描述激电效应的非线性扩散方程

从岩矿石激电效应的电化学机理出发，通过研究矿物-溶液界面离子的运动规律，给出了描述离子浓度的暂态变化和空间变化的有关偏微分方程．根据界面双电层结构理论以及方程组的稳态解，导出了描述激电效应的非线性扩散方程，给出相应的初始与边界条件，提出了一种激电理论模型．用有限差分法对方程分别在时间域和频率域进行了数值计算，显示了岩矿石的激发极化特性．数值计算结果表明，这一激电理论模型不论是在时间域、频率域还是在小电流激励下的线性区及大电流激励下的非线性区都能很好地描述激电现象．

NONLINEAR DIFFUSION EQUATION DESCRIBING IP EFFECT

Based on the electrochemical theory of IP effect, the coupled partial differentialequation describing the temporal and spatial variations in the concentrations of ionscan be written out by studying the patterns of the ions' moction on the interface.According to the structure of the electrical double layer and the stationary solution ofthe equations, we derive a nonlinear diffusion equation supplemented by relevantinitial and boundary values, and put forward a theoretical model of IP. We haveobtained numerical solution in time and frequency domain respectively with the helpof computer using the difference approximation. These results revealed the inducedpolarization properties of minerals. The results calculated from this model prove thatthis theoretical model can describe the IP effect correctly in linear and nonlinearregions.