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A theoretical model of electroosmosis through a circular pore of radius $a$that traverses a membrane of thickness $h$ is investigated. Both thecylindrical surface of the pore and the outer surfaces of the membrane arecharged. When $h\gg a$ end effects are negligible: results of full numericalcomputations of electroosmosis in an infinite pore agree with theory. When$h=0$, end effects dominate, and computations again agree with analysis. Forintermediate values of $h/a$, an approximate analysis that combines these twolimiting cases captures the main features of computational results when theDebye length $\kappa^{-1}$ is small compared with the pore radius $a$. However,the approximate analysis fails when $\kappa^{-1}\gg a$, when the charge clouddue to the charged cylindrical walls of the pore spills out of the ends of thepore, and the electroosmotic flow is reduced. When this spilling out isincluded in the analysis, agreement with computation is restored.

Electroosmosis in a finite cylindrical pore: simple models of end effects