Reconsideration of Gel Polarization Model Based on Solubility-Based Flux Model for RO and UF Membrane Fouling

In reverse osmosis (RO) and ultrafiltration (UF) membrane filtration of soluble substances, concentration polarization can raise the solute concentration at the membrane surface above its saturated solubility, triggering precipitation until local equilibrium is reached. This surface precipitation reduces the permeate flux. We propose a solubility-based flux model demonstrating that, irrespective of whether the foulant is inorganic or organic, and regardless of the fouling pathway or the concentration profile within the fouling layer, the permeate flux converges to a constant value—the solubility-based critical flux—once the solute concentration at the fouling-layer surface reaches the saturated solubility. Application of the model to experimental data confirms its validity. Furthermore, the solubility-based flux model clarifies that the gelation concentration obtained from the classical gel polarization model corresponds physically to the saturated solubility of the solute in the bulk feed. This finding provides a practical guideline for membrane system design and optimal operation, including estimation of the maximum achievable water recovery.