A two dimensional, across the channel, isothermal, two-phase flow model for proton exchange membrane fuel cells (PEMFCs) is developed to investigate the interaction of dry Nafion (R) ionomer volume fraction (L-M(dry)) and cathode relative humidity (RHc) in PEMFCs. The agglomerate model is used to describe the catalyst layers properties, in which the agglomerate is covered by ionomer and liquid water films. The optimum ionomer water content is suggested by maximising the oxygen diffusion rate through the ionomer film. The effects of L-M(dry) and RHc on membrane and ionomer swelling and the cell performance are studied. The predicted current densities at fixed cell voltages are analysed by the Kriging surrogate model and used to optimise the L-M(dry) and RHc based on analysing their interaction. The simulation results show that the optimum ionomer water content increases as the ionomer content increases. At higher current densities, e.g. 1.0 A cm(-2), the best cell performance is achieved with L-M(dry) of 10%, corresponding to 0.3 mg cm(-2), with fully humidified inlet gases. The optimum RHc is between 60% and 80% for L-M(dry) of 40%. The modelling results also show that at higher current densities, the optimum RHc initially decreases then increases as L-M(dry) increases. The optimum RHc decreases from 76% to 73% as L-M(dry) increases from 10% to 30% then it increases up to 85% as L-M(dry) increases to 50%. (C) 2014 Elsevier Ltd. All rights reserved.