Benchmark 2 misattributes concentration gradient energy term

[guyer]

As reported by @daubners, the free energy in Benchmark 2 includes a term " $\frac{\kappa_{c}}{2}|\nabla c|^{2}$ " and says it is based on Ref. [ZHU] (and, indirectly, on Ref. [KKS]) and on Ref. [WBM]. None of these sources include a gradient energy term in concentration, although Ref. [WBM] does remark "a more general model might also include contributions due to the gradients of the other thermodynamic variables".

This term isn't "wrong", but it shouldn't be attributed to [ZHU] or [WBM].

Related: after Eq. (7), there is a typo in the coefficients: " $k_c = k_\phi = 3$ " should read " $\kappa_c = \kappa_\phi = 3$. "

Note: these issues carry over from the original benchmark paper.

[wd15]

Can I just implement what you've suggested? Would anyone require a discussion about this?

[guyer]

I don't know that it needs discussion; just a question of how to phrase it. Something like

the free energy of the system is based on a more general formulation (including concentration gradient energy) of that presented in Ref. ZHU...

[daubners]

I guess this would be the correct reference
https://doi.org/10.1103/PhysRevE.47.1893

[guyer]

Agreed

[guyer]

...along with [ZHU] for the multi-phase