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Micromachines 2017, 8(12), 341; doi:10.3390/mi8120341

Analytical Solution of Electro-Osmotic Peristalsis of Fractional Jeffreys Fluid in a Micro-Channel

School of Mathematics and Statistics, Linyi University, Linyi 276000, China
School of Mathematics and Statistics, Shandong University, Weihai 264209, China
Author to whom correspondence should be addressed.
Received: 18 September 2017 / Revised: 8 November 2017 / Accepted: 19 November 2017 / Published: 23 November 2017
(This article belongs to the Special Issue Micro/Nano-Chip Electrokinetics, Volume II)
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The electro-osmotic peristaltic flow of a viscoelastic fluid through a cylindrical micro-channel is studied in this paper. The fractional Jeffreys constitutive model, including the relaxation time and retardation time, is utilized to describe the viscoelasticity of the fluid. Under the assumptions of long wavelength, low Reynolds number, and Debye-Hückel linearization, the analytical solutions of pressure gradient, stream function and axial velocity are explored in terms of Mittag-Leffler function by Laplace transform method. The corresponding solutions of fractional Maxwell fluid and generalized second grade fluid are also obtained as special cases. The numerical analysis of the results are depicted graphically, and the effects of electro-osmotic parameter, external electric field, fractional parameters and viscoelastic parameters on the peristaltic flow are discussed. View Full-Text
Keywords: electro-osmotic flow; peristalsis; fractional calculus; Jeffreys fluid; Laplace transform electro-osmotic flow; peristalsis; fractional calculus; Jeffreys fluid; Laplace transform

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Guo, X.; Qi, H. Analytical Solution of Electro-Osmotic Peristalsis of Fractional Jeffreys Fluid in a Micro-Channel. Micromachines 2017, 8, 341.

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