Multi-model assessment of fluoride transport in reverse osmosis and nanofiltration: role of initial concentration and pore-scale interactions

This study primarily investigates the effect of feed concentration on the fluoride ion permeability coefficient (Ps) and reflection coefficient (σ) for two membranes: TW30 (reverse osmosis) and NF270 (nanofiltration), using three transport models: the Kedem–Katchalsky (KK), Spiegler–Kedem (SK), and the Nernst–Planck model coupled with film theory (NP-TF). Pore size estimation was performed using three distinct models: Steric hindrance pore (SHP), Ferry (neglecting solute-pore wall interactions), and Verniory (accounting for frictional forces). Experiments were conducted with sodium fluoride (NaF) solutions in distilled water across fluoride concentrations ranging from 10 to 25 mg/L. A linear relationship was observed between the initial fluoride concentration and σ for both membranes, accompanied by a progressive decrease in Ps. This concentration dependence was more pronounced for the NF270 membrane than for the TW30 membrane. The NF270 membrane's pore diameter varied significantly by model: 0.193 nm (SHP), 0.221 nm (Ferry), 0.243 nm (Verniory). This highlights complex solute transport involving diffusive-convective flow, influenced by steric exclusion and pore frictional forces. Conversely, TW30's dense polyamide structure facilitates diffusive transport via solution-diffusion. Its hydraulic pore diameter averages 0.17 nm. Thus, size exclusion and frictional effects persist but play a reduced role in fluoride rejection.