激电效应的非线性扩散方程及其形式解

来源期刊：中国有色金属学报1999年第3期

论文作者：王玲 何继善

文章页码：655 - 660

关键词：激发极化；电化学机理；非线性扩散方程

Key words：induced polarization; electrochemical mechanism; nonlinear diffusion equation

摘    要：矿物的激发极化效应，总是与发生在矿物/溶液界面上的各种电极过程紧密相关的。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，写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对方程组稳态解的分析，导出了描述激电效应的非线性扩散方程。由于方程的非线性及复杂的边界条件，作者采用了本征表象中的扰动展开方法，近似处理了该数学问题，得到了方程的形式解，并提出了将电化学理论与非线性理论相结合的一种新的激电理论。

Abstract: The IP effect of minerals is always closely related to the processes of various electrical polarizations taking place on the interface between the mineral and electrolyte. Based on the electrochemical theory of IP effect, the coupled particle differential equations describing the temporal and spatial variations in the concentrations of ions can be written out by studying the patterns of the ions' motion on the interface. According to the structure of the electrical double layer and the stationary solution of the equations, a nonlinear diffusion equation has been derived. Due to the nonlinearity of the equation and the complexity of the boundary conditions, this problem was deal treated by approximately using perturbation method in eigen representation and get formal solution of it. A new IP theory of combining electrochemical theory with nonlinear theory was put forward.