Abstract
This paper obtains an explicit analytical solution for nonlinear Poisson‐Boltzmann equation by the homotopy perturbation method, which does not require a small parameter in the equation under study, so it can be applied to both the weakly and strongly nonlinear problems. The obtained results show the evidence of the usefulness of the homotopy perturbation method for obtaining approximate analytical solutions for nonlinear equations.
Highlights
Oyanader and Arce [11] suggested a more effective, accurate, and mathematically friendly solution for prediction of the electrostatic potential, commonly used on electrokinetic research and its related applications
The nonlinear Poisson-Boltzmann equation reduces to the following linear equation: u = λ2u
We will suggest an alternative approach to the search for an explicit analytical solution for (1.1) by homotopy perturbation method [2, 3]
Summary
Oyanader and Arce [11] suggested a more effective, accurate, and mathematically friendly solution for prediction of the electrostatic potential, commonly used on electrokinetic research and its related applications. In order to obtain an explicit mathematical expression for the electrostatic potential, we have to solve the following nonlinear Poisson-Boltzmann equation:. Where u is the dimensionless electrical potential, λ the dimensionless inverse Debye length. The nonlinear term on the right-hand side of (1.1) is related to the free charge density. A very common simplification invokes the Debye-Huckel approximation usually written as sinh u ≈ u. The nonlinear Poisson-Boltzmann equation reduces to the following linear equation:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
