An Exact, Fully Nonlinear Solution of the Poisson-Boltzmann Equation with Anti-symmetric Electric Potential Profiles

Kwok Wing Chow 1 , Henry C. W. Chu 2 ,  and Chiu-On Ng 1
  • 1 Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong
  • 2 Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA


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.

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The International Journal of Nonlinear Sciences and Numerical Simulation publishes original papers on all subjects relevant to nonlinear sciences and numerical simulation. The journal is directed at researchers in nonlinear sciences, engineers, and computational scientists, economists, and others, who either study the nature of nonlinear problems or conduct numerical simulations of nonlinear problems.