Viscoelectric effect on electroosmotic flow in a cylindrical microcapillary

Electroosmotic flow, under the Debye-Hückel approximation, has been widely analyzed in the specialized literature. This is a severe restriction in practice, where zeta potentials as high as 100-200 mV are encountered frequently. Under this condition, the variation of the viscosity with the electric field in the electric double layer (EDL), known as the viscoelectric effect, can lead to a considerable variation in comparison to the Helmholtz-Smoluchowsky equation for the electroosmotic velocity. The objective of this work is to analyze the electroosmotic flow in a cylindrical capillary at high zeta potentials in the thin EDL approximation, taking into account the viscoelectric effect. In order to obtain the potential distribution, the Poisson-Boltzmann equation was solved by using the matched asymptotic expansions method, and then, by applying the same technique, the flow field was determined from the momentum equation by considering that the viscosity of the electrolyte changes according to the relationship η = η₀ [1 + fE²] , where η₀ is the viscosity evaluated in the absence of an electric field, f is the viscoelectric constant and E is the intrinsic electric field in direction transversal to the EDL. For asserting the correctness of the asymptotic solution, this result was compared against a numerical solution, and a very good agreement between them was found. The results show that the viscoelectric effect has a noticeable influence by reducing the electroosmotic flow velocity in about 10% in comparison to the standard Helmholtz-Smoluchowski velocity.