Alternating current electroosmotic flow of the Jeffreys fluids through a slit microchannel

TLDR

The study examines linear viscoelastic fluids modeled by the Jeffreys model. The authors derive semi‑analytical solutions for time‑periodic electroosmotic flow of Jeffreys fluids in a slit microchannel by solving the Poisson‑Boltzmann, momentum, and constitutive equations, accounting for a depletion layer, and perform numerical studies of how oscillating Reynolds number, retardation time, and wall zeta potential affect velocity amplitude. The velocity expressions for depletion and bulk layers show that increasing retardation time reduces velocity amplitude at low to moderate Reynolds numbers, leaves it unchanged at high Reynolds numbers, and that higher wall zeta potential consistently enhances EOF velocity, particularly within the depletion layer.

Abstract

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, λ2ω, and normalized wall zeta potential, ψ¯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.