Constant water activity hic isotherm

[ronald-jaepel]

The HIC Isotherm used in our recent bayesian optimization parameter determination paper https://doi.org/10.1016/j.chroma.2022.463408

It is based on the Wang2016 HIC isotherm but fixes the numerical instability and unexpected behavior at low protein concentrations by replacing q^(n beta) with 0.1^(n beta).

In our internal tests it is able to explain HIC gradient elutions well. We haven't gotten around to testing breakthrough experiments but I don't anticipate any problems there. The manuscript exploring the HIC isotherm in detail is in preparation, but as the equation has been revealed in the bayesopt paper I wanted to add it to CADET now already so others can use it / experiment with it as well.

Included are the flux implementation, the jacobian and a barebones documentation in the @brief section. Not included are tests and a full documentation.

Tests are not included because I don't know how to trigger that the tests are evaluated. I'll add them after Jazib Hassan adds that part of the tutorial :)

[lieres]

I would recommend replace q^(n beta) by a polynomial in an interval [0 epsilon] around the origin. That polynomial should be 0 at q=0 and have the same function value and first derivative as q^(n beta) at q=epsilon. We had similar problems with the Freundlich isotherm (https://forum.cadet-web.de/t/dealing-with-non-differentiable-adsorption-models/352).

[ronald-jaepel]

Thank you for the input.

So, because this isotherm contains no q^(n beta) anymore, am I correct in assuming that the polynomial replacement won't be necessary here? At least I haven't noticed any stability problems with this isotherm.

In the implementation of the Wang2016 isotherm (PR #116) the entire isotherm gets replaced with a 2nd degree Taylor series at q<=0 and c_i<=0. I'm pretty sure that was added by someone from your team (probably Bill) when you first helped us set the Wang isotherm up in Cadet3.

Regarding the link to the Freundlich isotherm: I can't access that, it appears to be private.

[lieres]

If the isotherm doesn't contain the term q^(n beta) anymore, my comment is probably pointless. If you are interested, I can still give you access to that private post.

I remember that some approximation below zero was neccessary, even though unphysical, due to numerical noise.

[ronald-jaepel]

As discussed, here is a set of parameters for the HICCWA isotherm.
HICCWA_parameters.xlsx

[schmoelder]

Now tracked in #121