Redox flow batteries (RFBs) are enjoying a renaissance due to their ability to store large amounts of electrical energy relatively cheaply and efficiently. In this review, we examine the components of RFBs with a focus on understanding the underlying physical processes. The various transport and kinetic phenomena are discussed along with the most common redox couples.

CO2 reduction conducted in electrochemical cells with planar electrodes immersed in an aqueous electrolyte is severely limited by mass transport across the hydrodynamic boundary layer. This limitation can be minimized by use of vapor-fed, gas-diffusion electrodes (GDEs), enabling current densities that are almost two orders of magnitude greater at the same applied cathode overpotential than what is achievable with planar electrodes in an aqueous electrolyte. The addition of porous cathode layers, however, introduces a number of parameters that need to be tuned in order to optimize the performance of the GDE cell. In this work, we develop a multiphysics model for gas diffusion electrodes for CO2 reduction and used it to investigate the interplay between species transport and electrochemical reaction kinetics. The model demonstrates how the local environment near the catalyst layer, which is a function of the operating conditions, affects cell performance. We also examine the effects of catalyst layer hydrophobicity, loading, porosity, and electrolyte flowrate to help guide experimental design of vapor-fed CO2 reduction cells.

In this review, we have examined the different models for polymer-electrolyte fuel cells operating with hydrogen. The major focus has been on transport of the various species within the fuel cell. The different regions of the fuel cell were examined, and their modeling methodologies and equations were elucidated. In particular, the 1-D fuel-cell sandwich was discussed thoroughly because it is the most important part of the fuel-cell assembly. Models that included other effects such as temperature gradients and transport in other directions besides through the fuel-cell sandwich were also discussed. Models were not directly compared to each other; instead they were broken down into their constitutive parts. The reason for this is that validation of the models is usually accomplished by comparison of simulation to experimental polarization data (e.g., Figure 3). However, other data can also be used such as the net flux of water through the membrane. In fitting these data, the models vary not only in their complexity and treatments but also in their number and kind of fitting parameters. This is one reason it is hard to justify one approach over another by just looking at the modeling results. In general, it seems reasonable that the more complex models, which are based on physical arguments and do not contain many fitting parameters, are perhaps closest to reality. Of course, this assumes that they fit the experimental data and observations. This last point has been overlooked in the validation of many models. For example, a model may fit the data very well for certain operating conditions, but if it does not at least predict the correct trend when one of those conditions is changed, then the model is shown to be valid only within a certain operating range. This review has highlighted the important effects that should be modeled. These include two-phase flow of liquid water and gas in the fuel-cell sandwich, a robust membrane model that accounts for the different membrane transport modes, nonisothermal effects, especially in the directions perpendicular to the sandwich, and multidimensional effects such as changing gas composition along the channel, among others. For any model, a balance must be struck between the complexity required to describe the physical reality and the additional costs of such complexity. In other words, while more complex models more accurately describe the physics of the transport processes, they are more computationally costly and may have so many unknown parameters that their results are not as meaningful. Hopefully, this review has shown and broken down for the reader the vast complexities of transport within polymer-electrolyte fuel cells and the various ways they have been and can be modeled.