Yc. Qian et al., AN ALGORITHM FOR THE CALCULATION OF THE ELECTRICAL POTENTIAL DISTRIBUTION IN A CHARGED CAPILLARY WITH GENERAL ELECTROLYTES, Journal of colloid and interface science, 190(1), 1997, pp. 55-60
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.