Adaptive finite-element: Solution of the nonlinear Poisson-Boltzmann equation: A charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface

W. Richard Bowen, Adel O. Sharif

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

A Galekin finite-element approach combined with an error estimator and automatic mesh refinement has been used to provide a flexible numerical solution of the Poisson-Boltzmann equation. A Newton sequence technique was used to solve the nonlinear equations arising from the finite-element discretization procedure. Errors arising from the finite-element solution due to mesh refinement were calculated using the Zienkiewicz-Zhu error estimator, and an automatic remeshing strategy was adopted to achieve a solution satisfying a preset quality. Examples of the performance of the error estimator in adaptive mesh refinement are presented. The adaptive finite-element scheme presented in this study has proved to he an effective technique in minimizing errors in finite-element solutions for a given problem, in particular those of complex geometries. As an example, numerical solutions are presented for the case of a charged spherical particle at various distances from a charged cylindrical pore in a charged planar surface. Such a scheme provides a quantification of the significance of electrostatic interactions for an important industrial technology-membrane separation processes.

Original languageEnglish
Pages (from-to)363-374
Number of pages12
JournalJournal of Colloid and Interface Science
Volume187
Issue number2
DOIs
Publication statusPublished - 15 Mar 1997
Externally publishedYes

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Keywords

  • Adaptivity
  • Boltzman equation
  • Finite element
  • Membrane
  • Poisson
  • Sphere-pore interaction

ASJC Scopus subject areas

  • Colloid and Surface Chemistry
  • Physical and Theoretical Chemistry
  • Surfaces and Interfaces

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