Ultrafiltration Simulator: MWCO, Pore Size & Rejection Curves

simulator intermediate ~10 min
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R = 82% — BSA (67 kDa) rejection by 50 kDa membrane

A 50 kDa MWCO ultrafiltration membrane rejects 82% of bovine serum albumin (67 kDa), demonstrating that rejection transitions gradually around the cutoff rather than as a sharp step function.

Formula

R(MW) = 1 − exp(−(MW/MWCO)²)  [Sigmoidal rejection model]
J = ε·r²·ΔP / (8·μ·L)  [Hagen-Poiseuille pore flow]
r_p ≈ 0.066 × MWCO^0.395  [Pore radius correlation, nm]

Size-Exclusion Separation

Ultrafiltration membranes separate dissolved macromolecules based on size. Unlike reverse osmosis, which relies on solution-diffusion through a dense polymer, UF membranes have physical pores (2-50 nm) that allow small molecules and water to pass while retaining larger solutes. The key parameter is the molecular weight cutoff (MWCO) — the molecular weight at which 90% rejection is achieved.

The Rejection Curve

Rejection does not occur as a sharp step at the MWCO. Because real membranes have a distribution of pore sizes, the rejection curve is sigmoidal — gradually rising from low rejection for small solutes to near-complete rejection for large ones. The sharpness of this transition determines the membrane's selectivity. Track-etched membranes have narrow pore distributions and sharper cutoffs, while phase-inversion membranes show broader transitions.

Flux & Fouling

Pure water flux through UF membranes follows the Hagen-Poiseuille equation for flow through cylindrical pores: flux scales with pore radius squared and transmembrane pressure. However, in real operation, protein adsorption, cake layer formation, and pore blocking progressively reduce flux — a phenomenon called fouling. Crossflow operation, where feed flows tangentially across the membrane surface, minimizes cake buildup and maintains higher flux.

Industrial Applications

Ultrafiltration is indispensable in biopharmaceutical manufacturing for protein concentration and buffer exchange, in dairy processing for whey protein recovery, in water treatment for pathogen removal, and in industrial wastewater treatment. Ceramic UF membranes offer superior chemical and thermal stability for harsh environments, while polymeric membranes (PES, PVDF) dominate cost-sensitive applications.

FAQ

What is molecular weight cutoff (MWCO)?

MWCO is defined as the molecular weight at which 90% of the solute is rejected by the membrane. It provides a practical measure of the membrane's effective pore size. A 50 kDa MWCO membrane retains most proteins larger than 50,000 Daltons.

How does pore size relate to MWCO?

Pore radius scales approximately as rp ≈ 0.066 × MWCO^0.395 nm. A 50 kDa MWCO corresponds to roughly 3-5 nm pore radius, while a 300 kDa membrane has pores around 8-12 nm. The relationship is empirical because molecular shape also matters.

What is the difference between UF and MF?

Ultrafiltration (UF, 1-300 kDa MWCO, 2-50 nm pores) separates proteins and colloids, while microfiltration (MF, 0.1-10 μm pores) removes bacteria and large particles. UF operates at higher pressures (1-5 bar) than MF (0.1-2 bar) due to smaller pore sizes.

Why is the rejection curve not a sharp cutoff?

Real membranes have a pore size distribution rather than uniform pores. This means rejection transitions gradually from near-zero for small solutes to near-complete for large ones. The breadth of this transition depends on the membrane's pore size distribution — narrower distributions give sharper cutoffs.

Sources

Embed

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