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Accuracy Assessment of Numerical Solutions of the Nonlinear Poisson–Boltzmann Equation for Charged Colloidal Particles

Authors
Journal
Journal of Colloid and Interface Science
0021-9797
Publisher
Elsevier
Publication Date
Volume
201
Issue
1
Identifiers
DOI: 10.1006/jcis.1997.5374
Keywords
  • Accuracy Assessment
  • Numerical Solution
  • Electrostatic Interaction
  • Electrical Double Layer
  • Poisson–Boltzmann Equation
Disciplines
  • Mathematics

Abstract

Abstract A method is proposed to evaluate the accuracy of numerical solutions of the nonlinear Poisson–Boltzmann equation for charged colloidal particles. 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 examples that the assessment method is reasonable. In addition, the first example indicates that the Debye–Huckel approximation is acceptable at wider ranges of r cand ζ than normally considered, if a relative error ( ER) of about 10% can be tolerated. The second example suggests that the results of Loeb et al.of the electric potentials (1961) should be interpolated linearly or nonlinearly to achieve higher accuracy when they are used in further calculations.

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