The resistance to mass transfer associated with molecules penetrating the mouths of very small ports, often referred to as a surface barrier, is explored in the context of several entropic models. The mass transfer coefficient for hard spheres passing through a barrier comprised of slit-pore mouths is obtained by molecular dynamics simulation. An analytical expression is derived for the transfer coefficient of hard rectangular blocks passing through a similar barrier. The contributions of free area and velocity screening effects are examined. In the limit when the ratio of diffusant size to pore mouth size is near unity, the transfer coefficient of the spheres scales as the nominal free area, while that of the blocks scales as the free area squared. For both models, relatively small changes in pore mouth size can cause order of magnitude changes in the surface barrier resistance in this regime.