平行板微管道间Maxwell流体的高Zeta势周期电渗流动

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

本文研究了两平行板微管道中线性黏弹性流体的周期电渗流动,其中线性黏弹性流体的本构关系是由广义Maxwell模型描述的.将电渗力作为体力,解析求解了非线性的Poisson-Boltzmann(P-B)方程,柯西动量方程和广义Maxwell本构方程.通过数值计算,分析了无量纲壁面Zeta势Ψ_0、周期电渗流(electroosmotic flow,EOF)振荡雷诺数Re和无量纲弛豫时间λ_1ω对速度剖面的影响.结果表明:对给定的电动宽度K(表示微管道的特征尺度与双电层厚度的比值)、弛豫时间λ_1ω和振荡雷诺数Re,高Zeta势Ψ_0产生较大的EOF速度振幅,并且速度剖面的变化主要集中在双电层(electric double-layer,EDL)的狭窄的区域.此外,随着弛豫时间的增长流体的弹性显著增加,速度的变化可以延伸到整个流动的区域中.对给定的雷诺数Re,较长的弛豫时间λ_1ω导致EOF速度剖面较快的变化,且速度剖面的振幅逐渐增大.

In this study, semi-analytical solutions are presented for the time periodic electroosmotic flow （EOF） 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 potential φo, the periodic EOF electric oscillating Reynolds number Re, and normalized relaxation times ,λ1ω on velocity profiles are presented. Results show that for prescribed electrokinetic width K, relaxation time λ1ω and oscillating Reynolds number Re, higher Zeta potentialφo 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 （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 change of the EOF velocity profile, and the amplitude becomes larger gradually.