moving boundary - PDE numerics

[montavala]

Hello. I have a problem with numerical mathematics and programming. My case is:
I have SiC layer covered with another one (mixture-oxide of alumina and silica (mullite)). This is exposed to the air on typical t=1400C.
The O2 diffuses through the mullite layer, and reacts with SiC, giving SiO2. Si diffuses through mullite and Al diffuses through silica. The question is: How to model such case and how to know the concentrations of Al, Si, and the positions of boundary between SiC and oxide at some time?
Lets assume that I have all the necessary diffusion coefficients.

 

[hacksaw]

you'll need more than the diffusion rates of non-reacting species in this case.

are you dealing with the end-point equilibrium?

 

[metengr]

This is a mass transport problem related to diffusion of ions in oxides (treated as such). I would recommend review of the following reference books;
"An Introduction to Transport Phenomena in Materials Engineering" (pages 506-518) by D. Gaskell or "Transport Phenomena in Materials Processes" (pages 491-499) by DR Poirier and GH Geiger.

 

[montavala]

Answer to Hacksaw:
I will also have an equation for the oxygen diffusion plus the reaction with SiC. It is the typical parabolic law:
(m/A)^2=kp*t. m-weight change, A-surface, t-time, kp-const.
On the other side I will also have the reaction of SiO2 with H2O from the air which will case the evaporation of Si species. However, I assume this process to be slow, and in first step can be neglected.

 

[hacksaw]

Is your question about treating multicomponent diffusion or how to solve the equations, etc.?

 

[montavala]

It is more a question of solving equations.

 

[hacksaw]

the diffusion equations can and have been solved analytically and numerically for the case you are describing. sounds like a lot of fun!

 

[montavala]

Do you have a reference for the solution of this problem?

 

[hacksaw]

you are dealing with a multicomponent diffusion, any number of texts and software packages deal with that subject.

you are not solving a moving boundary problem, rather your solution are concentration profiles that evolve in time.

for really current methods, go through the j. applied physics, it wil point you in the right direction