平行板微管道间Maxwell流体的高Zeta势周期电渗流动

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ψ₀ 、 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ψ₀ 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λ₁ω 导致EOF速度剖面较快的变化, 且速度剖面的振幅逐渐增大.

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

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 potentialψ₀, 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 λ ₁ω and oscillating Reynolds number Re, higher Zeta potential ψ₀ 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 λ ₁ω, 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 λ ₁ω will lead to quick change of the EOF velocity profile, and the amplitude becomes larger gradually.