| Summary: | This master thesis studies the applicability of continuum mean-field theories such as the Poisson-Nernst-Planck equations and the Stokes equation. In particular, we investigate electro-osmotic flow of water and protons in infinite cylindrical nano-scale pores with a uniform surface charge density, representing pores in polymer electrolyte membranes. The impact of different modifications to the continuum theory is explored. Including finite-size ions in the Poisson-Boltzmann equation and spatially dependent profiles for permittivity and viscosity, values are found for the water drag coefficient and the pore conductivity. For surface charge densities sigma_s = -0.1 to sigma_s = -0.5 C m^-2, values of 2-5 are found for the water drag coefficient, compared to 7.5 to 22 for the unmodified equations. Similarly, values for the pore conductivity range from $5.5$-30 S m^-1 when including the modifications, compared to 13-100 S m^-1 for the unmodified equations. A final modification to the Poisson-Boltzmann equations is made by including a field dependent explicit model for the permittivity. This model yields a permittivity profile comparable to predictions based on microscopic simulations, but with a lower permittivity near the wall. The proton concentration exhibits pronounced saturation effects near the wall.
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