WIP: transport efficiency models

[isaacsquires]

Description

Adding new methods for calculating the transport efficiency beyond Bruggeman coefficient. This includes:

• log square root
• log
• linear
• half volume fraction
• Bruggeman
• Tortuosity factor

These were taken from 10.1016/j.ces.2007.03.041 and http://dx.doi.org/10.1016/j.coche.2016.02.006

Fixes #2111

Type of change

Please add a line in the relevant section of CHANGELOG.md to document the change (include PR #) - note reverse order of PR #s. If necessary, also add to the list of breaking changes.

• New feature (non-breaking change which adds functionality)
• Optimization (back-end change that speeds up the code)
• Bug fix (non-breaking change which fixes an issue)

Key checklist:

• No style issues: $ pre-commit run (see CONTRIBUTING.md for how to set this up to run automatically when committing locally, in just two lines of code)
• All tests pass: $ python run-tests.py --all
• The documentation builds: $ python run-tests.py --doctest

You can run unit and doctests together at once, using $ python run-tests.py --quick.

Further checks:

• Code is commented, particularly in hard-to-understand areas
• Tests added that prove fix is effective or that feature works

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[isaacsquires]

TODO:

• write tests for each option
• add to documentation outlining different options
• change default behaviour of tortuosity factor to not crash when tau not found in param set

[TomTranter]

I think we should include references to the papers that propose the relations and maybe rename them to align a bit better with the descriptions given in this table by Shen and Chen. There a few more in the table we could include too.

[TomTranter]

I also feel like tortuosity itself should be a submodel on its own and transport efficiency should use that. This would allow for uploading experimental data and interpolating against porosity.

[isaacsquires]

So as I see it, the tor variable implemented at the moment is the transport efficiency as defined here, where trasport efficiency $B$ is defined as $D_{eff}=BD$ in the diffusivity case. This related to tortuosity factor $\tau$ and the Bruggeman coefficient $n$ by $B = \epsilon / \tau=\epsilon ^{(1+n)/n}$ with $n=2$ for the standard Bruggeman formulation for spheres (this does collapse to $B=\epsilon^{1.5}$, taken from here)

So if we are to implement transport efficiency as two submodels, one for tortuosity factor and one for transport efficiency, I feel like transport efficiency would end up just being a simple relation to tortuosity factor i.e. $B=\epsilon/\tau$. We would then just have to reframe all the other relations in terms of $\tau$, e.g. $\tau = \epsilon^{-1/n}$ for Bruggeman. And actually the interesting variation in interpretations and approaches comes in the framing of the transport efficiency.

[TomTranter]

Hey @isaacsquires really sorry I haven't responded to this yet properly. Had a short holiday over Easter and then been swamped with other work things. I haven't forgotten about it and hopefully look again tomorrow

[TomTranter]

transport efficiency would end up just being a simple relation to tortuosity factor

This is currently how the implementation is coded. What are the alternatives?

[TomTranter]

Merged into a branch on our code base to keep working on it