Abstract
Analytical solutions of the Nernst-Planck, Poisson and continuity equations for a membrane undergoing reverse osmosis in a cross-flow system reveal that the flow of alternating ionic charge induced in the membrane during impedance measurements is actively assisted by the flow of water. The actively driven current manifested "inductive" responses in impedance measurements of a Filmtec BW30 reverse osmosis membrane mounted in an Inphaze flat-bed cross-flow module after 16 hours of filtering a mineral salt solution seeded with CaCl2 and NaHCO3 at pressure of 900 kPa. Fitted transfer functions resolved conduction and capacitive properties of four membrane layers, diffusion/concentration phenomenon and a pseudo "inductor" shunted by a conductor. A 10-fold decrease in the shunt conductance correlated with smaller increases in the conductance values for the filtrate and membranous layers, and the onset of fouling diagnosed by a rapid increase in flux decline.
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