关键词: 双电层, PoissonBoltzmann方程, 毛细管, 积分方程

Abstract: 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.

Key words: Electrical double layer, Poisson Boltzmann equation, Capillary, Numerical solution