Analytic extensions of the Debye-H?ckel approximation to the Poisson-Boltzmann equation
Journal
Journal of Engineering Mathematics
Journal Volume
70
Journal Issue
4
Pages
333-342
Date Issued
2011
Author(s)
Abstract
The Poisson-Boltzmann equation (P-B) is used as an analytic model in a wide variety of fields in chemistry and physics, because it describes the charge distribution in a solute. Being highly nonlinear, there are only a few known solutions for simple boundary geometries and, beyond, iterative numerical schemes are often employed. This study, on the other hand, presents a systematic perturbation solution of the P-B using a non-dimensional electrokinetic-thermal energy ratio λ which, when it approaches zero, reduces the P-B to the Debye-Hückel approximation. Perturbation-series solutions are obtained for five basic examples, and lead to the surprising result that, even when λ is as large as 3 or larger, the perturbation solution is very accurate with only a few terms included in the series. This is because the perturbation analysis generates very rapidly vanishing coefficients at higher-order approximations. This result has the important implication that the perturbation method presented in this study could be applied quite generally for investigating more complicated problems. © 2010 Springer Science+Business Media B.V.
SDGs
Type
journal article