In this paper, a two-dimensional model has been developed to simulate the liquid water transport in a cathode gas diffusion layer with different porosity gradients in polymer electrolyte membrane fuel cells (PEMFCs). Due to the complexity of porous media, the simulation was carried out by lattice Boltzmann method. According to dimensionless numbers that characterize liquid water transport in porous media, simulation conditions were similar to the liquid water transfer into the gas diffusion layer of PEMFC. Different gas diffusion layers were created randomly by solid circular particles with an average diameter of [Formula: see text] and the numerical code was validated by conducting several tests. The results indicated that capillary force is the main factor in liquid water transport in the gas diffusion layer, while viscous and gravitational forces do not have a significant effect. In addition to improve the water management, the gas diffusion layer should have a positive porosity gradient, i.e. the porosity increases along the thickness. Also, under the same boundary conditions and at the average porosity (0.659), the saturation distribution curves in three porous media were compared including the gas diffusion layer with porosity gradient, the gas diffusion layer with the micro-porous layer, and the gas diffusion layer with uniform porosity. The average liquid water saturation in the gas diffusion layer with the 10% porosity gradient was 20.2% lower than in the gas diffusion layer with uniform porosity and 10.5% lower than the gas diffusion layer + micro-porous layer. Furthermore, upon elevation of the porosity gradient in the gas diffusion layer, the average liquid water saturation in the gas diffusion layer decreased. Specifically, as the porosity gradient rose from 10% to 14% and 18.5%, the average liquid water saturation values decreased to 29.8% and 38.8%, respectively compared with the gas diffusion layer with uniform porosity.

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The Casimir force between two rough surfaces grown through statistical growth models is studied, both theoretically and numerically. The models include the random deposition (RD), the random deposition with surface relaxation (RDSR), and the restricted solid-on-solid growth (RSOS). To calculate the Casimir force, the pairwise summation (PWS) method in [Formula: see text] dimensions is used. First, the force between two growing surfaces with RD equations, Edwards–Wilkinson, (EW) and Kardar–Parisi–Zhang (KPZ) equations is theoretically investigated. Then, using the Monte Carlo simulation, the rough surfaces with RD, RDSR, and RSOS models in [Formula: see text] dimensions are simulated in different growth times, and the Casimir force between each pair of rough surfaces in each time step is calculated. The results show that the force between the surfaces increases as the roughness increases.

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