A semi-analytical solution for electric double layers near an elliptical cylinder
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A theoretical analysis on the electric double layer formed near the surface of an infinite cylinder with an elliptical cross section and a prescribed electric potential in an ionic conductor was performed using the linearized Gouy–Chapman theory. A semi-analytical solution in terms of the Mathieu functions was obtained. The distributions of the electric potential, cations, anions, and electric field were calculated. The effects of various physical and geometric parameters were examined. The fields vary rapidly near the elliptical boundary and are nearly uniform at far field. Electric field concentrations were found at the ends of the semi-major and semi-minor axes of the ellipse. These concentrations are sensitive to the physical and geometric parameters.
KeywordsElliptical cylinder Electric double layer Semi-analytical solution Electric field concentration
This work was supported by the National Natural Science Foundation of China (Grants 11502108 and 11232007), the Program for New Century Excellent Talents in Universities (Grant NCET-12-0625), the Natural Science Foundation of Jiangsu Province (Grant BK20140037), the Fundamental Research Funds for Central Universities (Grant NE2013101), and a project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).
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