Nanofiltration Simulator: Membrane Pore Transport & Solute Rejection

simulator intermediate ~10 min
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R = 82% — solute rejection at λ = 0.5

A nanofiltration membrane with 1 nm pore radius rejects 82% of solutes with 0.5 nm radius at 10 bar, demonstrating the steep size-selectivity characteristic of nanoporous membranes.

Formula

J = εrp²ΔP / (8μδ) — Hagen-Poiseuille flux through nanopores
R = 1 - Cp/Cf — solute rejection ratio
σ = (1 - (1-λ)²)² — steric sieving coefficient

Filtering at the Molecular Scale

Nanofiltration membranes contain pores just 0.5–5 nanometers wide — large enough to pass water molecules and small ions, but small enough to block larger solutes, divalent ions, and organic molecules. This selectivity operates at the boundary between molecular sieving and solution-diffusion transport, combining elements of both ultrafiltration's size exclusion and reverse osmosis's chemical selectivity.

Pore Transport Physics

Water flux through nanopores follows a modified Hagen-Poiseuille equation, where flux scales with the square of pore radius and linearly with applied pressure. Solute transport involves both convective drag (carried along by water flow) and diffusion through the pore. The ratio of solute to pore radius (λ) determines the steric hindrance factors that quantify how much the pore walls slow solute transport relative to free solution.

The Rejection Curve

Nanofiltration's defining feature is its sharp rejection curve: as solute size approaches pore size, rejection rises steeply from near-zero to near-complete. This enables selective separations impossible with other methods — for example, removing calcium and magnesium (water hardness) while passing sodium and chloride, or concentrating pharmaceutical intermediates while letting solvents pass through.

Engineering Better Membranes

Modern nanofiltration research focuses on next-generation membrane materials: graphene oxide laminates with atomically precise channels, metal-organic frameworks (MOFs) with tunable pore chemistry, and aquaporin-inspired biomimetic membranes. These advanced materials promise higher flux, sharper selectivity, and improved fouling resistance compared to conventional thin-film composite polyamide membranes that have dominated the field for decades.

FAQ

What is nanofiltration?

Nanofiltration (NF) is a pressure-driven membrane separation process using membranes with pore sizes of 0.5–5 nm. It bridges the gap between ultrafiltration (larger pores) and reverse osmosis (essentially no pores). NF selectively removes multivalent ions, organic molecules, and small colloids while passing monovalent salts — useful for water softening, dye removal, and pharmaceutical purification.

How does pore size determine what gets filtered?

The ratio λ = solute radius / pore radius controls rejection. When λ approaches 1, steric exclusion blocks the solute almost completely. The Kedem-Katchalsky model shows rejection rises steeply from 0 to nearly 1 as λ increases from 0.3 to 0.8. This creates a sharp molecular weight cutoff (MWCO) characteristic of each membrane.

What is the molecular weight cutoff (MWCO)?

MWCO is the molecular weight at which the membrane rejects 90% of the solute. For nanofiltration, MWCO typically ranges from 200 to 1000 Daltons. It depends primarily on pore size distribution — membranes with narrow pore distributions have sharper cutoffs, enabling more precise separations.

What limits nanofiltration performance?

Membrane fouling (deposition of rejected solutes on the membrane surface) is the primary limitation. Concentration polarization — accumulation of rejected solutes near the membrane — reduces effective driving force and increases osmotic pressure. Operating strategies include cross-flow filtration, periodic backwashing, and surface modification to resist fouling.

Sources

Embed

<iframe src="https://homo-deus.com/lab/nanotechnology/nanofiltration/embed" width="100%" height="400" frameborder="0"></iframe>
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