AC Eletroosmotic Flow Of Non-Newtonian Fluids Between Two Miro-Parallelplates

Analytical solutions are presented using method of separation of variables for the time periodic EOF flow of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the general Maxwell model and Jeffrey model. The solution involves analytically solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation, the general Maxwell constitutive equation and Jeffrey constitutive equation. By numerical computations, the influences of the electrokinetic width K denoting the characteristic scale of half channel width to Debye length, the periodic EOF electric oscillating Reynolds number Re, normalized relaxation timesλ1ωand retardation timeλ2ωon velocity profiles are presented. For the general Maxwell fluid, results show that for prescribed electrokinetic width K, lower oscillating Reynolds number Re and shorter relaxation timeλ1ωreduces the plug-like EOF velocity profile of Newtonian fluids. For given Reynolds number Re and electrokinetic width K, longer relaxation timeλ1ωleads to rapid oscillating EOF velocity profiles with increased amplitude. With the increase of the K, the velocity variations are restricted to a very narrow region close to the EDL for small relaxation time. However, with the increase of the relaxation time, the elasticity of the fluid becomes conspicuous and the velocity variations can be expanded to the whole flow field. For the Jeffrey fluid, as normalized retardation timeλ2ωincrease for fixed Re, the flow response to the imposed electric field becomes faster. This implies that the flow feels the presence of the AC electric field very quickly and in shorter time asλ2ωincreases. Similarly, for prescribed relaxation timeλ2ω, increasing oscillating Reynolds number Re leads to rapid oscillating EOF velocity profiles. At the same time, the amplitudes of the EOF velocity decrease gradually. At the distance far away from the EDL, the EOF velocity almost approaches to zeros.Moreover, the time periodic evolution of the velocity profiles provide a detail insight of the flow characteristic of this flow configuration.