A dielectric model was proposed for a concentration polarization layer with an exponentially distributed conductivity, and the dielectric spectrum presented for the pressure-driven membrane. A theoretical equation describing the relation between the conductivity distribution and capacitance and/or conductance was obtained, and also, the relation between the characteristic of the dielectric spectrum under high and/or low frequencies and concentration polarization module could be then expressed. Compared with the linearly distributed conductivity, the exponentially distributed conductivity can offer a better description. It was indicated that the dielectric spectrum, its characteristic and the relaxation strength changed significantly with the variation of the concentration polarization module. A numerical simulation on the dielectric spectrum of system containing the membrane, bulk solution and concentration polarization layer has also been presented. Compared with capacitance, the frequency dependence on conductance appears more sensitive to the change of the concentration polarization module, which will provide a valuable reference for monitoring the membrane separation.

Key words: dielectric spectrum, concentration polarization, membrane process, pressure-driven