In this work, a crossover model is newly developed to account rigorously for the crossover of vanadium ions through the membrane and resultant side reactions occurring in both positive and negative electrodes. The crossover model is then numerically coupled with previously developed three-dimensional (3-D), transient, thermal VRFB model in which key physicochemical phenomena including the electrochemical reactions, waste heat generation, resultant species and heat transport are all included. Using the comprehensive VRFB model, we investigate the effects of vanadium crossover between the negative and positive electrodes during a single charge/discharge cycle. Numerical simulations successfully capture capacity loss related to vanadium crossover, clearly showing the difference in species distributions due to side reactions. The results show that due to effect of vanadium ion crossover, more charging time and less discharging time have been achieved. (C) 2015 Elsevier Ltd. All rights reserved.