Nanofiltration Water Treatment: How the Membrane Selects Ions

Where does nanofiltration sit between UF and RO?

Nanofiltration occupies a deliberate niche. Ultrafiltration removes colloids, macromolecules and pathogens but passes essentially all dissolved salts; reverse osmosis rejects almost everything including monovalent ions, at the cost of high pressure. NF bridges the two, with an effective pore radius of roughly 0.5-1 nm and a molecular weight cut-off (MWCO) of about 200-1000 Da.

The practical consequence is selective desalination: NF can soften and partially desalt a water without stripping it to near-zero conductivity. If you need barrier removal of particulates only, see our companion note on spiral-wound and hollow-fibre membrane systems and the sibling article on ultrafiltration membrane design; if you need full desalination, compare against reverse-osmosis system design.

Why does NF reject divalent ions but pass NaCl?

This is the physics that makes NF distinctive, and it is not simple sieving. Bare ionic radii (Na⁺ ≈ 0.10 nm, Cl^- ≈ 0.18 nm, even hydrated ≈ 0.3-0.4 nm) are all smaller than the NF pore, so a purely steric membrane would pass them freely. Yet NF rejects sulphate strongly. The reason is a second, electrostatic mechanism acting alongside size exclusion.

Polyamide and polypiperazine NF films carry fixed charge at their surface and inside the pores. At natural pH the deprotonation of carboxylic groups leaves a net negative membrane charge. This sets up a Donnan potential at the feed-membrane interface that repels co-ions (here, anions) of the same sign as the membrane. To preserve electroneutrality, cations are held back with them. The effect scales strongly with valence:

• Divalent co-ions (SO₄^2-) feel roughly the square of the Donnan effect a monovalent ion does, so they are excluded very strongly (> 95%).
• Divalent counter-ions (Ca²⁺, Mg²⁺) are dragged back by charge coupling with the retained anions and by their larger hydrated size.
• Monovalent salt (NaCl) experiences only weak Donnan exclusion, so a large fraction permeates.

The result is the signature NF rejection order: SO₄^2- > Mg²⁺ ≈ Ca²⁺ > Cl^- > Na⁺. A third mechanism, dielectric exclusion (the energy penalty of moving a hydrated ion from bulk water into the low-permittivity confined pore), reinforces divalent rejection, especially in tight NF membranes.

What is the Donnan-steric pore model?

The workhorse framework for NF is the Donnan-Steric Pore Model (DSPM), and its extension DSPM-DE which adds the dielectric term. It treats the membrane as a bundle of cylindrical pores of radius r_p carrying a volumetric fixed charge X_d, and couples two ideas: partitioning of ions at each pore mouth (steric + Donnan + dielectric), and transport through the pore by the extended Nernst-Planck equation.

The three flux terms are diffusion (concentration gradient), electromigration (the Donnan/streaming potential that keeps the permeate electroneutral) and convection (drag by the water flux). The steric partition coefficient is Φ = (1 − λ)², where λ = r_i/r_p is the ratio of ion to pore radius. Fitting DSPM to two or three reference salts (typically NaCl, MgSO₄) yields r_p, effective thickness/porosity and X_d, which then predict multi-ion rejection. This is why NF selection is a modelling exercise, not a lookup table.

Worked example: divalent vs monovalent rejection

Consider a borehole water to be softened by NF, containing 90 mg/L Ca²⁺, 25 mg/L Mg²⁺, 120 mg/L SO₄^2- and 200 mg/L Cl^- with 130 mg/L Na⁺. Bench data on the chosen membrane give observed rejections of R_Ca = 94%, R_Mg = 95%, R_SO4 = 98%, R_Cl = 35%, R_Na = 40%. Permeate concentration follows from the observed rejection:

• Calcium: C_p = 90 × (1 − 0.94) = 5.4 mg/L.
• Magnesium: C_p = 25 × 0.05 = 1.25 mg/L.
• Sulphate: C_p = 120 × 0.02 = 2.4 mg/L.
• Chloride: C_p = 200 × 0.65 = 130 mg/L.

Feed hardness as CaCO₃ = 90 × (100/40.1) + 25 × (100/24.3) ≈ 224 + 103 = 327 mg/L. Permeate hardness = 5.4 × 2.5 + 1.25 × 4.1 ≈ 13.5 + 5.1 = 19 mg/L, a 94% reduction to a soft water. Note the chloride passes almost unchanged: the water is softened and part-desalted, but not stripped. That retained monovalent conductivity is exactly what makes the permeate palatable and low-corrosivity compared with RO permeate, which usually needs remineralising.

How much lower is NF pressure than RO?

Because NF passes monovalent salt, the osmotic pressure it must overcome is far smaller than for RO on the same water. Water flux is driven by the net driving pressure, transmembrane pressure minus the osmotic differential:

For a brackish water at ~2000 mg/L TDS, RO must beat roughly 1.5-2 bar of osmotic pressure and typically runs at 10-20 bar. Because NF lets much of the NaCl through, both σ and the retained salt are lower, and NF achieves comparable flux at 3-10 bar. On a softening duty, NF specific energy is often 0.3-0.8 kWh/m³ against 0.8-2.5 kWh/m³ for equivalent RO. That energy gap, plus avoiding lime-softening sludge, is the core commercial case for NF where full desalination is not required. A rigorous membrane process design and energy audit should compare the two on lifecycle cost, not headline rejection alone.

NF vs UF vs RO: a positioning table

The table places NF between its neighbours on the properties that actually drive selection.

Read across the divalent and monovalent rows: NF is the only process that decouples them, which is precisely its reason to exist.

What limits NF flux: polarisation and fouling?

Rejected solutes accumulate in a boundary layer at the membrane, raising the wall concentration above the bulk. This concentration polarisation increases local osmotic pressure and scaling risk, and is governed by film theory:

Because NF concentrates divalent ions preferentially, the wall is enriched in exactly the scale-formers (CaCO₃, CaSO₄, BaSO₄). Designers therefore watch the wall saturation index and cap recovery, dose antiscalant, and maintain cross-flow (turbulence) to keep k high and the polarisation factor near 1.1-1.3. NF is also prone to organic and biofouling from the natural organic matter (NOM) it is often deployed to remove, so pretreatment (UF or coagulation ahead of NF) and periodic clean-in-place are standard. Fluxes are typically held at a conservative 15-30 L/m²·h to stay below the critical flux where irreversible fouling accelerates.

Where is nanofiltration the right choice?

NF earns its place whenever the target is a specific fraction of the dissolved load rather than blanket desalination:

• Water softening — membrane removal of hardness without regenerant brine or lime sludge.
• Sulphate removal — e.g. offshore injection water to prevent BaSO₄/SrSO₄ scaling and reservoir souring.
• Colour and NOM removal — stripping humic/fulvic substances to control disinfection by-product precursors in potable supply.
• Selective separation — fractionating monovalent from divalent salts, or concentrating an organic while passing salt, in food, dairy and pharma.
• Caustic and acid recovery — NF membranes stable at extreme pH let mercerising caustic or process acids be recovered while rejecting organic and multivalent contaminants.

The unifying thread is selectivity by charge and size at modest pressure. Where the brief is complete desalination or trace-organic removal to near-zero, RO remains the answer; where it is barrier filtration only, UF suffices. For industrial reuse schemes, NF frequently sits between the two as a targeted polishing or softening stage.