Inquiry with Modeling Hydrogen Diffusion Through Palladium Filters in MATLAB

I am currently working on a project involving the simulation of hydrogen diffusion through palladium filters with various geometric shapes. Specifically, I need to determine the permeability of the palladium filter and understand how this permeability changes when the shape, thickness and compositions of the filter is altered.

I am planning to use MATLAB, particularly the PDE Toolbox, to set up and solve the relevant diffusion equations. I wonder is that possible using MATLAB.

Thank you so much !

[John D'Errico]

This is far too vague of a question to get a useful answer. Yes, you can solve most well-posed problems, though you have not said enough to even know if this truly falls into the category of well-posed problems.

But yes, simple diffusion is something you can model in general. How you will deal with parameters like the shape and composition is something you will need to work out. I would strongly suggest you spend time talking with your teacher.

Then spend some time learning to use the PDE toolbox, to solve a simple problem with a well understood solution. Don't jump into the deep end of the pool before you can swim.

[Torsten]

Diffusion processes through filters happen on extremely small scales. How do you plan to set up different geometries, shapes or thicknesses in the PDE toolbox if there are millions of pores to be considered ? You should make experiments and deduce empirical correlations for different filter types instead of simulating in my opinion.

[John D'Errico]

It very much depends upon how you will model diffusion. If you would hope to model the diffusion process on an atomic/molecular level, then you can do literally nothing, because this will be far too complex a process. Even if you could formulate equations, they would take far too long to solve to produce anything meaningful. That means you need to model the process at a very high level, where all you need to worry about are large scale parameters like diffusivity. You need to worry about isotropy for diffusion, if the substrate is isotropic, then much the better as it makes the model simpler yet.

Honestly though. I'm not sure what you are looking to learn here. If you make the model simple enough, then all you need are things like the thickness of the media, the area, and the diffusivity. You should be able to calculate the flow at that point, with no need for a PDE solver. The point being, once the media becomes fully saturated, then there is no time dependency.

Answer 1

[Ziggy Hoffnung]

For details on the equations which PDE Toolbox can solve, see this link:

https://www.mathworks.com/help/pde/ug/equations-you-can-solve.html