AN ALGORITHM FOR THE CALCULATION OF THE ELECTRICAL POTENTIAL DISTRIBUTION IN A CHARGED CAPILLARY WITH GENERAL ELECTROLYTES

Knowledge of the electrical potential distribution is an essential bas is for analyzing the flow behavior of electrolytes in a charged capill ary, such as electroviscous effects, The cylindrical Poisson-Boltzmann equation (PBE) governs the distribution in the capillary, The PBE is a differential equation that is difficult to solve analytically, espec ially when the capillary is filled with general electrolytes, In this paper we propose a numerical algorithm to obtain the electrical potent ial distribution in a charged capillary filled with arbitrary electrol ytes, First, we introduce a Poisson-Boltzmann integral equation (PBIE) governing the potential distribution and derived from the physical pr inciples for electrostatic fields and thermodynamic systems, Then we s olve the PBIE numerically by iteration, In numerical calculation only the discrete potential is used, and the potential differentials of the first and higher orders are not required, This algorithm essentially removes the difficulty caused by very steep variation of the potential near the wall of the capillary and is easily ex-tended to cover the m ore general case of arbitrary electrolytes, The results of the example s given in the paper show that the algorithm proposed here is correct, effective, accurate (the relative errors are less than 0.01% when nor malized surface potential xi less than or equal to 8), and easily impl emented on a personal computer. (C) 1997 Academic Press.