A three-dimensional continuum model is explored to investigate the effects of radially dependent system parameters, such as relative permittivity and viscosity, on the transport of proton and wa- ter in nanoscale cylindrical pores of a fully hydrated polymer electrolyte membrane (PEM). The model employs Poisson, Nernst–Planck, and Stokes equations. Based on evidence from the literature for the presence of a stagnant water layer near the pore surface, we assume that a no-slip surface is located inside the pore, a few Angstroms from the pore wall. To solve the system numerically, the steady-state solution for the transport of protons and water is considered to be a perturbation around the equilibrium solution. Our results indicate that a radial variation of relative permittivity has the greatest influence on pore conductivity, reducing it by about 50% when compared to that of constant permittivity. On the other hand, viscosity plays the dominant role when the effective water drag within such pores is considered. We conclude that a continuum approach, including constant viscosity, is applicable in nanoscale models provided that the location of the no-slip surface is prop- erly specified and the radial variation of the relative permittivity is taken into consideration.    «

A three-dimensional continuum model is explored to investigate the effects of radially dependent system parameters, such as relative permittivity and viscosity, on the transport of proton and wa- ter in nanoscale cylindrical pores of a fully hydrated polymer electrolyte membrane (PEM). The model employs Poisson, Nernst–Planck, and Stokes equations. Based on evidence from the literature for the presence of a stagnant water layer near the pore surface, we assume that a no-slip surface is...    »