  In this paper, we explore osmotic transport by means of molecular dynamics
(MD) simulations. We first consider osmosis through a membrane, and investigate
the reflection coefficient of an imperfectly semi-permeable membrane, in the
dilute and high concentration regimes. We then explore the diffusion-osmotic
flow of a solute-solvent fluid adjacent to a solid surface, driven by a
chemical potential gradient parallel to the surface. We propose a novel
non-equilibrium MD (NEMD) methodology to simulate diffusion-osmosis, by
imposing an external force on every particle, which properly mimics the
chemical potential gradient on the solute in spite of the periodic boundary
conditions. This NEMD method is validated theoretically on the basis of
linear-response theory by matching the mobility with their Green-Kubo
expressions. Finally, we apply the framework to more realistic systems, namely
a water-ethanol mixture in contact with a silica or a graphene surface.
