ELECTROOSMOSIS THROUGH PORES WITH NONUNIFORMLY CHARGED WALLS

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Abstract
The movement of fluid through a charged capillary by the action of an electric field is analyzed in the case where the charge density on the capillary wall varies with axial position. The capillary's radius is assumed much greater than the Debye screening length of the fluid. Our results show that the mean fluid velocity within the capillary is given exactly by the classical Helmholtz equation with the local zeta potential replaced by the average zeta potential, determined by integrating the local value over the length of the capillary. If the magnitude of the local zeta potential exceeds the thermal potential (kT/e), the relationship between zeta potential and wall charge is nonlinear, so that the Helmholtz equation cannot be used to calculate the average charge from a measured electroosmotic flow or streaming potential. Although the mean electroosmotic velocity depends only on the average zeta potential, the fluid velocity field within the capillary is a strong function of the distribution of zeta potential along the wall and even displays flow separation and circulation.