Time Periodic Electro-osmotic Flow Of Non-Newtonian Fluid Through A Microchannel

ABSTRACT:In this study, semi-analytical solutions are presented for the time periodic EOF flow of linear viscoelastic fluids between micro-parallel plates/micro-circular cylinders. 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, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of the dimensionless wall Zeta potential Ψ0, the periodic Electroosmotic flow (EOF), electric oscillating Reynolds number Re, normalized relaxation times λ1ω, the ratio β of wall zeta potential and the ratio a of inner radius than outer radius with micro-circular cylinders on velocity profiles are presented. For micro-parallel plates, results show that the prescribed electrokinetic width K, relaxation time λ1ω and oscillating Reynolds number Re, higher Zeta potential Ψ0will lead to larger amplitude of EOF velocity. And the variations of velocity profile are restricted to a very narrow region close to the Electric double-layer (EDL). In addition, with the increase of relaxation time λ1ω, 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 λ1ω will lead to quick changes of the EOF velocity profiles, and the amplitude becomes larger gradually. For micro-circular cylinder, results show that the typical Helmholtz-Smoluchowski velocity profile will be occurred, for given electrokinetic width K, the Zeta potential ratio β of the wall, the ratio a of inner to outer cylindrical radius of circle-microchannel, lower oscillating Reynolds number and shorter relaxation time λ1ω. The variations of velocity profile part of concentrated on area of narrow EDL which close to the wall. For given relaxation time λ1ω and the increasing oscillating Reynolds number Re will lead to the EOF velocity profile vibrating quickly and at the same time the amplitude of EOF velocity reduced gradually. For given relaxation time λ1ω, the electrokinetic width K, the ratio a of inner to outer cylindrical radius of circle-microchannel and the lower Reynolds number the changing figure of EOF velocity profile is similar with the figure of previous studied result. Along with the increase of oscillating Reynolds number, the amplitudes of velocity which except the two EDL far away from surface of cylinder becomes more and more small and tend to zero. The increasing relaxation time λ1ω lead to the EOF velocity profile becomes very easy to change under the applied electric, the velocity profile vibrating rapidly more.