A new nonequilibrium molecular dynamics method for simulating flow and diffusion within membranes is presented. The method involves two fixed volumes, separated by the permeable medium, which are maintained at fixed, though different, chemical potential. By monitoring the flow and diffusion of the fluid particles through the nonequilibrium interstitial region one can simulate mass transfer processes in a manner which parallels real laboratory experiments. The method is applied to a simple microporous membrane system and it is shown that slip flow, rather than viscous shear, is the predominant mechanism governing the permeation of moderately dense hard-sphere fluids in very fine pores.