A solution-diffusion membrane passes water in proportion to the pressure left over after osmotic pressure is subtracted, and passes salt at a roughly constant rate regardless of pressure. Osmotic pressure follows van't Hoff's law; the two transport equations are:
π ≈ 0.808 · TDS(g/L) [bar, van't Hoff approx.]
Jw = Aw · (ΔP − Δπ) [water flux, L/m²·h]
Js = B · Cfeed [salt flux, mg/m²·h]
Cp = Js / Jw [permeate salinity]
Cc = Cf / (1 − r) [brine salinity, mass balance]
Raising the applied pressure increases Jw and dilutes the permeate (Cp falls) — real membranes get "cleaner" under more pressure because water passage grows faster than salt passage. Raising the recovery ratio concentrates the leftover brine, which raises the average osmotic pressure the pump must overcome and reduces flux. An energy-recovery device (ERD) reclaims part of the pressure still in the brine stream and returns it to the pump, cutting specific energy consumption — the single biggest advance in modern seawater RO economics.
- Blue dots — water molecules; the fraction crossing the membrane tracks Jw.
- Amber dots — dissolved salt; most are rejected, a few slip through as permeate salinity.
- City lights — scale with the population the plant's freshwater output can supply.