Abstract
A numerical model based on the finite volume formulation to predict laminar flows hydrodynamics and mass transfer of aqueous solutions (570< Sc<3200) in the feed channel of spiral-wound and plate-and-frame systems is presented and experimentally validated. Particular attention is devoted to the physical modelling of the solute transport inside the membrane that yields parameters pertaining to solute–membrane interactions and are incorporated on the mass transfer boundary condition at the membrane surface. A correction factor, dependent on the solute mass concentration at the membrane surface, is proposed for the osmotic pressure phenomenological equation. The experimental cell is a slit ( 200 mm×30 mm×2 mm) that simulates the two-dimensional developing flow in the channels of spiral-wound modules. The predictions are validated against experimental data of apparent rejection coefficients and permeate fluxes, exhibiting an excellent agreement. A correlation for the concentration boundary layer thickness, a measure of the concentration polarisation, based on the predicted values of the solute concentration profiles, δ ω h =15.5 l h 0.4Re −0.4 Sc −0.63 Re p −0.04[1−186Sc −1.0 Re p −0.21] is proposed in the operating condition ranges of 250< Re<1000, 0.02< Re p<0.1 and 800< Sc<3200.
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