Push pressure above the osmotic pressure and clean water crosses the membrane; the leftover brine gets saltier along the module. Arrows show the local water flux through the membrane; yellow dots are salt ions kept behind.
The science
Osmotic pressure. Dissolved salt pulls water across a semipermeable membrane towards the salty side. For dilute NaCl the van't Hoff law gives π = i c R T with i = 2, about 0.85 bar per g/L at 25 C. Seawater (35 g/L) is near 30 bar.
Flux. Water crosses at J = A (ΔP - Δπ), where A is the membrane permeability and Δπ the osmotic pressure difference between the membrane wall and the permeate. Nothing passes until the applied pressure exceeds Δπ.
Along the module. Water leaves the feed, so flow falls and the brine concentration rises, which raises π and lowers J further down the channel. The model slices the module and updates flow and salt mass slice by slice. A salt mass balance Qf Cf = Qc Cc + Qp Cp holds exactly.
Concentration polarization. Rejected salt piles up at the wall: Cwall = Cbulk exp(J/k). Poor mixing or fouling (small k) raises the wall salinity and cuts the output.
Energy. Specific energy is roughly ΔP / (recovery x pump efficiency); 1 bar x 1 m3 = 0.0278 kWh. Temperature raises A by about 3 % per degree.
Simplifications. NaCl-equivalent salinity, constant rejection, no pressure drop along the channel, no scaling or fouling dynamics, no energy recovery device. The sliced module is a schematic of a spiral-wound element.