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.

Polymer-electrolyte fuel cells are a promising energy-conversion technology. Over the last several decades significant progress has been made in increasing their performance and durability, of which continuum-level modeling of the transport processes has played an integral part. In this review, we examine the state-of-the-art modeling approaches, with a goal of elucidating the knowledge gaps and needs going forward in the field. In particular, the focus is on multiphase flow, especially in terms of understanding interactions at interfaces, and catalyst layers with a focus on the impacts of ionomer thin-films and multiscale phenomena. Overall, we highlight where there is consensus in terms of modeling approaches as well as opportunities for further improvement and clarification, including identification of several critical areas for future research. Fuel cells may become the energy-delivery devices of the 21 st century. Although there are many types of fuel cells, polymer-electrolyte fuel cells (PEFCs) are receiving the most attention for automotive and small stationary applications. In a PEFC, fuel and oxygen are combined electrochemically. If hydrogen is used as the fuel, it oxidizes at the anode releasing proton and electrons according toThe generated protons are transported across the membrane and the electrons across the external circuit. At the cathode catalyst layer, protons and electrons recombine with oxygen to generate waterAlthough the above electrode reactions are written in single step, multiple elementary reaction pathways are possible at each electrode. During the operation of a PEFC, many interrelated and complex phenomena occur. These processes include mass and heat transfer, electrochemical reactions, and ionic and electronic transport. * Electrochemical Society Active Member. z E-mail: azweber@lbl.govOver the last several decades significant progress has been made in increasing PEFC performance and durability. Such progress has been enabled by experiments and computation at multiple scales, with the bulk of the focus being on optimizing and discovering new materials for the membrane-electrode-assembly (MEA), composed of the proton-exchange membrane (PEM), catalyst layers, and diffusionmedia (DM) backing layers. In particular, continuum modeling has been invaluable in providing understanding and insight into processes and phenomena that cannot be resolved or uncoupled through experiments. While modeling of the transport and related phenomena has progressed greatly, there are still some critical areas that need attention. These areas include modeling the catalyst layer and multiphase phenomena in the PEFC porous media.While there have been various reviews over the years of PEFC modeling 1-7 and issues, [8][9][10][11][12][13][14] as well as numerous books and book chapters, there is a need to examine critically the field in terms of what has been done and what needs to be done. This review serves that purpose with a focus on transport modeling of PEFCs. This is not meant to be an exhaustive review...

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