Time periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates with high Zeta potential

Abstract

In this study, semi-analytical solutions are presented for the time periodic (electroosmotic flow) of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the nonlinear Poisson-Boltzmann (P-B) equation, the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of the dimensionless wall Zeta potential0, the periodic EOF electric oscillating Reynolds number Re, and normalized relaxation times 1 on velocity profiles are presented. Results show that for prescribed electrokinetic width K, relaxation time 1 and oscillating Reynolds number Re, higher Zeta potential 0 will lead to larger amplitude of EOF velocity, and the variation of velocity is restricted to a very narrow region close to the Electric double-layer. In addition, with the increase of relaxation time 1, the elasticity of the fluid becomes conspicuous and the velocity variations can be expanded to the whole flow field. For prescribed Re, longer relaxation time 1 will lead to quick change of the EOF velocity profile, and the amplitude becomes larger gradually.