Osmosis, diffusion, convection.

We present a tutorial on the mechanisms of and connections among osmosis, diffusion, and convection. For simplicity, we consider only two-component nonelectrolyte solutions under isothermal conditions. Further, we confine our attention to laminar convection with application to the case of flow through narrow channels, as might occur in membranes containing pores or slits. The application of equilibrium and near-equilibrium thermodynamics to flow processes is just like considerations of mechanics with friction, or hydrodynamics. The description of flow processes of more than two atomistic components, either solutions or suspensions, is identical in the dilute limit to the description we give, except possibly when the curvature of the flow field (at the velocity profile) is significant. Flow fields, therefore, naturally divide into three regimes: 1) "one-dimensional" flow fields, e.g., solutions or suspensions in extended regions, whose velocity profile is macroscopically flat (compared to the atomistic curvature); 2) flow fields with significant curvature, e.g., Poiseuille or turbulent fields; and 3) high curvature fields, e.g., narrow flow channels.