Alternating Current Electro-Osmotic Flow of the Maxwell Fluids Through a Circular Micro-Pipe
Alternating Current Electro-Osmotic Flow of the Maxwell Fluids Through a Circular Micro-Pipe
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DOI：
10.1017/jmech.2012.138
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发表时间：
2013-06
影响因子：
1.7
通讯作者：
L. Sun;Yongjun Jian;Long Chang;H. Zhang;Quansheng Liu
中科院分区：
文献类型：
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作者：
L. Sun;Yongjun Jian;Long Chang;H. Zhang;Quansheng Liu
给出了线性粘弹性流体通过圆柱微管时周期EOF流动的解析解。这里使用的线性粘弹性流体用一般麦克斯韦模型来描述。考虑麦克斯韦流体大分子与通道表面相互作用产生的损耗效应，对线性化泊松-玻尔兹曼方程、柯西动量方程和一般麦克斯韦本构方程进行解析求解。整体流动分为枯竭层和枯竭层外的大块流动。分别得到了两层的速度表达式。通过数值计算，给出了周期EOF电振荡雷诺数Re、黛博拉数De、耗尽层厚度δ和麦克斯韦与牛顿流体粘度比γ对速度剖面的影响。在一定的De下，随着Re的增大，EOF速度随速度大小的减小而发生较大的变化。对于给定的Re，较大的De给出较大的EOF速度大小。在给定的较低Re下，增加γ会导致较大的速度幅值。然而，在较高Re下，速度幅值随粘度比γ而减小，特别是在耗尽层内。此外，对于固定的Re和De，较大的耗尽层厚度会导致较小的EOF速度大小。最后，研究了De对能量耗散的影响。这些结果提供了对这种流动结构的流动特性的详细了解。
Analytical solutions are presented for time periodic EOF flow of linear viscoelastic fluids through a cylindrical micro-pipe. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson-Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation considering the depletion effect produced by the interaction between macro-molecules of the Maxwell fluid and the channel surface. The overall flow is divided into depletion layer and bulk flow outside of depletion layer. The velocity expressions of these two layers were obtained, respectively. By numerical computations, the influences of the periodic EOF electric oscillating Reynolds number Re, Deborah number De, depletion layer thickness δ and the viscosity ratio γ of Maxwell to Newtonian fluids on velocity profile are presented. For a prescribed De, the increasing Re will cause large changes of the EOF velocity with decreasing velocity magnitude. For a given Re, large De gives large EOF velocity magnitude. Increasing γ will lead to larger velocity amplitude for a given lower Re. However, at higher Re, the velocity amplitude decreases with the viscosity ratio γ, especially within the depletion layer. In addition, large depletion layer thickness gives small EOF velocity magnitude for fixed Re and De. Finally, the influence of De on energy dissipation is studied. These results provide a detail insight of the flow characteristic of this flow configuration.