An Exact, Fully Nonlinear Solution of the Poisson-Boltzmann Equation with Anti-symmetric Electric Potential Profiles
-
Kwok Wing Chow
and
Chiu-On Ng
Abstract
The electric potential in an electro-osmotic flow is governed by the Poisson-Boltzmann (P-B) equation. A new solution is obtained by solving the fully nonlinear P-B model in a rectangular channel using the Hirota bilinear method, without invoking the Debye-Hückel (D-H) (linearization) approximation. This new solution is anti-symmetric about the centerline of two parallel plates, representing the case of opposite charges on two walls of a microchannel. The electric potentials and velocity fields derived from both the complete and linearized P-B equations are compared. Significant deviations are revealed, in particular for cases with high zeta potential. If a boundary slip on the wall is permitted, the electro-osmotic flow corresponding to this anti-symmetric wall potential can still induce a net fluid flow. These results will have important applications in characterizing bi-directional flows within microchannels, capillary tubes, membranes and porous materials.
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Mathematical Models for Erosion and the Optimal Transportation of Sediment
- Comments on “He's Homotopy Perturbation Method for Calculating Adomian Polynomials”
- Biomechanical Analysis of Eyring Prandtl Fluid Model for Blood Flow in Stenosed Arteries
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- Extended Reductive Perturbation Method and Its Relation to the Re-normalization Method
- Neural Network Approaches to Data Fusion Calculation and Correction in Wireless Sensor Network – A Case Study Comparison between BPN, RBFN and GRNN
- A Catfish Effect Inspired Harmony Search Algorithm for Optimization
- An Exact, Fully Nonlinear Solution of the Poisson-Boltzmann Equation with Anti-symmetric Electric Potential Profiles
- Study on Nonlinear Oscillations of Gear Systems with Parametric Excitation Solved by Homotopy Analysis Method
