restriction that the double layer thickness (k 01 ) was small Knowledge of the electrical potential distribution is an essential compared with the capillary radius r c . Rice and Whitehead basis for analyzing the flow behavior of electrolytes in a charged (2) extended Smoluchowski's results to narrow capillaries capillary, such as electroviscous effects. The cylindrical Poissonhaving arbitrary values of kr c (0 รต kr c รต ฯฑ) by means of Boltzmann equation (PBE) governs the distribution in the capilcorrection factors. However, the Debye-Hu ยจckel approximalary. The PBE is a differential equation that is difficult to solve tion was used in their approach. Rice and Whitehead's results analytically, especially when the capillary is filled with general were applicable only to surface potentials of less than 25 electrolytes. In this paper we propose a numerical algorithm to mV for a monovalent electrolyte. Following Rice and Whiteobtain the electrical potential distribution in a charged capillary head's work, Levine et al. (3) improved the Rice-Whitehead filled with arbitrary electrolytes. First, we introduce a Poisson-Boltzmann integral equation (PBIE) governing the potential dis-correction factor theory and made it effective at higher surtribution and derived from the physical principles for electrostatic face potentials. Bowen and Jenner (4) further extended the fields and thermodynamic systems. Then we solve the PBIE nuapproach to any symmetric electrolyte for anions and cations merically by iteration. In numerical calculation only the discrete of different mobilities and developed an algorithm for nupotential is used, and the potential differentials of the first and merical solution of the nonlinear Poisson-Boltzmann equahigher orders are not required. This algorithm essentially removes tion in cylindrical coordinates. In the algorithm of Bowen the difficulty caused by very steep variation of the potential near and Jenner, a transform M(R) ร
tanh(F(R)/4) of the scaled the wall of the capillary and is easily extended to cover the more potential F(R), initially developed by Strauss et al. (5) for general case of arbitrary electrolytes. The results of the examples spherical cells, was adopted to avoid the very steep variation given in the paper show that the algorithm proposed here is corof the potentials near the wall of the capillary. However, rect, effective, accurate (the relative errors are less than 0.01% M(R)'s differentials from the first to the fourth order were when normalized surface potential j ยฃ 8), and easily implemented on a personal computer.