Authors: Chang Yi Wang ChihYu Kuo Chien C Chang
Publish Date: 2010/07/27
Volume: 70, Issue: 4, Pages: 333-342
Abstract
The Poisson–Boltzmann equation PB 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 PB using a nondimensional electrokinetic–thermal energy ratio λ which when it approaches zero reduces the PB to the Debye–Hückel approximation Perturbationseries 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 higherorder 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
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