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

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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.