🎓 Lesson 13
D5
Concentration Polarization & Critical Flux Determination
Concentration polarization is when dissolved stuff builds up near a membrane surface during filtration, making it harder for clean water to pass through.
🎯 Learning Objectives
- ✓ Calculate critical flux for a given feed solution and membrane using mass transfer correlations
- ✓ Analyze the effect of crossflow velocity and Reynolds number on concentration polarization magnitude
- ✓ Explain the relationship between critical flux and long-term membrane performance stability
- ✓ Apply dimensionless groups (e.g., Sherwood, Schmidt, Reynolds numbers) to predict polarization severity
📖 Why This Matters
In mining water reclamation, tailings pond effluents are treated via ultrafiltration (UF) and reverse osmosis (RO) to meet discharge or reuse standards. Uncontrolled concentration polarization causes premature flux decline, frequent cleaning, and unexpected scaling—leading to 20–40% higher OPEX in membrane plants. Understanding and quantifying critical flux isn’t academic: it’s the design threshold that separates stable operation from rapid fouling.
📘 Core Principles
Concentration polarization arises from convective solute transport toward the membrane exceeding diffusive and shear-induced back-transport. As permeate flows through the membrane, rejected solutes accumulate in a boundary layer — forming a gel-like or hyperconcentrated region. Critical flux is the maximum permeate flux below which polarization remains mild and reversible; above it, polarization intensifies nonlinearly, often triggering irreversible fouling. The theory integrates boundary layer hydrodynamics (via mass transfer coefficients) and thermodynamic limits (osmotic pressure rise). Key parameters include feed concentration, diffusivity, hydrodynamics (Re, Sc), and membrane rejection coefficient.
📐 Critical Flux Estimation Using Mass Transfer Correlation
The critical flux (J_crit) is estimated by equating the convective solute flux to the diffusive back-transport at the onset of significant polarization. Widely used empirical–semiempirical correlations (e.g., based on Sherwood number) link J_crit to crossflow hydrodynamics and solute properties. The most practical form for engineering design uses the limiting concentration (C_gel) and mass transfer coefficient (k_m).
Critical Flux (J_crit)
J_crit = k_m × ln(C_m / C_b) × (1 − R)⁻¹Estimates the maximum permeate flux before severe concentration polarization initiates, based on mass transfer and rejection.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| J_crit | Critical flux | m/s | Maximum sustainable permeate flux before polarization accelerates |
| k_m | Mass transfer coefficient | m/s | Rate of solute diffusion away from membrane surface, governed by flow regime |
| C_m | Membrane surface concentration | g/L | Concentration at membrane–boundary layer interface (often approximated as C_gel) |
| C_b | Bulk feed concentration | g/L | Average solute concentration in bulk feed stream |
| R | Solute rejection coefficient | dimensionless | Fraction of solute rejected by membrane (R = 1 − C_p/C_b) |
Typical Ranges:
UF treating mine drainage (CaSO₄): 40 – 70 L/m²·h
RO desalination (NaCl): 15 – 25 L/m²·h
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Fouling Classification and Mitigation Be...