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Time periodic electroosmotic flow of micropolar fluids through microparallel channel

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Abstract

The time periodic electroosmotic flow of an incompressible micropolar fluid between two infinitely extended microparallel plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-H¨uckel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and microrotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.

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Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Zhaodong Ding, Yongjun Jian & Liangui Yang

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  1. Zhaodong Ding
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  2. Yongjun Jian
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  3. Liangui Yang
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Correspondence to Yongjun Jian.

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Supported by the National Natural Science Foundation of China (Nos. 11472140 and 11362012), the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (No.NJYT-13-A02), the Inner Mongolia Grassland Talent (No. 12000-12102013), and the Opening fund of State Key Laboratory of Nonlinear Mechanics

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Ding, Z., Jian, Y. & Yang, L. Time periodic electroosmotic flow of micropolar fluids through microparallel channel. Appl. Math. Mech.-Engl. Ed. 37, 769–786 (2016). https://doi.org/10.1007/s10483-016-2081-6

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  • DOI: https://doi.org/10.1007/s10483-016-2081-6

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2010 Mathematics Subject Classification

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