(1.湖南師范大學(xué)物理系，長沙 410081；2.中南工業(yè)大學(xué)資環(huán)建筑工程學(xué)院，長沙 410083)
摘 要: 礦物的激發(fā)極化效應(yīng)，總是與發(fā)生在礦物/溶液界面上的各種電極過程緊密相關(guān)的。從巖礦石激電效應(yīng)的電化學(xué)機理出發(fā)，通過研究礦物/溶液界面離子的運動規(guī)律，寫出了描述離子濃度的暫態(tài)變化和空間變化的有關(guān)偏微分方程。根據(jù)界面雙電層結(jié)構(gòu)理論以及對方程組穩(wěn)態(tài)解的分析，導(dǎo)出了描述激電效應(yīng)的非線性擴散方程。由于方程的非線性及復(fù)雜的邊界條件，作者采用了本征表象中的擾動展開方法，近似處理了該數(shù)學(xué)問題，得到了方程的形式解，并提出了將電化學(xué)理論與非線性理論相結(jié)合的一種新的激電理論。
關(guān)鍵字: 激發(fā)極化；電化學(xué)機理；非線性擴散方程
（1. Department of Physics, Hunan Normal University, Changsha 410081, P. R. China
2. College of Resource, Environment and Civil Engineering,
Central South University of Technology, Changsha 410083, P. R. China）
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.
Key words: induced polarization; electrochemical mechanism; nonlinear diffusion equation
