Effects of the electric field on ion crossover in vanadium redox flow batteries Xiao-Guang Yang a,1 , Qiang Ye a,⇑ , Ping Cheng a , Tim S. Zhao b,⇑ a Ministry of Education Key Laboratory of Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China b Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China highlights  Effects of the electric field on ion crossover and capacity decay in VRFB are studied.  The model enables the Donnan-potential jumps to be captured at electrode/membrane interfaces.  Electric field arises and affects ion crossover even at the open-circuit condition.  Enhancing electric-field-driven crossover can mitigate the capacity decay rate. article info Article history: Received 7 November 2014 Received in revised form 3 February 2015 Accepted 8 February 2015 Keywords: Vanadium redox flow battery Modeling Crossover Capacity decay Electro-osmosis flow abstract A thorough understanding of the mechanisms of ion crossover through the membranes in vanadium redox flow batteries (VRFBs) is critically important in making improvements to the battery’s efficiency and cycling performance. In this work, we develop a 2-D VRFB model to investigate the mechanisms of ion crossover and the associated impacts it has on the battery’s performance. Unlike previously described models in the literature that simulated a single cell by dividing it into the positive electrode, membrane, and negative electrode regions, the present model incorporates all possible ion crossover mechanisms in the entire cell without a need to specify any interfacial boundary conditions at the mem- brane/electrode interfaces, and hence accurately captures the Donnan-potential jumps and steep gradi- ent of species concentrations at the membrane/electrode interfaces. With our model, a particular emphasis is given to investigation of the effect of the electric field on vanadium ion crossover. One of the significant findings is that an electric field exists in the membrane even under the open-circuit con- dition, primarily due to the presence of the H + concentration gradient across the membrane. This finding suggests that vanadium ions can permeate through the membrane from H + -diluted to H + -concentrated sides via migration and convection. More importantly, it is found that the rate of vanadium ion crossover and capacity decay during charge and discharge vary with the magnitude of the electric field, which is influenced by the membrane properties and operating conditions. The simulations suggest that enhanc- ing the electric-field-driven flow is a potential approach to minimizing the battery’s capacity decay. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction Redox flow batteries (RFBs) have been considered as one of the most promising energy storage technologies that can be combined with intermittent renewable energy sources like wind and solar [1–5]. Unlike conventional rechargeable batteries, the RFBs store energy in electrolytes contained in external tanks, while energy conversion occurs in electrode compartments; thus the energy capacity of a RFB is decoupled from its power capacity, making it a unique candidate for large-scale electrical energy storage.Among the various RFB systems proposed in the literature, the all-vanadi- um redox flow battery (VRFB), invented and pioneered by Skyllas- Kazacos and her co-workers in 1980s [6], distinguishes itself by capitalizing on four different oxidation states of the same element, i.e. V 2+ /V 3+ in the negative half-cell and VO 2þ =VO þ 2 in the positive half-cell. As such, conversion between electrical and chemical energy is achieved via the following reactions: http://dx.doi.org/10.1016/j.apenergy.2015.02.038 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding authors. Tel.: +86 21 3420 6955 (Q. Ye), +852 23588647 (T.S. Zhao). E-mail addresses: qye@sjtu.edu.cn (Q. Ye), metzhao@ust.hk (T.S. Zhao). 1 Present address: Electrochemical Engine Center (ECEC), The Pennsylvania State University, University Park, PA 16802, USA. Applied Energy 145 (2015) 306–319 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy