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Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel. (English) Zbl 1308.76327
Summary: Using the method of separation of variables, semi-analytical solutions are presented for the time periodic EOF flow of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the Jeffreys model. The solution involves solving the Poisson-Boltzmann (PB) equation, together with the Cauchy momentum equation and the Jeffreys constitutive equation considering the depletion effect produced by the interaction between macro-molecules of the Jeffreys fluid and the channel surface. The overall flow is divided into depletion layer and bulk flow outside of depletion layer. The velocity expressions of these two layers were obtained, respectively. By numerical computations, the influence of oscillating Reynolds number, Re, normalized retardation time, $$\lambda_{2}\omega$$, and normalized wall zeta potential, $$\psi=w$$, on velocity amplitude is presented. Results show that the magnitude of the velocity amplitude becomes smaller with the increase of retardation time for small and intermediate Re. For large Re, the velocity is almost unchanged near the EDL with retardation time. Moreover, high zeta potential results in larger the magnitude of EOF velocity no matter whether the Re is large or not, especially within the depletion layer.{