality, diffusion is often a complex and nonlinear process, and many real-world systems do not reach steady-state. Additionally, this equation does not take into account other factors that may affect diffusion, such as convection or chemical reactions.

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