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Alternating Current Electro-Osmotic Flow of the Maxwell Fluids Through a Circular Micro-Pipe

Published online by Cambridge University Press:  20 December 2012

L.-X. Sun ,
Y.-J. Jian ,
L. Chang ,
H.-Y. Zhang  and
Q.-S. Liu
L.-X. Sun
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, China
Y.-J. Jian*
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, China
L. Chang
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, China School of Mathematics and Statistics, Inner Mongolia Finance and Economics College, Hohhot, Inner Mongolia 010051, China
H.-Y. Zhang
Affiliation:
College of Mathematical Science, Baotou teacher's college, Inner Mongolia 014030, China
Q.-S. Liu
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, China
*
*Corresponding author ([email protected])
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Abstract

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.

Keywords

Time periodic EOFGeneralized Maxwell fluidsCircular micro-pipeOscillating Reynolds numberRelaxation timesViscosity ratio
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 2 , June 2013 , pp. 233 - 240
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

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