There is not model. You must humidify the inlet gases at different relative humidities and keep working at open circuit during several hours. So, when you start to demand electric current both hydration of the membrane and/or condansate water in the channels of bipolar plates will be different.
You may flood and/or dry the PEM fuel cell and evaluate the effect on polarization by the model published in Journal of Power Sources 101 (2001) 275-286. The literature models mentioned therein (see References) could also be useful for you.
Recemment, I use the curve of constant current discharge and a model of relaxation, I can calculate the water concentration in the cathode. This method is valid only for monocelullaire pile.
If you are referring to the fuel cell in a physical sense, the fuel cell has the potential to flood every time it starts up in a cold environment. This is due to ice formation on the cathode side. By blocking O2 from reaching the cell, this causes the cathode potential to shift from O2/H2O reaction to H+/H2 reaction (negative Ecath). Therefore, ending up with a positive Eanode and negative Ecathode.
This is some of the basic principal to one case, but there are researches working in the field that can better answer this question.
There are lot of models in the literature that can be used to understand the effect of water concentration on the polarization curve of a pem fuel cell. For sure several parameters are affected by water concentration such as membrane conductivy, and binary diffusion coefficient in the piorous layer. Moreover if two phase model have to be considered you have to take in to account also the effect of liquid water blockage in to the channels . Generally speaking the flooding is reflected in the concentration (polarization) part of the IV curve , otherwise the drying is more pertinent to the ohmic part of the IV curve . In any case flooding or drying the whole polarization curve is affected.
My objet is to replace platinum by catalytic reaction. To know the functioning of the catalytic membrane, I owe the opposite the reaction mechanism, kinetics and the transport of material in interface. For it, I try to determine reaction parameters as the concentration of the reactive, the thickness of the catalytic coat, constant kinetics, limited current, the coefficient of overvoltage, etc.. The model of relaxation is a mathematical model established from the catalytic mechanism.
I have just finished reviewing a good article pertinent to that subject, it will be soon published in the JHE. The paper and the references therein would be very helpful to you....
I too second you on that...experimenting would be better than modelling. In this way you'll atleast know which parameters are relevant to the whole model and those that are innocuous.
We are not aware of any PEM Fuel Cell that can be used to intentionally flood and dry the cell. We suggest that you directly get in touch with the fuel cell companies.
I think we can build a model from the theoretical background. However, I would suggest both modelling and experimenting with a view to answer the research question/s. This will also allow us to make comparison between both methods, and see which one addresses our objective/s better. Can you send the theoretical background to me?
"Ito, H., T. Maeda, A. Kato, et al., Gas Purge for Switching from Electrolysis to Fuel Cell Operation in Polymer Electrolyte Unitized Reversible Fuel Cells. Journal of the Electrochemical Society, 2010. 157(7): p. B1072-B1080."
In this paper the authors model the drying up of a flooded PEM fuel cell.
If it is just the model of how the membrane water content affects the fuel cell polarisation I guess you can check up this well known paper:
"Springer, T.E., J. Zawodzinski, Thomas A., and S. Gottesfeld, Polymer Electrolyte Fuel Cell Model. J. Electrochem. Soc., 1991. 138(8): p. 2334-2342."
Our recent paper in Chemical Engineering Science [J. Marquis and M.-O. Coppens, Chem Eng Sci 102, 151-162 (2013) - http://dx.doi.org/10.1016/j.ces.2013.08.003 ] explicitly accounts for water, in a way that it can easily be included or removed, and discusses its effects. The percentage of liquid water saturation is based on the work of X. Wang and T.V. Nguyen, Journal of the Electrochemical Society, 155 (2008), pp. B1085–1092, which uses an experimentally validated correlation for the capillary flow.