  Reverse osmosis (RO) and electrodialysis (ED) are the two most important
membrane technologies for water desalination and treatment. Their modes of
operation and transport mechanisms are very different, but on a closer look
also have many similarities. In this concise version of our tutorial review, we
describe state-of-the-art theory for both processes, focusing on simple
examples that are helpful for the non-specialist and useful for classroom
teaching. Both processes are described by the solution (SF) theory which
combines ion and water transport across membranes with chemical and mechanical
equilibrium at membrane/solution interfaces. We present a derivation of SF
theory based on force balances on water and ions and show how the various
terms, convection, diffusion, and electromigration, are derived, and how solute
partitioning is implemented. Finally, we demonstrate how SF theory accurately
describes the osmosis experiment where water and ions are transported in
opposite directions across a membrane.
