电毛细管中非线性PB积分方程及其数值解  

Poisson Boltzmann Integral Equation in A Charged Capillary and Its Numerical Solutions

作　　者：钱勇先[1] 

机构地区：[1]江汉石油学院物探系

出　　处：《电化学》1996年第4期408-412,共5页Journal of Electrochemistry

摘　　要：依据电毛细管非线性ＰｏｉｓｓｏｎＢｏｌｔｚｍａｎｎ微分方程的物理原理，导出其积分形式的ＰＢ方程．并采用数值迭代法给出相应方程的数值解．数值计算只用到电势Ψ的离散值，不需要Ψ的导数值，从根本上解决了因电势在管壁陡然变化引起数值解法的困难．文中给出的计算实例表明该算法是正确的、有效的和高精度的（相对误差小于０．０１％），且在ＰＣ机上容易实现．The nonlinear Poisson Boltzmann integral equation (PBIE) governing electrostatic potential distribution in a charged capillary filled with symmetric electrolytes is derived from the same physical principles as used in deriving nonlinear Poisson Boltzmann differential equation, usually called PBE. PBIE is then numerically solved by iteration. In iterate computation discrele values of electrical potential is soly needed, and the first or higher orders of the differential of the potential is not used any more. This does essentially remove the difficulty caused by the very steep variation of the potential near the wall of the capillary. The results of the seven examples given in the paper show that the method proposed here is correct, effective, and accurate (the relative errors less than 0.01%), and easy to practice on a personal computer.

关 键 词：双电层 毛细管 积分方程 数值解 电解液 PB方程 

分 类 号：O657.8[理学—分析化学]