ACCURACY ASSESSMENT OF NUMERICAL-SOLUTIONS OF THE NONLINEAR POISSON-BOLTZMANN EQUATION FOR CHARGED COLLOIDAL PARTICLES

A method is proposed to evaluate the accuracy of numerical solutions o f the nonlinear Poisson-Boltzmann equation for charged colloidal parti cles. It is derived from the principles of electrostatic fields and is formulated as an integral equation. It is valid for arbitrary surface potential and complex geometry. Two examples are given: for a charged capillary and for a charged spherical particle. It is shown by the ex amples that the assessment method is reasonable. In addition, the firs t example indicates that the Debye-Huckel approximation is acceptable at wider ranges of r(c) and zeta than normally considered, if a relati ve error (ER) of about 10% can be tolerated. The second example sugges ts that the results of Loeb et al. of the electric potentials (1961) s hould be interpolated linearly or nonlinearly to achieve higher accura cy when they are used in further calculations. (C) 1998 Academic Press .