中文摘要：

提出了电导率呈指数型分布的浓差极化层的介电模型．利用传递方程研究了压力驱动膜过程的介电谱，并导出层内电导率分布与宏观测量的电容和电导之间定量关系的理论表达式，得到介电谱高低频特征值与浓差极化模数之间的关系．计算结果表明，较之线性分布电导率，指数型分布电导率能更好地描述浓差极化层的介电谱．研究表明，介电谱及其特征值和弛豫强度随浓差极化模数和层厚度显著变化．对由分离膜、主体溶液和浓差极化层组成的复合体系的介电谱进行了数值模拟，发现电导较之电容其频率依存关系对浓差极化模数的变化更为敏感，上述研究为利用介电谱在线监测膜分离过程提供了有价值的理论参考．

英文摘要：

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 spec- trum 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.