Freundlich LDF differes between documentation and implementation.

[ronald-jaepel]

The Freundlich isotherm is documented as:

$q^\ast_i= k_{F,i}c_{p,i}^{1/n_{i}}$

but is implemented as

$q^\ast_i= k_{F,i}|c_{p,i}|^{1/n_{i}}$

The implementation change of taking the absolute value of $c_p$ is to prevent negative concentrations from crashing the simulation. This can happen if $1/n$ is chosen such that it leads to an even root being taken of $c_p$, e.g. $n=2$.

The linearization that we have implemented for small concentrations (to stabilize the derivative for $c_p \approx 0$) could also be used to stabilize the negative concentrations.

Should we update the documentation to match the implementation or update the implementation to use the linearization for small and negative $c_p$ values?

@lieres what do you think?

[lieres]

The linearization is generally more physical and should be preferred over taking the absolute value.

Then, the documentation should follow the code.